Active Exam PrepHigher Education Commission (HEC) - Education Testing Council (ETC)๐ฅ 200 Past Paper MCQs
Full Name: Higher Education Aptitude Test (HAT)
This Test is taken by Education Testing Council (ETC), Higher Education Commission for admissions and scholarships of MS degrees.
16 years / equal Education in Engineering & Technology, Computer Science, Mathematics, Statistics, Physics.
This test comprises of:
30% English/Verbal Reasoning
30% Analytical Reasoning/Intelligence Tests
40% Quantitative Reasoning/Quantitative Aptitude Test
๐ Exam Specifications & Official Testing Profile
Verified Standards (2026)
Conducting AuthorityHigher Education Commission (HEC) - Education Testing Council (ETC)
Total Marks & Questions100 Marks (100 MCQs)
Time Allowed120 Minutes (2 Hours)
Passing / Qualifying Criteria50% Qualifying Marks (HEC Scholarship Cutoff: 70%+)
Negative MarkingNo Negative Marking
Score Validity2 Years from the date of result declaration
Representative questions from authentic past papers with detailed step-by-step solutions and verified formulas.
๐ท๏ธ HEC HAT-I โข Oct 2024 (Morning Batch)
Quantitative Reasoning
Question 1 of 200
A train 180 meters long is traveling at a constant speed of 54 km/h. How many seconds will it take to completely pass a railway platform of length 270 meters?
(A)25 seconds
(B)30 seconds
(C)35 seconds
(D)40 seconds
โ Correct Answer: Option B
(30 seconds)
๐ก Step-by-Step Explanation:
1. Total distance = Length of train + Length of platform = 180m + 270m = 450 meters.
2. Convert speed: 54 km/h = 54 ร (5/18) = 15 m/s.
3. Time = Total Distance / Speed = 450 / 15 = 30 seconds.
๐ท๏ธ HEC HAT-General โข Aug 2024 (Session-1)
Quantitative Reasoning
Question 2 of 200
Pipe A can fill a water tank in 10 hours, while Pipe B can fill the same tank in 15 hours. If both pipes are opened simultaneously, how long will it take to fill the tank completely?
๐ท๏ธ HEC HAT-III โข Nov 2023
Quantitative Reasoning
Question 8 of 200
A card is drawn at random from a standard, well-shuffled pack of 52 playing cards. What is the probability that the card drawn is either a King or a Heart?
๐ท๏ธ HEC USAT-CS โข Aug 2023
Quantitative Reasoning
Question 10 of 200
Find the sum of the infinite geometric series: 18, 6, 2, 2/3, ...
(A)24
(B)27
(C)36
(D)54
โ Correct Answer: Option B
(27)
๐ก Step-by-Step Explanation:
First term a = 18, common ratio r = 6/18 = 1/3. Sum Sโ = a / (1 - r) = 18 / (1 - 1/3) = 18 / (2/3) = 18 ร (3/2) = 27.
๐ท๏ธ HEC HAT-General โข Oct 2024
Analytical Reasoning
Question 11 of 200
Five executives (P, Q, R, S, T) sit in a circular conference table facing the center. P is between S and T. Q is immediately to the left of T. Who is sitting immediately to the right of P?
(A)S
(B)T
(C)Q
(D)R
โ Correct Answer: Option B
(T)
๐ก Step-by-Step Explanation:
Facing center in circular clockwise order: T -> P -> S -> R -> Q. Since P is between S and T with Q to the left of T, looking from P's perspective facing center, T is to P's immediate right and S is to P's immediate left.
๐ท๏ธ HEC HAT-I โข Aug 2024
Analytical Reasoning
Question 12 of 200
If all Zips are Zaps, and some Zaps are Zops, which of the following conclusions MUST be true?
(A)All Zips are Zops
(B)Some Zips are Zops
(C)Some Zaps are Zips
(D)No Zips are Zops
โ Correct Answer: Option C
(Some Zaps are Zips)
๐ก Step-by-Step Explanation:
If all A are B, then by immediate conversion, Some B are A ('Some Zaps are Zips') is necessarily true.
๐ท๏ธ NTS NAT-IE โข June 2024
Analytical Reasoning
Question 13 of 200
In a code language, if 'MADRAS' is coded as 'NBESBT', how will 'BOMBAY' be coded in that same system?
(A)CPNCBX
(B)CPNCBZ
(C)CPOCBZ
(D)CQOCBZ
โ Correct Answer: Option B
(CPNCBZ)
๐ก Step-by-Step Explanation:
Each letter is shifted forward by +1 position: B->C, O->P, M->N, B->C, A->B, Y->Z โน CPNCBZ.
๐ท๏ธ HEC HAT-General โข Oct 2024
Verbal Reasoning
Question 14 of 200
PROSAIC : POETRY ::
(A)Lethargic : Activity
(B)Pedestrian : Novelty
(C)Mundane : Imagination
(D)Cacophonous : Music
โ Correct Answer: Option D
(Cacophonous : Music)
๐ก Step-by-Step Explanation:
Prosaic describes something that lacks poetic beauty; cacophonous describes sound that lacks musical harmony.
๐ท๏ธ NTS GAT-B โข Sept 2024
Verbal Reasoning
Question 15 of 200
Select the word most OPPOSITE in meaning to INIMICAL:
(A)Hostile
(B)Friendly & Favorable
(C)Ambiguous
(D)Dangerous
โ Correct Answer: Option B
(Friendly & Favorable)
๐ก Step-by-Step Explanation:
Inimical means harmful or hostile. Its direct antonym is Friendly / Favorable / Amiable.
๐ท๏ธ HEC HAT-I โข July 2025 (Paper-II)
Intelligence Tests
Question 16 of 200
Only birds have feathers. If the statement is true, which of the following statement is automatically true?
(A)Most birds have white feathers.
(B)Birds fly in the air.
(C)All feathers are light.
(D)Snakes do not have feathers.
โ Correct Answer: Option D
(Snakes do not have feathers.)
๐ก Step-by-Step Explanation:
Only birds have feathers means no other creatures like snakes have feathers. So, snakes do not have feathers is true.
๐ท๏ธ HEC HAT-I โข Oct 2025 (Official Paper)
Intelligence Tests
Question 17 of 200
โA starving or a sick beggar should be given alms, because...โ
(A)A beggar, too, has a right...
(B)Alms giving... is not forbidden
(C)Beggars should be well-fed...
(D)Every human being is a servant of God...
โ Correct Answer: Option D
(Every human being is a servant of God...)
๐ก Step-by-Step Explanation:
This provides a moral and ethical justification rooted in human brotherhood.
๐ท๏ธ HEC HAT-I โข Aug 2025 (Batch-2)
Intelligence Tests
Question 18 of 200
A railway station always has
(A)A tea stall
(B)A train
(C)A railway line
(D)A Wistle
โ Correct Answer: Option C
(A railway line)
๐ก Step-by-Step Explanation:
A railway line is fundamentally required for a railway station to exist, as trains cannot reach it without tracks.
๐ท๏ธ HEC HAT-I โข July 2025 (Official Paper)
Intelligence Tests
Question 19 of 200
Worms can crawl but birds can only fly and hop. Valid statement?
(A)Birds can talk.
(B)Some birds can crawl.
(C)Birds can't crawl.
(D)Warms come out...
โ Correct Answer: Option C
(Birds can't crawl.)
๐ก Step-by-Step Explanation:
If birds can only fly and hop, they are logically excluded from the ability to crawl.
๐ท๏ธ HEC HAT-I โข Dec 2025 (Evening Session)
Intelligence Tests
Question 20 of 200
TASWAR younger NIMRA; NIMRA younger TASWAR. (First two true).
(A)False
(B)Uncertain
(C)True
(D)None of the above
โ Correct Answer: Option A
(False)
๐ก Step-by-Step Explanation:
Statement 1 says: Taswar is younger than Nimra. (True)
Statement 2 says: Nimra is younger than Taswar. (True)
If the first statement is true, Taswar must be the younger one. Therefore, the second statement (which claims Nimra is younger) cannot possibly be true at the same time. The two facts directly contradict each other, making the premise False.
๐ท๏ธ HEC HAT-I โข March 2025 (Phase-1)
Intelligence Tests
Question 21 of 200
In the year 2005 A.D. demand for the consumer goods will
(A)Decline
(B)Increase
(C)Remain same
(D)Decrease
โ Correct Answer: Option B
(Increase)
๐ก Step-by-Step Explanation:
The text explicitly states: "Increased demand for consumer goods will... demand setting up of more industries."
If the present trend continues then the year 2005 A.D.
(A)The world will be more polluted
(B)Billions of people will go without meals.
(C)The world will be more crowded
(D)All the above are correct
โ Correct Answer: Option D
(All the above are correct)
๐ก Step-by-Step Explanation:
The passage highlights increased pollution, crowding, and hundreds of millions sleeping without a meal.
๐ท๏ธ HEC HAT-I โข Oct 2025 (Morning Session)
Intelligence Tests
Question 23 of 200
There will be the greatest increase in population figure in:
(A)The poor countries
(B)China
(C)India
(D)Russia
โ Correct Answer: Option A
(The poor countries)
๐ก Step-by-Step Explanation:
As stated in the text, 90% of the population increase is attributed to poor countries.
๐ท๏ธ HEC HAT-I โข Nov 2025 (Evening Session)
Quantitative Aptitude Test
Question 24 of 200
Insert missing grid:
7 8 1
3 7 4
1 -- 8
(A)8
(B)9
(C)7
(D)10
โ Correct Answer: Option B
(9)
๐ก Step-by-Step Explanation:
The Pattern
In each row, the middle number is the sum of the left number and the right number:
\(\text{Left}+\text{Right}=\text{Middle}\)
Verification
Row 1: \(7 + 1 = \mathbf{8}\)
Row 2: \(3 + 4 = \mathbf{7}\)
Solving for Row 3
Applying the same rule to the third row:
\(1+8=\mathbf{9}\)
๐ท๏ธ HEC HAT-I โข Oct 2025 (Phase-2)
Quantitative Aptitude Test
Question 25 of 200
The average price of 3 books is Rs. 18. Which of the following could be with price of one of the books?
(A)57
(B)56
(C)55
(D)52
โ Correct Answer: Option D
(52)
๐ก Step-by-Step Explanation:
Calculate the Total Price of the Books:The average price of the 3 books is Rs. 18.
\(\text{Total Price}=\text{Average Price}\times \text{Number of Books}\)
\(\text{Total Price}=18\times 3=\text{Rs. 54}\)
Evaluate the Constraints:
The combined cost of all 3 books together must equal exactly Rs. 54. Assuming the price of each individual book must be a positive number (greater than Rs. 0), no single book can cost as much as or more than the total amount of Rs. 54.
Check the Given Options:
A (57): Impossible, since it is greater than the total budget of Rs. 54.
B (56): Impossible, since it is greater than Rs. 54.
C (55): Impossible, since it is greater than Rs. 54.
D (52): Possible. If one book costs Rs. 52, the remaining two books could have a combined cost of Rs. 2 (e.g., Rs. 1 each).
๐ท๏ธ HEC HAT-I โข Aug 2025 (Batch-2)
Quantitative Aptitude Test
๐ท๏ธ HEC HAT-I โข Oct 2025 (Morning Session)
Quantitative Aptitude Test
Question 28 of 200
A student secures an average of 78 percent in four subjects. How many marks must he get in his fifth subject if he is to get average 80 percent in all the five subjects?
(A)84
(B)89
(C)88
(D)86
โ Correct Answer: Option C
(88)
๐ก Step-by-Step Explanation:
To find the score needed in the fifth subject, we can look at the total percentage points required:
Calculate the total points required for 5 subjects:
To maintain an overall average of 80% across 5 subjects:
\(5\times 80=400\text{ points}\)
Calculate the total points earned in the first 4 subjects:
With an average of 78% across 4 subjects:
\(4\times 78=312\text{ points}\)
Find the required score for the 5th subject:
Subtract the points already earned from the total points needed:
\(400-312=\mathbf{88\%}\)
๐ท๏ธ HEC HAT-I โข July 2025 (Phase-2)
Quantitative Aptitude Test
Question 29 of 200
Series:
15, 6, 13, 6, 11, 6, __, __
(A)9, 6
(B)9, 4
(C)8, 6
(D)10, 6
โ Correct Answer: Option A
(9, 6)
๐ก Step-by-Step Explanation:
The odd-positioned numbers decrease consistently by 2 (\(15 \rightarrow 13 \rightarrow 11 \rightarrow \mathbf{9}\)), while the even-positioned numbers remain static as the value 6.
๐ท๏ธ HEC HAT-I โข Jan 2025 (Evening Session)
Quantitative Aptitude Test
Question 30 of 200
Complete the series: 0, 3, 12, 27, __
(A)36
(B)42
(C)48
(D)54
โ Correct Answer: Option C
(48)
๐ก Step-by-Step Explanation:
Formula is 3 ร nยฒ: 3ร0ยฒ=0, 3ร1ยฒ=3, 3ร2ยฒ=12, 3ร3ยฒ=27, 3ร4ยฒ = 48.
๐ท๏ธ HEC HAT-I โข Oct 2025 (Paper-I)
Quantitative Aptitude Test
๐ท๏ธ HEC HAT-I โข July 2025 (Paper-I)
English Language Comprehension
Question 32 of 200
(Without warning) it began to rain.
(A)At his beck and call
(B)All of a sudden
(C)At heart
(D)At fault
โ Correct Answer: Option B
(All of a sudden)
๐ก Step-by-Step Explanation:
"All of a sudden" means suddenly or without warning.
๐ท๏ธ HEC HAT-I โข Oct 2025 (Official Paper)
English Language Comprehension
Question 33 of 200
The clothes in that store are a little (old fashioned).
(A)Behind the times
(B)Brand new
(C)Broke
(D)Better off
โ Correct Answer: Option A
(Behind the times)
๐ก Step-by-Step Explanation:
"Behind the times" means old-fashioned or out of date.
๐ท๏ธ HEC HAT-I โข May 2025 (Batch-2)
English Language Comprehension
Question 34 of 200
The government minister was finally forced to (tell the truth) about the illegal funds.
(A)Call the shots
(B)Chew the fat
(C)Clear the decks
(D)Come clean
โ Correct Answer: Option D
(Come clean)
๐ก Step-by-Step Explanation:
"Come clean" means to fully confess or tell the truth about something.
๐ท๏ธ HEC HAT-I โข July 2025 (Morning Session)
English Language Comprehension
Question 35 of 200
Her mother gave her (a scolding) when she returned home late from school.
(A)Every other
(B)An earful
(C)Elbow room
(D)Elbow grease
โ Correct Answer: Option B
(An earful)
๐ก Step-by-Step Explanation:
"An earful" is a long and angry scolding or lecture.
๐ท๏ธ HEC HAT-I โข Aug 2025 (Paper-II)
English Language Comprehension
Question 36 of 200
The government leader was forced to (retract his statement) about the money he received.
(A)Eat his heart out
(B)Ease off
(C)Egg them on
(D)Eat his words
โ Correct Answer: Option D
(Eat his words)
๐ก Step-by-Step Explanation:
"Eat one's words" means to retract a statement or admit that one was wrong.
๐ท๏ธ HEC HAT-I โข Nov 2025 (Paper-I)
English Language Comprehension
Question 37 of 200
I had to (wear my best clothes) for the job interview.
(A)Dress up
(B)Drown my sorrows
(C)Drop in the bucket
(D)Double-check
โ Correct Answer: Option A
(Dress up)
๐ก Step-by-Step Explanation:
"Dress up" means to wear your best or formal clothes for a special occasion.
๐ท๏ธ HEC HAT-I โข March 2024 (Phase-1)
Intelligence Tests
Question 38 of 200
โFather reads newspapers daily in the morning because...โ
(A)It is his old habit
(B)It is natural for educated men
(C)He is interested in advertisements
(D)He wants to know fresh news
โ Correct Answer: Option D
(He wants to know fresh news)
๐ก Step-by-Step Explanation:
The primary purpose of a daily newspaper is to provide current information and updates on events.
๐ท๏ธ HEC HAT-I โข Feb 2024 (Evening Session)
Intelligence Tests
Question 39 of 200
โChildren should not see television regularly for long time because...โ
(A)It weakness childrenโs eye-sight
(B)They find interest in cartoons only
(C)Movies are better pastime
(D)Children are subjected to moral effect of negative character
โ Correct Answer: Option A
(It weakness childrenโs eye-sight)
๐ก Step-by-Step Explanation:
Prolonged screen time is medically associated with eye strain and potential vision issues in developing children.
๐ท๏ธ HEC HAT-I โข Feb 2024 (Batch-1)
Intelligence Tests
Question 40 of 200
A & B start walking in opposite directions. A covers 3 miles and B covers 4 miles. Then A turns right and walks 4 miles and B turns left and walks 3 miles. How far is each from the starting point?
(A)8 miles
(B)5 miles
(C)4 miles
(D)6 miles
โ Correct Answer: Option B
(5 miles)
๐ก Step-by-Step Explanation:
Using the Pythagorean theorem (32+42=25), the displacement for both A and B from the origin is 25โ=5 miles.
๐ท๏ธ HEC HAT-I โข Jan 2024 (Phase-2)
Intelligence Tests
Question 41 of 200
Leather is considered as the best material for shoes, because leather is:
(A)Water proof
(B)Easily available
(C)Flexible and durable
(D)Durable
โ Correct Answer: Option C
(Flexible and durable)
๐ก Step-by-Step Explanation:
Leather's natural ability to conform to the foot while resisting wear makes it the ideal material for high-quality footwear.
๐ท๏ธ HEC HAT-I โข July 2024 (Morning Session)
Intelligence Tests
Question 42 of 200
Rearrange IFULTETNAN and pick letter (iv):
(A)E
(B)N
(C)T
(D)I
โ Correct Answer: Option D
(I)
๐ก Step-by-Step Explanation:
Unscrambled word is LIEUTENANT; the letter corresponding to 'iv' is 'I'.
๐ท๏ธ HEC HAT-I โข Feb 2024 (Batch-2)
Intelligence Tests
Question 43 of 200
A contractor has 20 men... 18 days, 1/3 work done. How many additional men needed to finish in 28 days total?
(A)64
(B)40
(C)44
(D)60
โ Correct Answer: Option C
(44)
๐ก Step-by-Step Explanation:
Calculation shows total 64 men are needed for the remaining 2/3 work; subtracting the original 20 leaves 44.
๐ท๏ธ HEC HAT-I โข Nov 2024 (Phase-2)
Quantitative Aptitude Test
Question 51 of 200
Series: 16, 23, 20, 27, 24, 31, โโ?
(A)24
(B)27
(C)26
(D)28
โ Correct Answer: Option D
(28)
๐ก Step-by-Step Explanation:
The Pattern
This sequence follows an alternating mathematical pattern of adding 7, then subtracting 3:
\(16 + 7 = 23\)
\(23 - 3 = 20\)
\(20 + 7 = 27\)
\(27 - 3 = 24\)
\(24 + 7 = 31\)
Solving for the Next Number
Following the established pattern, the next operation is to subtract 3:
\(31-3=\mathbf{28}\)
๐ท๏ธ HEC HAT-I โข Nov 2024 (Phase-1)
Quantitative Aptitude Test
Question 52 of 200
There are a number of birds sitting on a branch of a tree. A hunter fired with his gun, only two birds fell down. How many were left on the tree?
(A)10
(B)18
(C)21
(D)None
โ Correct Answer: Option D
(None)
๐ก Step-by-Step Explanation:
A standard riddle/logic item; the sound of the gunshot causes all surviving birds to fly away.
๐ท๏ธ HEC HAT-I โข Jan 2024 (Paper-I)
Quantitative Aptitude Test
๐ก Step-by-Step Explanation:
This sequence is determined by looking at the differences between consecutive terms, which follow two alternating geometric progressions that both multiply by 3 at each step:
First Difference Series (Odd transitions):
\(9 - 7 = \mathbf{2}\)
\(24 - 18 = \mathbf{6}\) \((2 \times 3)\)
\(\text{Next difference} = 6 \times 3 = \mathbf{18}\)
\(\text{Following difference} = 18 \times 3 = \mathbf{54}\)
Second Difference Series (Even transitions):
\(18 - 9 = \mathbf{9}\)\(51 - 24 = \mathbf{27}\) \((9 \times 3)\)
\(\text{Next difference} = 27 \times 3 = \mathbf{81}\)
Find the 6th number:
Add the next difference (\(18\)) to the 5th number (\(51\)):
\(51+18=\mathbf{69}\)
Find the 7th number:
Add the next difference (\(81\)) to the newly found 6th number (\(69\)):
\(69+81=\mathbf{150}\)
Verification of the next term:
Add the next difference (\(54\)) to the 7th number (\(150\)):
\(150+54=\mathbf{204}\)
๐ท๏ธ HEC HAT-I โข Sept 2024 (Batch-1)
Quantitative Aptitude Test
Question 55 of 200
Insert the missing number
7 15 32 __ 138 281
(A)65
(B)67
(C)64
(D)69
โ Correct Answer: Option B
(67)
๐ก Step-by-Step Explanation:
Each number in the sequence is found by multiplying the previous number by 2, and then adding an increasing number (+1, +2, +3, +4...):
\(7 \times 2 + 1 = \mathbf{15}\)
\(15 \times 2 + 2 = \mathbf{32}\)
\(32 \times 2 + 3 = \mathbf{67}\)
\(67 \times 2 + 4 = \mathbf{138}\)
\(138 \times 2 + 5 = \mathbf{281}\)
๐ท๏ธ HEC HAT-I โข March 2024 (Paper-I)
Quantitative Aptitude Test
๐ก Step-by-Step Explanation:
The sequence alternates between two operations:
multiplying the previous number by 2 and adding 1, then multiplying by 2 and subtracting 1:
\(8 \times 2 + 1 = \mathbf{17}\)
\(17 \times 2 - 1 = \mathbf{33}\)
\(33 \times 2 + 1 = \mathbf{67}\)
\(67 \times 2 - 1 = \mathbf{133}\)
Find the 6th number: Following the alternating pattern, multiply the 5th number (\(133\)) by 2 and add 1:
\(133\times 2+1=266+1=\mathbf{267}\)
Find the 7th number: Next, multiply the newly found 6th number (\(267\)) by 2 and subtract 1:
\(267\times 2-1=534-1=\mathbf{533}\)
๐ท๏ธ HEC HAT-I โข Nov 2024 (Batch-1)
Quantitative Aptitude Test
Question 57 of 200
Find the next term in the series: 2 3/4, 3, 3 1/2, 4 1/3, โฆ
(A)5 1/3
(B)5 2/3
(C)6
(D)6 1/4
โ Correct Answer: Option B
(5 2/3)
๐ก Step-by-Step Explanation:
Incremental fractional expansion yields 5 2/3 (17/3) as the next term.
๐ท๏ธ HEC HAT-I โข Nov 2024 (Morning Session)
Quantitative Aptitude Test
๐ท๏ธ HEC HAT-I โข Nov 2024 (Batch-1)
Quantitative Aptitude Test
Question 59 of 200
How far must the fish be from the higher pole, if the two birds flying at identical speeds leave their respective perches simultaneously and reach the fish at the same time?
(A)28 m
(B)20 m
(C)22 m
(D)25 m
โ Correct Answer: Option C
(22 m)
๐ก Step-by-Step Explanation:
Let the horizontal distance from the base of the higher (20-m) pole to the fish be \(x\) meters. Since the canal is 50 meters wide, the horizontal distance from the lower (10-m) pole to the fish is \((50 - x)\) meters.
Set up the Pythagorean Theorem:
Because both birds fly at identical speeds and reach the fish at the same time, the straight-line distance (the hypotenuse of each right triangle) they fly must be exactly equal:
\(\text{Distance}_{\text{Higher Bird}}^{2}=\text{Distance}_{\text{Lower Bird}}^{2}\)
\(20^{2}+x^{2}=10^{2}+(50-x)^{2}\)
Expand and Solve for \(x\):
\(400+x^{2}=100+(2500-100x+x^{2})\)
Cancel out \(x^{2}\) from both sides:
\(400=2600-100x\)\(100x=2600-400\)
\(100x=2200\)\(x=\mathbf{22}\text{ m}\)
Thus, the fish must be exactly 22 meters away from the base of the higher pole.
๐ท๏ธ HEC HAT-I โข Sept 2024 (Batch-1)
Quantitative Aptitude Test
Question 60 of 200
Expression \(x^{2}โ3x+5\) has a minimum value for x equal to:
(A)3.2
(B)Zero
(C)1.5
(D)2.4
โ Correct Answer: Option C
(1.5)
๐ก Step-by-Step Explanation:
The expression \(f(x) = x^2 - 3x + 5\) is a quadratic equation where the coefficient of \(x^{2}\) is positive (\(a = 1\)). This means its graph is a parabola that opens upward, and its lowest point (minimum value) occurs at its vertex.
To find the value of \(x\) at the vertex, we use the vertex formula:
\(x=-\frac{b}{2a}\)
Identify the coefficients:
\(a = 1\)
\(b = -3\)
Plug the numbers into the formula:
\(x=-\frac{-3}{2(1)}=\frac{3}{2}=\mathbf{1.5}\)
Therefore, the expression reaches its minimum value when \(x\) is equal to 1.5.
๐ท๏ธ HEC HAT-I โข July 2024 (Batch-1)
Quantitative Aptitude Test
Question 61 of 200
Sequence: 2, 5, 28, 17, 126, ...
(A)217
(B)35
(C)37
(D)43
โ Correct Answer: Option C
(37)
๐ก Step-by-Step Explanation:
This sequence alternates between two distinct arithmetic patterns based on odd and even positions:
Odd Positions (1st, 3rd, 5th terms):
These follow the formula \(n^3 + 1\) for consecutive integers \(n = 1, 3, 5\):
1st term: \(1^3 + 1 = \mathbf{2}\)
3rd term: \(3^3 + 1 = \mathbf{28}\)
5th term: \(5^3 + 1 = \mathbf{126}\)
Even Positions (2nd, 4th, 6th terms):
These follow the formula \(n^2 + 1\) for consecutive integers \(n = 2, 4, 6\):
2nd term: \(2^2 + 1 = \mathbf{5}\)
4th term: \(4^2 + 1 = \mathbf{17}\)
6th term (Target): \(6^2 + 1 = \mathbf{37}\)
Solving for the Next Number
Since the next slot is the 6th term (an even position), we evaluate the second pattern rule:
\(6^{2}+1=36+1=\mathbf{37}\)
๐ท๏ธ HEC HAT-I โข July 2024 (Evening Session)
Quantitative Aptitude Test
Question 62 of 200
The length of a rectangle is increased by 2 cm and its width is decreased by 2 cm. The length of the diagonal of the rectangle (length > width).
(A)decrease
(B)Unchanged
(C)increase
(D)depends
โ Correct Answer: Option C
(increase)
๐ก Step-by-Step Explanation:
Initial Diagonal:
Let the initial length of the rectangle be \(L\) and the initial width be \(W\). According to the Pythagorean theorem, the initial diagonal \(d_{1}\) is:
\(d_{1}^{2}=L^{2}+W^{2}\)
New Diagonal:
The new length becomes \((L + 2)\) and the new width becomes \((W - 2)\). The new diagonal \(d_{2}\) is:
\(d_{2}^{2}=(L+2)^{2}+(W-2)^{2}\)
Expand the New Diagonal Equation:
\(d_{2}^{2}=(L^{2}+4L+4)+(W^{2}-4W+4)\)
\(d_{2}^{2}=(L^{2}+W^{2})+4L-4W+8\)
Substitute \(d_{1}^{2}\) into the Expression:
\(d_{2}^{2}=d_{1}^{2}+4(L-W)+8\)
Analysis of the Condition (\(L > W\))
The problem specifies that the initial length is greater than the width (\(L > W\)).
This means that \((L - W)\) is a positive number.
Because \(4(L - W) + 8\) is positive, it means that \(d_2^2 > d_1^2\).
Therefore, the new diagonal is actually greater than the original diagonal.
๐ท๏ธ HEC HAT-I โข Sept 2024 (Phase-1)
English Language Comprehension
Question 63 of 200
Okay I'm (listening). Please continue with your story.
(A)All ears
(B)All thumbs
(C)As a rule
(D)At heart
โ Correct Answer: Option A
(All ears)
๐ก Step-by-Step Explanation:
"All ears" means listening eagerly or attentively.
๐ท๏ธ HEC HAT-I โข Sept 2024 (Batch-2)
English Language Comprehension
Question 64 of 200
He refused my proposal so I will have to (start over from the beginning).
(A)Go back to the drawing board
(B)Bury the hatchet
(C)By the skin of my teeth
(D)Bring to mind
โ Correct Answer: Option A
(Go back to the drawing board)
๐ก Step-by-Step Explanation:
"Go back to the drawing board" means to start planning again because a previous attempt failed.
๐ท๏ธ HEC HAT-I โข Sept 2024 (Official Paper)
English Language Comprehension
Question 65 of 200
He is always spending his money drinking so he is always (without money).
(A)Backed out
(B)Banked on
(C)Broke
(D)Behind the times
โ Correct Answer: Option C
(Broke)
๐ก Step-by-Step Explanation:
"Broke" means having no money; bankrupt.
๐ท๏ธ HEC HAT-I โข May 2024 (Paper-II)
English Language Comprehension
Question 66 of 200
She is constantly (thinking about) her husband's problems at work.
(A)Dashing off
(B)Driving at
(C)Dropping by
(D)Dwelling on
โ Correct Answer: Option D
(Dwelling on)
๐ก Step-by-Step Explanation:
"Dwelling on" means to think or speak about something for a long time, often obsessively.
๐ท๏ธ HEC HAT-I โข July 2024 (Phase-2)
English Language Comprehension
Question 67 of 200
He has (a relaxed) style of managing his company.
(A)An easing off
(B)An every so often
(C)An easy going
(D)An end in itself
โ Correct Answer: Option C
(An easy going)
๐ก Step-by-Step Explanation:
"Easy going" refers to a person or style that is relaxed and tolerant.
๐ท๏ธ HEC HAT-I โข May 2024 (Morning Session)
English Language Comprehension
Question 68 of 200
Their new house has a lot more (space) than the old one.
(A)Eyes in the back of its head
(B)Elbow room
(C)Eager beaver
(D)Elbow grease
โ Correct Answer: Option B
(Elbow room)
๐ก Step-by-Step Explanation:
"Elbow room" means adequate space to move or work in; freedom to act.
๐ท๏ธ HEC HAT-I โข Dec 2024 (Morning Session)
English Language Comprehension
Question 69 of 200
It will (relax him) if he goes to the beach for the weekend.
(A)Do him good
(B)Do his best
(C)Do the trick
(D)Draw the line
โ Correct Answer: Option A
(Do him good)
๐ก Step-by-Step Explanation:
"Do someone good" means to be beneficial to someone's health or well-being.
๐ท๏ธ HEC HAT-I โข Oct 2023 (Official Paper)
Intelligence Tests
Question 70 of 200
IRON is to METAL as BARLEY is
(A)Food
(B)Nail
(C)Cereal
(D)Wheat
โ Correct Answer: Option C
(Cereal)
๐ก Step-by-Step Explanation:
As Iron belongs to METALS similarly Barley belongs to the group of Cereals.
๐ท๏ธ HEC HAT-I โข Jan 2023 (Paper-I)
Intelligence Tests
Question 71 of 200
There is some similarity in three of the following groups, but the fourth is different in some way. Select the different group.
(A)C D F G H
(B)H I K L M
(C)K L N O P
(D)S T U W X
โ Correct Answer: Option D
(S T U W X)
๐ก Step-by-Step Explanation:
In C D F G H, H I K L M, K L N O P have first two alphabets of sequence and third alphabet missing in S T U W X the first three are in sequence but fourth is missing.
๐ท๏ธ HEC HAT-I โข Feb 2023 (Phase-2)
Intelligence Tests
Question 72 of 200
โBoys and girls should never smoke because...โ
(A)They are young in age
(B)Father will give them...
(C)It is a foreign habit
(D)It is injurious for health
โ Correct Answer: Option D
(It is injurious for health)
๐ก Step-by-Step Explanation:
Smoking causes significant medical harm, which is the primary rational reason to avoid it.
๐ท๏ธ HEC HAT-I โข Aug 2023 (Morning Session)
Intelligence Tests
Question 73 of 200
A man faces north and covers 12 km. turns west and covers 6 km, then turns South and covers 3 km, and turns west again and covers 6 km. How far is he from the starting point?
(A)18 km
(B)10 km
(C)15 km
(D)12 km
โ Correct Answer: Option C
(15 km)
๐ก Step-by-Step Explanation:
Total net displacement: 9 km North and 12 km West. Total distance = 92+122โ=225โ=15 km.
๐ท๏ธ HEC HAT-I โข Dec 2023 (Morning Session)
Intelligence Tests
Question 74 of 200
If the day that will dawn 2 days after tomorrow is Friday, what day of the week dawned two days before yesterday?
(A)Wednesday
(B)Friday
(C)Thursday
(D)Saturday
โ Correct Answer: Option D
(Saturday)
๐ก Step-by-Step Explanation:
Let's break the timeline down step by step to find the exact day:
Find Today:
"2 days after tomorrow" is equal to 3 days from today (Tomorrow = +1 day, 2 days after that = +3 days).
If 3 days from today is Friday, counting 3 days backward tells us that today is Tuesday.
Find the Target Day:
"Two days before yesterday" is equal to 3 days ago (Yesterday = -1 day, 2 days before that = -3 days).
Counting 3 days backward from Tuesday (Monday, Sunday, Saturday) gives us Saturday.
๐ท๏ธ HEC HAT-I โข March 2023 (Paper-II)
Intelligence Tests
Question 75 of 200
Shakil and Kiran are children of Faisal. Ram is the father of Shakil and Kiran is not the son of Faisal. What is Kiran to Faisal?
(A)Son-in-law
(B)Niece
(C)Daughter
(D)Mother
โ Correct Answer: Option C
(Daughter)
๐ก Step-by-Step Explanation:
Since Kiran is a child of Faisal but not a son, she must be Faisal's daughter.
๐ท๏ธ HEC HAT-I โข Aug 2023 (Phase-1)
Intelligence Tests
Question 76 of 200
Rearrange EGNAEGNETM and pick letter (iv):
(A)T
(B)N
(C)G
(D)E
โ Correct Answer: Option D
(E)
๐ก Step-by-Step Explanation:
Unscrambled word is MANAGEMENT; the letter corresponding to the key's 'iv' is 'E'.
Merchant buys 4.75 tonnes at 20/kg. 20% wastage. Selling price for 25% profit?
(A)Rs. 31.20
(B)Rs. 31.25
(C)Rs. 25
(D)Rs. 26.25
โ Correct Answer: Option B
(Rs. 31.25)
๐ก Step-by-Step Explanation:
The effective cost per usable kg becomes 25; a 25% profit on 25 equals 31.25.
๐ท๏ธ HEC HAT-I โข Jan 2023 (Evening Session)
Intelligence Tests
Question 78 of 200
X: I just heard that Faisal failed in the IAS exam. Y: Impossible : Faisal was very witty.
(A)Y thinks X is telling a lie.
(B)X knows Faisal has failed...
(C)Y assumes no witty individual can fail...
(D)X thinks Faisal has failed...
โ Correct Answer: Option C
(Y assumes no witty individual can fail...)
๐ก Step-by-Step Explanation:
Y's response implies a logical premise that being 'witty' is a sufficient condition to pass the exam.
๐ท๏ธ HEC HAT-I โข July 2023 (Official Paper)
Intelligence Tests
Question 79 of 200
Any increase in agricultural production will be because of
(A)Increase in the number of farmers
(B)Improvement in the agricultural technology
(C)Increase in the area under cultivation
(D)Government taking over all the land.
โ Correct Answer: Option B
(Improvement in the agricultural technology)
๐ก Step-by-Step Explanation:
The passage states any increase "will not be due to increase in the area... but by advancement in the agricultural technology."
๐ท๏ธ HEC HAT-I โข Aug 2023 (Batch-1)
Intelligence Tests
Question 80 of 200
The poor countries will contribute to the increase of population to the extent of
(A)100 per cent
(B)10 per cent
(C)30 per cent
(D)90 per cent
โ Correct Answer: Option D
(90 per cent)
๐ก Step-by-Step Explanation:
The text specifies that "90 per cent of the increase in population will be in the poor countries."
๐ท๏ธ HEC HAT-I โข Aug 2023 (Phase-2)
Quantitative Aptitude Test
Question 81 of 200
ะขo a certain number 8 is added. The sum is multiplied by 3, then the product is divided by 2 and 7 is subtracted from the quotient. The remainder left is 50. The number is:
(A)30
(B)40
(C)50
(D)60
โ Correct Answer: Option A
(30)
๐ก Step-by-Step Explanation:
We can solve this problem by working backward from the final remainder of 50:
Undo the subtraction:
Before subtracting 7, the number was:
\(50+7=57\)
Undo the division:
Before dividing by 2, the product was:
\(57\times 2=114\)
Undo the multiplication:
Before multiplying by 3, the sum was:
\(114\div 3=38\)
Undo the addition:
Before adding 8, the original number was:
\(38-8=\mathbf{30}\)
๐ท๏ธ HEC HAT-I โข Aug 2023 (Batch-1)
Quantitative Aptitude Test
Question 82 of 200
Insert the Missing number in Grid:
4 7 3,
32 69 51,
20 48 ?
(A)36
(B)42
(C)45
(D)39
โ Correct Answer: Option B
(42)
๐ก Step-by-Step Explanation:
In each column, subtracting the bottom number from the middle number always results in exactly 3 times the top number:
\(\text{Middle Number}-\text{Bottom Number}=3\times \text{Top Number}\)
(Alternatively: \(\text{Bottom Number} + (3 \times \text{Top Number}) = \text{Middle Number}\))
Verification
Column 1: \(32 - 20 = 12 \quad \rightarrow \quad 3 \times \mathbf{4} = 12\)
Column 2: \(69 - 48 = 21 \quad \rightarrow \quad 3 \times \mathbf{7} = 21\)
Applying the exact same rule to the third column:
\(51-\mathbf{?}=3\times 3\)
\(51-\mathbf{?}=9\)
\(\mathbf{?}=51-9=\mathbf{42}\)
๐ท๏ธ HEC HAT-I โข May 2023 (Paper-I)
Quantitative Aptitude Test
Question 83 of 200
Find the next number in the series: 8, 10, 16, 34, __
(A)72
(B)80
(C)88
(D)96
โ Correct Answer: Option C
(88)
๐ก Step-by-Step Explanation:
Differences multiply by 3: 10โ8=2; 16โ10=6 (2ร3); 34โ16=18 (6ร3). Next difference is 18ร3 = 54. 34 + 54 = 88.
๐ท๏ธ HEC HAT-I โข Jan 2023 (Batch-1)
Quantitative Aptitude Test
Question 84 of 200
Find the odd man out: 102, 34, 51, 59, 119
(A)34
(B)51
(C)59
(D)119
โ Correct Answer: Option C
(59)
๐ก Step-by-Step Explanation:
All numbers except 59 are multiples of 17 (17ร6=102, 17ร2=34, 17ร3=51, 17ร7=119). 59 is prime.
๐ท๏ธ HEC HAT-I โข Dec 2023 (Batch-1)
Quantitative Aptitude Test
Question 85 of 200
Find the odd man out: 64, 49, 625, 576, 121, 52
(A)64
(B)625
(C)121
(D)52
โ Correct Answer: Option D
(52)
๐ก Step-by-Step Explanation:
All others are perfect squares (82,72,252,242,112); 52 is not a square.
๐ท๏ธ HEC HAT-I โข Dec 2023 (Paper-II)
Quantitative Aptitude Test
Question 86 of 200
$2^3โ 2^{โ6}+2^{โ3}โ 2^6$ is closest to?
(A)62
(B)1
(C)8
(D)34
โ Correct Answer: Option C
(8)
๐ก Step-by-Step Explanation:
Simplify each term using exponent rules:
When multiplying numbers with the same base, you add their exponents (\(2^a \cdot 2^b = 2^{a+b}\)).
First term: \(2^3 \cdot 2^{-6} = 2^{3 + (-6)} = 2^{-3}\)
Second term: \(2^{-3} \cdot 2^6 = 2^{-3 + 6} = 2^3\)
Evaluate the simplified terms:
\(2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125\)
\(2^3 = 8\)
Add the values together:
\(0.125+8=\mathbf{8.125}\)
๐ท๏ธ HEC HAT-I โข Dec 2023 (Morning Session)
English Language Comprehension
Question 87 of 200
The teacher said the little boy was (her favorite).
(A)The apple of her eye
(B)An arm and a leg
(C)As well as
(D)At odds
โ Correct Answer: Option A
(The apple of her eye)
๐ก Step-by-Step Explanation:
"The apple of one's eye" refers to a person or thing that is greatly loved or treasured.
๐ท๏ธ HEC HAT-I โข May 2023 (Paper-I)
English Language Comprehension
Question 88 of 200
He is always (fighting) with his boss about something.
(A)As usual
(B)At last
(C)At odds
(D)At heart
โ Correct Answer: Option C
(At odds)
๐ก Step-by-Step Explanation:
"At odds" means in conflict or at variance; fighting or disagreeing.
๐ท๏ธ HEC HAT-I โข Aug 2023 (Official Paper)
English Language Comprehension
Question 89 of 200
I am going to go to night school to (review) my English.
(A)Bank on
(B)Brush up on
(C)Better off
(D)Bring to mind
โ Correct Answer: Option B
(Brush up on)
๐ก Step-by-Step Explanation:
"Brush up on" means to improve one's knowledge of something or to review it.
๐ท๏ธ HEC HAT-I โข Oct 2023 (Paper-II)
English Language Comprehension
Question 90 of 200
He says he absolutely doesn't want the same kind of car as (the average person) in his neighborhood.
(A)Every Tom, Dick, and Harry
(B)Every so often
(C)Elbow room
(D)Easy does it
โ Correct Answer: Option A
(Every Tom, Dick, and Harry)
๐ก Step-by-Step Explanation:
"Every Tom, Dick, and Harry" refers to ordinary people in general.
๐ท๏ธ HEC HAT-I โข Aug 2023 (Batch-1)
English Language Comprehension
Question 91 of 200
We (finished) by going to the bar for a drink after the concert.
(A)Eased off
(B)Ate out
(C)Ended up
(D)Egged them on
โ Correct Answer: Option C
(Ended up)
๐ก Step-by-Step Explanation:
"End up" means to eventually reach a particular place or state after a series of events.
๐ท๏ธ HEC HAT-I โข March 2022 (Paper-I)
Intelligence Tests
Question 92 of 200
Pick up the odd man out in the following group
(A)Telephone
(B)Battery
(C)Transistor
(D)Gear
โ Correct Answer: Option D
(Gear)
๐ก Step-by-Step Explanation:
Telephone, Battery and Transistor are amongst electronics while the Gear is a mechanical device.
๐ท๏ธ HEC HAT-I โข Nov 2022 (Batch-2)
Intelligence Tests
Question 93 of 200
Select the object which is different from others.
(A)Ship
(B)Car
(C)Motor Cycle
(D)Bicycle
โ Correct Answer: Option A
(Ship)
๐ก Step-by-Step Explanation:
Car, Motor cycle and Bicycle are driven on earth while Ship is sailed in water.
๐ท๏ธ HEC HAT-I โข Aug 2022 (Morning Session)
Intelligence Tests
Question 94 of 200
โSteam burns the body more severely than boiling because...โ
(A)It pierces through skin-pores
(B)Temperature is higher...
(C)Steam can drive engines...
(D)Steam has latent heat...
โ Correct Answer: Option D
(Steam has latent heat...)
๐ก Step-by-Step Explanation:
Steam at 100ยฐC contains latent heat of vaporization, which releases extra energy upon contact with skin.
๐ท๏ธ HEC HAT-I โข Aug 2022 (Evening Session)
Intelligence Tests
Question 95 of 200
Faisal will be 4 times as old in 30 years as he is now. How old is Faisal now?
(A)34 years
(B)30 years
(C)26 years
(D)10 years
โ Correct Answer: Option D
(10 years)
๐ก Step-by-Step Explanation:
If current age is x, then x+30=4x. Solving for x gives 3x=30, so x=10.
๐ท๏ธ HEC HAT-I โข July 2022 (Batch-2)
Intelligence Tests
Question 96 of 200
If all teachers are doctors, which can be deduced?
(A)Some Ys are Xs
(B)Some Ys are teachers
(C)All doctors are philosophers
(D)Some Xs are doctors
โ Correct Answer: Option D
(Some Xs are doctors)
๐ก Step-by-Step Explanation:
If teachers are doctors and some teachers are Xs, it follows that some Xs are doctors.
๐ท๏ธ HEC HAT-I โข Aug 2022 (Phase-2)
Intelligence Tests
Question 97 of 200
Which of the following must be true?
(A)Some doctors are teachers
(B)Some teachers are philosophers
(C)Some Xs not teachers
(D)Some Ys not doctors
โ Correct Answer: Option B
(Some teachers are philosophers)
๐ก Step-by-Step Explanation:
Since teachers are Xs and all Xs are philosophers, it must be true that some teachers (the ones that are Xs) are philosophers.
๐ท๏ธ HEC HAT-I โข March 2022 (Evening Session)
Intelligence Tests
Question 98 of 200
What would you do if you see a fellow passenger fall out of a running bus?
(A)Raise a hue and cry...
(B)Do not bother...
(C)Stop the bus and give first aid to the passenger,
(D)Inform the conductor.
โ Correct Answer: Option C
(Stop the bus and give first aid to the passenger,)
๐ก Step-by-Step Explanation:
Immediate life-saving action and assistance is the ethical and rational response to an emergency.
๐ท๏ธ HEC HAT-I โข Jan 2022 (Morning Session)
Intelligence Tests
Question 99 of 200
The world population in 2005 A.D. will be
(A)65 billion
(B)65 million
(C)6.5 million
(D)6.5 billion
โ Correct Answer: Option D
(6.5 billion)
๐ก Step-by-Step Explanation:
The passage explicitly states: "According to conservative estimates by 2005 A.D. population will increase to 6.5 billion to make the situation worst for the poor countries..."
๐ท๏ธ HEC HAT-I โข Nov 2022 (Evening Session)
Quantitative Aptitude Test
Question 100 of 200
Write the middle figure between 83 and 98.
(A)90.5
(B)90
(C)91
(D)91.5
โ Correct Answer: Option A
(90.5)
๐ก Step-by-Step Explanation:
Arithmetic mean:
(83+98)/2=181/2=90.5.
(Note: 91 is a common whole-int answer).
๐ท๏ธ HEC HAT-I โข Aug 2022 (Phase-1)
Quantitative Aptitude Test
๐ก Step-by-Step Explanation:
The sequence follows an alternating arithmetic pattern, adding 1, then adding 5:
\(11 + 1 = 12\)
\(12 + 5 = 17\)
\(17 + 1 = 18\)
\(18 + 5 = 23\)
\(23 + 1 = 24\)
Solving for the Missing Numbers
Following the established pattern, the next two operations are to add 5, then add 1:
\(24 + 5 = \mathbf{29}\)
\(29 + 1 = \mathbf{30}\)
๐ท๏ธ HEC HAT-I โข Dec 2022 (Phase-2)
Quantitative Aptitude Test
๐ก Step-by-Step Explanation:
This sequence is formed by the cubes of consecutive positive integers (nยณ):
1ยณ = 1
2ยณ = 8
3ยณ = 27
4ยณ = 64
5ยณ = 125
6ยณ = 216
Solving for the Missing Numbers
Following the pattern, the next two numbers are the cubes of 7 and 8:
\(7^3 = 7 \times 7 \times 7 = \mathbf{343}\)
\(8^3 = 8 \times 8 \times 8 = \mathbf{512}\)
๐ท๏ธ HEC HAT-I โข Jan 2022 (Paper-II)
Quantitative Aptitude Test
Question 103 of 200
If the fish were equidistant from the two banks and the birds leave the respective poles simultaneously and reach the fish at the same time, which one of the following statements must be true?
(A)The two birds fly an equal distance before they get to the fish
(B)The speed of bird on the 10-m high pole is less than that of the bird on the 20-m high pole
(C)The two birds have the same speed
(D)The speed of the bird on the 20-m high pole is less than that of the bird on toe 10-m high pole
โ Correct Answer: Option B
(The speed of bird on the 10-m high pole is less than that of the bird on the 20-m high pole)
๐ก Step-by-Step Explanation:
Analyze the Horizontal Distance:
Since the fish is equidistant from both banks, the horizontal distance from the base of each pole to the fish is exactly the same:
\(\text{Horizontal Distance}=\frac{50\text{ m}}{2}=25\text{ m}\)
Calculate the Straight-Line Distance for Each Bird:
The path each bird flies forms a right-angled triangle where the hypotenuse is the flight distance.
For the 20-m pole bird:
\(\text{Distance}_{1}=\sqrt{20^{2}+25^{2}}=\sqrt{400+625}=\sqrt{1025}\approx \mathbf{32.02}\text{ m}\)
For the 10-m pole bird:
\(\text{Distance}_{2}=\sqrt{10^{2}+25^{2}}=\sqrt{100+625}=\sqrt{725}\approx \mathbf{26.93}\text{ m}\)
Compare Speeds:
Since both birds start simultaneously and reach the fish at the exact same time, the bird that has to travel a longer distance must fly at a higher speed.The 20-m pole bird travels 32.02 m.The 10-m pole bird travels 26.93 m.Therefore, the bird on the 10-m pole travels less distance in the same amount of time, meaning its speed must be less than that of the bird on the 20-m high pole.
๐ท๏ธ HEC HAT-I โข March 2022 (Phase-1)
Quantitative Aptitude Test
Question 104 of 200
Approximately how much distance does each bird fly before it gets to the fish?
(A)21 m
(B)30 m
(C)25 m
(D)cannot be deduced
โ Correct Answer: Option B
(30 m)
๐ก Step-by-Step Explanation:
Set up the Equation:
Let \(x\) be the horizontal distance from the 20-m pole to the fish. The horizontal distance from the 10-m pole to the fish is then \((50 - x)\).Since both birds fly an equal straight-line distance (hypotenuse) to reach the fish:
\(20^{2}+x^{2}=10^{2}+(50-x)^{2}\)
Solve for \(x\):
\(400+x^{2}=100+2500-100x+x^{2}\)
\(400=2600-100x\)
\(100x=2200\implies x=\mathbf{22}\text{ m}\)
Calculate the Flight Distance:
Now, plug \(x = 22\) back into the Pythagorean theorem to find the actual line of flight:
\(\text{Distance}=\sqrt{20^{2}+22^{2}}=\sqrt{400+484}=\sqrt{884}\approx \mathbf{29.73}\text{ m}\)
Rounding to the closest available multiple-choice option yields 30 m.
๐ท๏ธ HEC HAT-I โข Oct 2022 (Evening Session)
Quantitative Aptitude Test
Question 105 of 200
Minimum value of $x^{3}+10x+7$?
(A)7
(B)-18
(C)Zero
(D)None of these
โ Correct Answer: Option D
(None of these)
๐ก Step-by-Step Explanation:
To find the minimum value of the cubic function \(f(x) = x^3 + 10x + 7\), we look at its first derivative to check for critical points (peaks or valleys):
Find the derivative:
\(f^{\prime }(x)=3x^{2}+10\)
Analyze the derivative:
Since any real number squared (\(x^{2}\)) is always zero or positive, \(3x^2 \ge 0\). Adding \(10\) means that:
\(f^{\prime }(x)\ge 10\quad \text{for all real values of }x.\)
Conclusion:
Because the derivative is always positive (\(f'(x) > 0\)), the graph of the function is strictly increasing from left to right. It has no local minimum or local maximum points.As \(x\) goes towards negative infinity (\(-\infty \)), the value of \(x^3 + 10x + 7\) also goes towards negative infinity (\(-\infty \)). Because it decreases without bound, it does not have a minimum real number value, making None of these the correct choice.
๐ท๏ธ HEC HAT-I โข Jan 2022 (Phase-2)
Quantitative Aptitude Test
๐ท๏ธ HEC HAT-I โข Sept 2022 (Phase-2)
Quantitative Aptitude Test
Question 107 of 200
How many three-figure can be formed from the digits 2, 6, 3, 5, 1?
(A)44
(B)60
(C)24
(D)68
โ Correct Answer: Option B
(60)
๐ก Step-by-Step Explanation:
Identify the variables:
Total number of available digits (\(n\)) = 5 (the digits are 2, 6, 3, 5, 1).
Number of digits to choose at one time (\(r\)) = 3.
Apply the Permutation Formula (assuming digits cannot be repeated):
When building an exam puzzle like this without explicit context, "repetition not allowed" is the standard convention.
\({}^{n}P_{r}=\frac{n!}{(n-r)!}\)
\({}^{5}P_{3}=\frac{5!}{(5-3)!}=\frac{5\times 4\times 3\times 2\times 1}{2\times 1}\)
\({}^{5}P_{3}=5\times 4\times 3=\mathbf{60}\)
Alternative Slot Method
There are 5 options for the first digit.
After picking the first digit, 4 options remain for the second digit.
After picking the second digit, 3 options remain for the third digit.
\(\text{Total Permutations}=5\times 4\times 3=\mathbf{60}\)
๐ท๏ธ HEC HAT-I โข Sept 2022 (Phase-1)
Quantitative Aptitude Test
Question 108 of 200
Find the value of: 1/(โ5 + โ3) + 1/(โ5 โ โ3)
๐ท๏ธ HEC HAT-I โข Aug 2022 (Batch-1)
Quantitative Aptitude Test
Question 109 of 200
A-10 litre mixture of milk and water cรณntains 30 percent water. Two litres of this mixture is taken away. How many litres of water should now be added so that the amount of milk in the mixture is double that of water.
(A)1.4
(B)0.8
(C)0.4
(D)0.7
โ Correct Answer: Option C
(0.4)
๐ก Step-by-Step Explanation:
Remaining mixture: 10 litres - 2 litres = 8 litres.
Milk in remaining mixture: 70% of 8 litres = 5.6 litres.
Water in remaining mixture: 30% of 8 litres = 2.4 litres.
Target ratio: Milk must be double the water.
Required water volume: 5.6 litres / 2 = 2.8 litres.
Water to add: 2.8 litres - 2.4 litres = 0.4 litres.
๐ท๏ธ HEC HAT-I โข Aug 2022 (Phase-1)
Quantitative Aptitude Test
Question 110 of 200
A man sells a radio and a mixer for Rs. 350 each. On one he gains 10 percent and on the other loses 10 percent. Thus on the whole, he
(A)Gains nearly 0.1 percent.
(B)Neither gains nor loses
(C)Loses nearly 1 percent
(D)Gains nearly 1 percent
โ Correct Answer: Option C
(Loses nearly 1 percent)
๐ก Step-by-Step Explanation:
When two items are sold at the same priceโone at a gain of \(x\%\) and the other at a loss of \(x\%\), the overall transaction always results in a loss. The formula to find this net loss percentage is:
\(\text{Loss }\%=\left(\frac{x}{10}\right)^{2}\)
Given \(x = 10\%\):
\(\text{Loss }\%=\left(\frac{10}{10}\right)^{2}=1^{2}=1\%\)
Step-by-Step ProofCalculate the Cost Price (CP) of the Radio (10% Gain):
\(\text{CP}_{1}=\frac{\text{Selling Price}}{1+\text{Gain }\%}=\frac{350}{1.10}=\text{Rs. }318.18\)
Calculate the Cost Price (CP) of the Mixer (10% Loss):
\(\text{CP}_{2}=\frac{\text{Selling Price}}{1-\text{Loss }\%}=\frac{350}{0.90}=\text{Rs. }388.89\)
Find the Totals:Total Cost Price:
\(\text{Rs. } 318.18 + \text{Rs. } 388.89 = \text{Rs. } 707.07\)
Total Selling Price:
\(\text{Rs. } 350 + \text{Rs. } 350 = \text{Rs. } 700.00\)
Calculate Net Loss Percentage:
\(\text{Net Loss}=\text{Rs. }707.07-\text{Rs. }700.00=\text{Rs. }7.07\)
\(\text{Loss }\%=\left(\frac{7.07}{707.07}\right)\times 100=1\%\)
๐ท๏ธ HEC HAT-I โข Aug 2022 (Official Paper)
English Language Comprehension
Question 111 of 200
That car must have cost him (an incredibly large amount of money).
(A)At heart
(B)At home
(C)The apple of his eye
(D)An arm and a leg
โ Correct Answer: Option D
(An arm and a leg)
๐ก Step-by-Step Explanation:
"An arm and a leg" refers to a very large amount of money.
๐ท๏ธ HEC HAT-I โข Sept 2022 (Official Paper)
English Language Comprehension
Question 112 of 200
I don't think that he is (to blame) for breaking the computer.
(A)At last
(B)At fault
(C)All thumbs
(D)Absent-minded
โ Correct Answer: Option B
(At fault)
๐ก Step-by-Step Explanation:
"At fault" means responsible for an undesirable situation; to blame.
๐ท๏ธ HEC HAT-I โข July 2022 (Official Paper)
English Language Comprehension
Question 113 of 200
(Usually) I get up and go jogging before breakfast every Sunday.
(A)At heart
(B)All in all
(C)All of a sudden
(D)As a rule
โ Correct Answer: Option D
(As a rule)
๐ก Step-by-Step Explanation:
"As a rule" means usually or generally.
๐ท๏ธ HEC HAT-I โข July 2022 (Paper-II)
English Language Comprehension
Question 114 of 200
She is (in a better position) since she sold her car.
(A)Blown over
(B)Beating around the bush
(C)Backing out
(D)Better off
โ Correct Answer: Option D
(Better off)
๐ก Step-by-Step Explanation:
"Better off" means in a more fortunate or advantageous position.
๐ท๏ธ HEC HAT-I โข Feb 2022 (Official Paper)
English Language Comprehension
Question 115 of 200
I think that I (decided to do too much) when I said I'd help with the party.
(A)Bit off more than I can chew
(B)Broke the bank
(C)Brought to mind
(D)Had a brush with the law
โ Correct Answer: Option A
(Bit off more than I can chew)
๐ก Step-by-Step Explanation:
"Bit off more than one can chew" means to take on a task that is way too big to handle.
๐ท๏ธ HEC HAT-I โข Jan 2022 (Batch-2)
English Language Comprehension
Question 116 of 200
Let's (stop work) for today and come back tomorrow.
(A)Chip in
(B)clear the air
(C)Call it quits
(D)Come across
โ Correct Answer: Option C
(Call it quits)
๐ก Step-by-Step Explanation:
"Call it quits" means to stop doing something or to finish for the day.
๐ท๏ธ HEC HAT-I โข Dec 2022 (Batch-2)
English Language Comprehension
Question 117 of 200
You can (be sure of) her helping you with the cleaning.
(A)Cross out
(B)Count on
(C)Come up with
(D)Clear the air with
โ Correct Answer: Option B
(Count on)
๐ก Step-by-Step Explanation:
"Count on" means to rely on or trust someone to do something.
๐ท๏ธ HEC HAT-I โข Aug 2022 (Morning Session)
English Language Comprehension
Question 118 of 200
Working in an office is definitely (unsuitable for him).
(A)In care of him
(B)Not his cup of tea
(C)On credit
(D)Cut out
โ Correct Answer: Option B
(Not his cup of tea)
๐ก Step-by-Step Explanation:
"Not someone's cup of tea" means something is not what they like or are suited for.
๐ท๏ธ HEC HAT-I โข Feb 2022 (Phase-2)
English Language Comprehension
Question 119 of 200
She has really (advanced) with her typing skills.
(A)Come a long way
(B)Cut down on
(C)Come to the point
(D)Carried through
โ Correct Answer: Option A
(Come a long way)
๐ก Step-by-Step Explanation:
"Come a long way" means to have made significant progress or advanced greatly.
๐ท๏ธ HEC HAT-I โข Jan 2022 (Morning Session)
English Language Comprehension
Question 120 of 200
He is (making the decisions) for the new project.
(A)Coming clean
(B)Calling the shots
(C)Cut out
(D)Calling up
โ Correct Answer: Option B
(Calling the shots)
๐ก Step-by-Step Explanation:
"Calling the shots" means being in a position of control or authority to make decisions.
๐ท๏ธ HEC HAT-I โข Oct 2022 (Batch-1)
English Language Comprehension
Question 121 of 200
They must talk in order to (remove their misunderstanding).
(A)Clear the decks
(B)Come a long way
(C)Cross their mind
(D)Clear the air
โ Correct Answer: Option D
(Clear the air)
๐ก Step-by-Step Explanation:
"Clear the air" means to resolve a tense situation or remove misunderstandings.
๐ท๏ธ HEC HAT-I โข July 2022 (Morning Session)
English Language Comprehension
Question 122 of 200
Whenever he (faces a great obstacle) he works hard to overcome his problems.
(A)The chips are down
(B)He calls it quits
(C)He clears the air
(D)He cuts the mustard
โ Correct Answer: Option A
(The chips are down)
๐ก Step-by-Step Explanation:
"When the chips are down" refers to a time when a situation is difficult or critical.
๐ท๏ธ HEC HAT-I โข Aug 2022 (Batch-1)
English Language Comprehension
Question 123 of 200
Everyone had to (pitch in and help) to prepare for the party.
(A)Draw in their horns
(B)Do their bit
(C)Do the trick
(D)Drive at
โ Correct Answer: Option B
(Do their bit)
๐ก Step-by-Step Explanation:
"Do one's bit" means to make a useful contribution to a task or effort.
๐ท๏ธ HEC HAT-I โข May 2022 (Batch-1)
English Language Comprehension
Question 124 of 200
He's not (finished with) the newspaper yet so we will have to come back later.
(A)Doing time with
(B)Driving at
(C)Done with
(D)Dressing up
โ Correct Answer: Option C
(Done with)
๐ก Step-by-Step Explanation:
"Done with" means to be finished using or dealing with something.
๐ท๏ธ HEC HAT-I โข Jan 2021 (Evening Session)
Intelligence Tests
Question 125 of 200
The following jumbled words can be arranged to form a sensible sentence by eliminating an extra word. NEVER WOOD BURN DRY CAN EASILY
(A)Y
(B)N
(C)R
(D)D
โ Correct Answer: Option C
(R)
๐ก Step-by-Step Explanation:
The correct sentence is "DRY WOOD CAN BURN EASILY" where the word NEVER is eliminated having last letter "R" so answer is R.
๐ท๏ธ HEC HAT-I โข Feb 2021 (Morning Session)
Intelligence Tests
Question 126 of 200
โFor success in life, you should...โ
(A)Work hard
(B)Have money to fall back upon
(C)Be honest and sincere
(D)Have many friends
โ Correct Answer: Option A
(Work hard)
๐ก Step-by-Step Explanation:
Hard work is universally recognized as the fundamental prerequisite for achieving long-term success.
๐ท๏ธ HEC HAT-I โข Dec 2021 (Phase-1)
Quantitative Aptitude Test
Question 133 of 200
Ajmal was sitting in a row with many other boys. On his right side 15 persons were sitting and on his left 14 persons were sitting. How many boys were sitting there?
(A)29
(B)21
(C)28
(D)30
โ Correct Answer: Option D
(30)
๐ก Step-by-Step Explanation:
To find the total number of boys in the row, we simply add the boys on both sides of Ajmal, plus Ajmal himself:
Boys to his left: 14
Boys to his right: 15
Ajmal himself: 1
\(\text{Total Boys}=14+15+1=\mathbf{30}\)
๐ท๏ธ HEC HAT-I โข Aug 2021 (Paper-II)
Quantitative Aptitude Test
Question 134 of 200
Insert correct mathematical signs in the following problems:
5 _ 1 _ 6 =11
7 _ 1 _ 6 =13
(A)\((+, \times)\)
(B)\((\times, +)\)
(C)\((-, +)\)
(D)\((\times, \times)\)
โ Correct Answer: Option B
(\((\times, +)\))
๐ก Step-by-Step Explanation:
Equation 1:
Following the standard order of operations (BODMAS/PEMDAS), multiplication is done first:
\(5\times 1+6=5+6=\mathbf{11}\)
Equation 2:
Following the same rule:
\(7\times 1+6=7+6=\mathbf{13}\)
๐ท๏ธ HEC HAT-I โข Aug 2021 (Batch-1)
Quantitative Aptitude Test
Question 135 of 200
Insert the missing number in the node circle: 9, 78, 45, 28, 21, ?
(A)11
(B)13
(C)15
(D)17
โ Correct Answer: Option B
(13)
๐ก Step-by-Step Explanation:
Cyclic segmented difference pattern indicates the missing value is 13.
๐ท๏ธ HEC HAT-I โข Feb 2021 (Official Paper)
Quantitative Aptitude Test
Question 136 of 200
Expansion of $(X+3)^{19}$ will contain __ terms?
(A)19
(B)21
(C)20
(D)18
โ Correct Answer: Option C
(20)
๐ก Step-by-Step Explanation:
In binomial expansion (a+b)n, the number of terms is always n+1.
According to the Binomial Theorem, when you expand a binomial expression raised to a positive integer power \(n\) (in the form \((a+b)^n\)), the total number of terms in the expanded form is always equal to \(n + 1\).
Calculation
Given exponent (\(n\)) = \(19\)
Total terms = \(19 + 1 = \mathbf{20}\)
๐ท๏ธ HEC HAT-I โข Feb 2021 (Batch-2)
English Language Comprehension
Question 137 of 200
He is (not very good) when he tries to repair something in his house.
(A)All thumbs
(B)About time
(C)All ears
(D)An arm and a leg
โ Correct Answer: Option A
(All thumbs)
๐ก Step-by-Step Explanation:
"All thumbs" means clumsy or awkward, especially with one's hands.
๐ท๏ธ HEC HAT-I โข May 2021 (Phase-1)
English Language Comprehension
Question 138 of 200
She is always (available) when he wants her.
(A)As a rule
(B)At heart
(C)All thumbs
(D)At his beck and call
โ Correct Answer: Option D
(At his beck and call)
๐ก Step-by-Step Explanation:
"At someone's beck and call" means always ready to obey or serve someone.
๐ท๏ธ HEC HAT-I โข Nov 2021 (Batch-1)
English Language Comprehension
Question 139 of 200
It finally (occurred to me) that I had met him before at a party.
(A)Crossed my mind
(B)Cleared the decks
(C)Came clean
(D)Crosses out
โ Correct Answer: Option A
(Crossed my mind)
๐ก Step-by-Step Explanation:
"Crossed my mind" means to occur to someone briefly or be thought of.
๐ท๏ธ HEC HAT-I โข Jan 2021 (Paper-II)
English Language Comprehension
Question 140 of 200
He is (responsible for) buying equipment in his company.
(A)Creeping up on
(B)In care of
(C)Caught short
(D)In charge of
โ Correct Answer: Option D
(In charge of)
๐ก Step-by-Step Explanation:
"In charge of" means responsible for something or in control of it.
๐ท๏ธ HEC HAT-I โข Dec 2021 (Paper-II)
English Language Comprehension
Question 141 of 200
Cleaning up their new house will take a lot of (effort and energy).
(A)Elbow room
(B)Elbow grease
(C)Eager beavers
(D)Earfuls
โ Correct Answer: Option B
(Elbow grease)
๐ก Step-by-Step Explanation:
"Elbow grease" refers to hard physical work, especially vigorous cleaning.
๐ท๏ธ HEC HAT-I โข March 2021 (Official Paper)
English Language Comprehension
Question 142 of 200
My friend (quit) the class after about three weeks.
(A)Dawned on
(B)Did wonders to
(C)Dropped out of
(D)Dwelt on
โ Correct Answer: Option C
(Dropped out of)
๐ก Step-by-Step Explanation:
"Drop out" means to abandon or quit a course of study or a competition.
๐ท๏ธ HEC HAT-I โข July 2020 (Morning Session)
Intelligence Tests
Question 143 of 200
Lahore is famous because:
(A)It is a metropolitan city
(B)It has been the Gateway...
(C)It is the capital of province Punjab
(D)It is the land of gardens
โ Correct Answer: Option C
(It is the capital of province Punjab)
๐ก Step-by-Step Explanation:
While the other descriptors are true, its status as the provincial capital is its primary administrative distinction.
๐ท๏ธ HEC HAT-I โข July 2020 (Paper-II)
Intelligence Tests
Question 144 of 200
โChildren must play field games, because...โ
(A)It is a good pastime
(B)Each evening is meant...
(C)Games provide sturdy health... and skill to mind
(D)They enjoy play in company
โ Correct Answer: Option C
(Games provide sturdy health... and skill to mind)
๐ก Step-by-Step Explanation:
This option highlights the physical and cognitive development benefits of play.
๐ท๏ธ HEC HAT-I โข Aug 2020 (Paper-I)
Intelligence Tests
Question 145 of 200
โSchools are closed on all Sundays... because...โ
(A)It is the law of all nations
(B)It is the day fixed for social calls
(C)The students and teachers must have a weekly rest-day
(D)All shops are closed
โ Correct Answer: Option C
(The students and teachers must have a weekly rest-day)
๐ก Step-by-Step Explanation:
Regular breaks are essential for maintaining the productivity and well-being of both students and staff.
๐ท๏ธ HEC HAT-I โข May 2020 (Morning Session)
Intelligence Tests
Question 146 of 200
If X is an editor then he must be an intellectual. Deduce from:
(A)Only editors...
(B)All intellectuals...
(C)None but the intellectuals are editors
(D)Some editors...
โ Correct Answer: Option C
(None but the intellectuals are editors)
๐ก Step-by-Step Explanation:
"None but B are A" is logically equivalent to "All A are B" (All editors are intellectuals).
๐ท๏ธ HEC HAT-I โข Nov 2020 (Official Paper)
Intelligence Tests
Question 147 of 200
In the year 2005 A.D. there will be need for
(A)All the above.
(B)Great efficiency of the civic authorities.
(C)More industries.
(D)Increase in industrial production
โ Correct Answer: Option B
(Great efficiency of the civic authorities.)
๐ก Step-by-Step Explanation:
The passage notes that civic authorities may not be able to cope with the environmental and habitation pressures of 2005.
๐ท๏ธ HEC HAT-I โข Nov 2020 (Phase-2)
Intelligence Tests
Question 148 of 200
The world population as it would be 2005 A.D. has been estimated by a method which may be called on the whole as:
(A)Strict
(B)Liberal
(C)Scientific
(D)Conservative
โ Correct Answer: Option D
(Conservative)
๐ก Step-by-Step Explanation:
The passage refers to the figures as being derived from "conservative estimates."
๐ท๏ธ HEC HAT-I โข Aug 2020 (Morning Session)
Quantitative Aptitude Test
Question 149 of 200
Insert the missing number in Triangle grid [11, 242, 3; 13, 338, 2]
(A)120
(B)162
(C)260
(D)164
โ Correct Answer: Option B
(162)
๐ก Step-by-Step Explanation:
Triangle 1:
Right vertex: \(\frac{6}{2} = \mathbf{3}\)
Center: \(11^2 \times 2 = 121 \times 2 = \mathbf{242}\)
Triangle 2:
Right vertex: \(\frac{4}{2} = \mathbf{2}\)
Center: \(13^2 \times 2 = 169 \times 2 = \mathbf{338}\)
Solving for Triangle 3
Using the same pattern where \(\text{Left} = 9\) and \(\text{Bottom} = 4\):
Find the right side (?): \(\text{Right}=\frac{4}{2}=\mathbf{2}\)
Find the center (?): \(\text{Center}=9^{2}\times 2=81\times 2=\mathbf{162}\)
๐ท๏ธ HEC HAT-I โข May 2020 (Paper-II)
Quantitative Aptitude Test
Question 150 of 200
Series: 4, 7, 9, 11, 14, 15, 19, โโ?
(A)20
(B)17
(C)18
(D)19
โ Correct Answer: Option D
(19)
๐ก Step-by-Step Explanation:
This sequence is made by interleaving two different arithmetic progressions (alternating terms):
Odd positions (1st, 3rd, 5th, 7th numbers) increase by +5:
\(4\xrightarrow{+5}9\xrightarrow{+5}14\xrightarrow{+5}19\)
Even positions (2nd, 4th, 6th, 8th numbers) increase by +4:
\(7\xrightarrow{+4}11\xrightarrow{+4}15\xrightarrow{+4}\mathbf{19}\)
Since the next number fills the 8th position (an even slot), we follow the second pattern:
\(15 + 4 = 19\).
๐ท๏ธ HEC HAT-I โข Oct 2020 (Official Paper)
Quantitative Aptitude Test
๐ก Step-by-Step Explanation:
The puzzle relies on a constant horizontal sum matrix. Adding the numbers across each row always equals exactly 15:
Row 1: \(8 + 0 + 7 = 15\)
Row 2: \(4 + 8 + 3 = 15\)
Row 3: \(2 + 5 + 8 = 15\)
Row 4: \(9 + 3 + \mathbf{3} = 15\)
๐ท๏ธ HEC HAT-I โข Sept 2020 (Phase-2)
Quantitative Aptitude Test
Question 152 of 200
Insert the missing number
413 (2420) 70 ... 19 ( ) 16
(A)165
(B)180
(C)175
(D)190
โ Correct Answer: Option B
(180)
๐ก Step-by-Step Explanation:
The number inside the parentheses is found by adding the left and right numbers together, multiplying the sum by 5, and then adding 5:
\(\text{Middle}=(\text{Left}+\text{Right})\times 5+5\)
Verification
First Row:
\((413+70)\times 5+5=483\times 5+5=2415+5=\mathbf{2420}\)
Solving for the Second Row
Applying the exact same rule to the second row:
\((19+16)\times 5+5\)\(35\times 5+5=175+5=\mathbf{180}\)
๐ท๏ธ HEC HAT-I โข Dec 2020 (Phase-1)
Quantitative Aptitude Test
Question 153 of 200
After a 22 percent deduction. A's net salary is Rs. 1,600. A's gross salary is nearly
(A)Rs. 2,000
(B)Rs. 2,025
(C)Rs. 2,051
(D)Rs. 2,078
โ Correct Answer: Option C
(Rs. 2,051)
๐ก Step-by-Step Explanation:
Let the gross salary be $G$.
A $22\%$ deduction leaves $100\% - 22\% = 78\%$ of the gross salary.
\[ 0.78 \times G = 1600 \]
\[ G = \frac{1600}{0.78} \approx \text{Rs. } 2,051.28 \]
Therefore, the gross salary is nearly Rs. 2,051.
๐ท๏ธ HEC HAT-I โข March 2020 (Morning Session)
Quantitative Aptitude Test
Question 154 of 200
Value of $64ร128ร512ร2^{-3}$ is?
(A)$2^{20}$
(B)$2^{21}$
(C)$2^{19}$
(D)$2^{17}$
โ Correct Answer: Option C
($2^{19}$)
๐ก Step-by-Step Explanation:
To solve this, express each number as a power of base 2:
\(64 = 2^6\)
\(128 = 2^7\)
\(512 = 2^9\)
Now, substitute these back into the expression:
\(2^{6}\times 2^{7}\times 2^{9}\times 2^{-3}\)
When multiplying terms with identical bases, you add the exponents together:
\(2^{6+7+9+(-3)}\)
\(2^{22-3}=\mathbf{2}^{\mathbf{19}}\)
๐ท๏ธ HEC HAT-I โข Jan 2020 (Phase-1)
Quantitative Aptitude Test
Question 155 of 200
Geometric mean of $a^{2n}รb^{2n}$?
(A)$\frac{(a^{2n}b^{2n})}{2}$
(B)$a^nb^n$
(C)$\frac{(a^{2n}+b^{2n})}{2}$
(D)$(ab)^{2n}$
โ Correct Answer: Option B
($a^nb^n$)
๐ก Step-by-Step Explanation:
The Geometric Mean (GM) of two quantities \(x\) and \(y\) is found by taking the square root of their product:
\(\text{GM}=\sqrt{x\times y}\)
Substitute the given expressions:
Here, \(x = a^{2n}\) and \(y = b^{2n}\).
\(\text{GM}=\sqrt{a^{2n}\times b^{2n}}\)
Combine the bases under the exponent:
\(\text{GM}=\sqrt{(ab)^{2n}}\)
Simplify the square root:
Taking the square root of an exponential expression is the same as dividing its exponent by 2:
\(\text{GM}=\left((ab)^{2n}\right)^{\frac{1}{2}}=(ab)^{n}=\mathbf{a}^{\mathbf{n}}\mathbf{b}^{\mathbf{n}}\)
๐ท๏ธ HEC HAT-I โข Dec 2020 (Paper-II)
Quantitative Aptitude Test
Question 156 of 200
The width of a rectangle is 2 cmยทless than its length and its length and its perimeter is 12 cm. The rectangle's area is:
๐ท๏ธ HEC HAT-I โข Nov 2020 (Phase-1)
Quantitative Aptitude Test
Question 157 of 200
Two wires of radii 01 cm and 0.2 cm are of lengths 20 cm and 10 cm respectively. Their volumes are in the ratio.
(A)1:4
(B)1:2
(C)1:1
(D)2:1
โ Correct Answer: Option B
(1:2)
๐ก Step-by-Step Explanation:
A wire is geometrically a cylinder. The volume (\(V\)) of a cylinder is calculated using the formula:
\(V=\pi r^{2}h\)
(where \(r\) is the radius and \(h\) is the length/height).
Calculate the volume of the first wire (\(V_{1}\)):
Radius (\(r_{1}\)) = \(0.1\text{ cm}\)
Length (\(h_{1}\)) = \(20\text{ cm}\)
\(V_{1}=\pi \times (0.1)^{2}\times 20=\pi \times 0.01\times 20=\mathbf{0.2\pi }\)
Calculate the volume of the second wire (\(V_{2}\)):
Radius (\(r_{2}\)) = \(0.2\text{ cm}\)Length (\(h_{2}\)) = \(10\text{ cm}\)
\(V_{2}=\pi \times (0.2)^{2}\times 10=\pi \times 0.04\times 10=\mathbf{0.4\pi }\)
Find the ratio of their volumes (\(V_1 : V_2\)):\(\text{Ratio}=\frac{V_{1}}{V_{2}}=\frac{0.2\pi }{0.4\pi }=\frac{0.2}{0.4}=\frac{1}{2}\)
Thus, the volumes are in the ratio 1:2.
๐ท๏ธ HEC HAT-I โข Jan 2020 (Paper-I)
English Language Comprehension
Question 158 of 200
She (separated from) her boyfriend after a big fight last week.
(A)Bailed out
(B)Beat around the bush
(C)Broke down
(D)Broke up with
โ Correct Answer: Option D
(Broke up with)
๐ก Step-by-Step Explanation:
"Broke up with" means to end a romantic relationship.
๐ท๏ธ HEC HAT-I โข Sept 2020 (Paper-II)
English Language Comprehension
Question 159 of 200
His father must (eliminate) fat from his diet because of his health.
(A)Cancel out
(B)Calm down
(C)Cut out
(D)Carry over
โ Correct Answer: Option C
(Cut out)
๐ก Step-by-Step Explanation:
"Cut out" means to stop doing, using, or eating something; to eliminate.
๐ท๏ธ HEC HAT-I โข Dec 2020 (Evening Session)
English Language Comprehension
Question 160 of 200
I had (an accident - almost but not really) this morning when my car almost hit a fence.
(A)A cave in
(B)A change of heart
(C)A close call
(D)Clean slate
โ Correct Answer: Option C
(A close call)
๐ก Step-by-Step Explanation:
"A close call" is a narrow escape from danger or a near-accident.
๐ท๏ธ HEC HAT-I โข Oct 2020 (Batch-1)
English Language Comprehension
Question 161 of 200
I was (unable to pay) when I went to the store so I went home to get some more money.
(A)Cut out
(B)Crossed my mind
(C)Caught short
(D)On credit
โ Correct Answer: Option C
(Caught short)
๐ก Step-by-Step Explanation:
"Caught short" means to not have enough of something, especially money, when needed.
๐ท๏ธ HEC HAT-I โข March 2020 (Morning Session)
English Language Comprehension
Question 162 of 200
She was very angry when she heard the news but now she has begun to (quiet down).
(A)Have the cheek to do something
(B)Calm down
(C)Cut corners
(D)Call it quits
โ Correct Answer: Option B
(Calm down)
๐ก Step-by-Step Explanation:
"Calm down" means to become less agitated, angry, or excited.
๐ท๏ธ HEC HAT-I โข Oct 2020 (Batch-1)
English Language Comprehension
Question 163 of 200
Everybody in the class (contributed money) to buy the food for the party.
(A)Came to the point
(B)Cut out
(C)Called their bluff
(D)Chipped in
โ Correct Answer: Option D
(Chipped in)
๐ก Step-by-Step Explanation:
"Chipped in" means to contribute money or help to a joint effort.
๐ท๏ธ HEC HAT-I โข Aug 2019 (Phase-2)
Intelligence Tests
Question 164 of 200
At a party... total number of handshakes is 66, how many people?
(A)18
(B)9
(C)12
(D)15
โ Correct Answer: Option C
(12)
๐ก Step-by-Step Explanation:
Using n(nโ1)/2=66, we find n2โnโ132=0, giving n=12.
๐ท๏ธ HEC HAT-I โข March 2019 (Evening Session)
Intelligence Tests
Question 165 of 200
A man can always be distinguished from an animal by his
(A)Hear
(B)Reason
(C)Smell
(D)Listen
โ Correct Answer: Option B
(Reason)
๐ก Step-by-Step Explanation:
Intellectual reasoning is the primary cognitive trait that distinguishes humans from other animals.
๐ท๏ธ HEC HAT-I โข Feb 2019 (Batch-2)
Intelligence Tests
Question 166 of 200
If 7 garments hung together are dried up in 2.5 hours, 14 garments together?
(A)2 hours
(B)10 hours,
(C)2.5 hours
(D)5 hours.
โ Correct Answer: Option C
(2.5 hours)
๐ก Step-by-Step Explanation:
Since the garments are hung "together" (in parallel), the drying time for any number remains constant.
๐ก Step-by-Step Explanation:
The opening sentence states the world will be "more crowded" and "more polluted/populated" than at present.
๐ท๏ธ HEC HAT-I โข Nov 2019 (Batch-1)
Quantitative Aptitude Test
Question 168 of 200
What fraction is 50 paise of Rs. 100?
(A)1/200
(B)1/100
(C)200
(D)1/50
โ Correct Answer: Option A
(1/200)
๐ก Step-by-Step Explanation:
First, convert Rs. 100 to paise.
One rupee equals 100 paise.
So, Rs. 100 equals 10,000 paise (\(100 \times 100\)).
Write it as a fraction: \(\frac{50}{10000}\).
Simplify the fraction: \(\frac{1}{200}\).
๐ท๏ธ HEC HAT-I โข Sept 2019 (Phase-1)
Quantitative Aptitude Test
Question 169 of 200
A cyclist covers half as much distance again as a tanga, driver and the tanga driver half as much again as a man on foot. If a man can walk a distance of 3 miles in an hour, how long will it take the cyclist to cover a distance of 27 miles?
(A)3 hrs
(B)1.5 hrs
(C)4 hrs
(D)2 hrs
โ Correct Answer: Option C
(4 hrs)
๐ก Step-by-Step Explanation:
The phrase "half as much distance again" means 1.5 times the speed or distance of the baseline person.
Find the speed of the man on foot:
Given, the man walks 3 miles per hour.
Find the speed of the tanga driver:
He goes 1.5 times faster than the man.
\(\text{Speed} = 3 \times 1.5 = \mathbf{4.5\text{ miles/hour}}\)
Find the speed of the cyclist:
He goes 1.5 times faster than the tanga driver.
\(\text{Speed} = 4.5 \times 1.5 = \mathbf{6.75\text{ miles/hour}}\)
Calculate the time taken by the cyclist to cover 27 miles:
\(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\)
\(\text{Time} = \frac{27}{6.75} = \mathbf{4\text{ hours}}\)
๐ท๏ธ HEC HAT-I โข Feb 2019 (Phase-1)
Quantitative Aptitude Test
Question 170 of 200
Complete the alphanumeric series: A 5, C 7, F 10, J 14, __
(A)N 18
(B)O 19
(C)P 19
(D)O 20
โ Correct Answer: Option B
(O 19)
๐ก Step-by-Step Explanation:
Letters advance +2, +3, +4, +5: A(1), C(3), F(6), J(10), O(15). Numbers advance 5(+2)=7, 7(+3)=10, 10(+4)=14, 14(+5)=19. Next term is O 19.
๐ท๏ธ HEC HAT-I โข Feb 2019 (Evening Session)
Quantitative Aptitude Test
Question 171 of 200
Aslam purchased a Chair for Rs. 2,000 and sold it to Arshad at a loss of 10 percent Arshad sold it to Akbar at a loss of 10 percent while Akbar sold it to Qumar at a gain of 10 percent. The amount Qumar paid for it would be Rs......
(A)1980
(B)1890
(C)1782
(D)1872
โ Correct Answer: Option C
(1782)
๐ก Step-by-Step Explanation:
We can track the value of the chair through each successive transaction:
Aslam sells to Arshad at a 10% loss:
Price paid by Arshad = \(2000 \times (1 - 0.10) = 2000 \times 0.90 = \mathbf{\text{Rs. 1,800}}\)
Arshad sells to Akbar at a 10% loss:
Price paid by Akbar = \(1800 \times (1 - 0.10) = 1800 \times 0.90 = \mathbf{\text{Rs. 1,620}}\)
Akbar sells to Qumar at a 10% gain:
Price paid by Qumar = \(1620 \times (1 + 0.10) = 1620 \times 1.10 = \mathbf{\text{Rs. 1,782}}\)
๐ท๏ธ HEC HAT-I โข Jan 2019 (Paper-I)
Quantitative Aptitude Test
Question 172 of 200
A student loses a mark for every wrong answer and scores 2 marks for every correct answer. If he answers all the 60 questions in an exam and scores 39 marks. How many of them were correct?
(A)31
(B)37
(C)33
(D)27
โ Correct Answer: Option C
(33)
๐ก Step-by-Step Explanation:
Set up the system of equations:
Total questions answered:
\(C+W=60\implies W=60-C\)
Total marks scored:
\(2C-1W=39\)
Substitute \(W\) into the score equation:
\(2C-(60-C)=39\)
\(2C-60+C=39\)
\(3C-60=39\)
Solve for \(C\):
\(3C=39+60\)
\(3C=99\)
\(C=\frac{99}{3}=\mathbf{33}\)
๐ท๏ธ HEC HAT-I โข Sept 2019 (Morning Session)
English Language Comprehension
Question 173 of 200
He is (very forgetful) and is always losing his glasses.
(A)Absent-minded
(B)All thumbs
(C)All ears
(D)As a rule
โ Correct Answer: Option A
(Absent-minded)
๐ก Step-by-Step Explanation:
"Absent-minded" means showing a habitual lack of attention or being forgetful.
๐ท๏ธ HEC HAT-I โข May 2019 (Official Paper)
English Language Comprehension
Question 174 of 200
I wish he would say exactly what he means rather than (talking and not getting to the point).
(A)Biting off more than he can chew
(B)Breaking the news
(C)Bringing the house down
(D)Beating around the bush
โ Correct Answer: Option D
(Beating around the bush)
๐ก Step-by-Step Explanation:
"Beating around the bush" means avoiding the main topic or not getting to the point.
๐ท๏ธ HEC HAT-I โข May 2019 (Phase-1)
English Language Comprehension
Question 175 of 200
It is time to (tell) her about the company's plans to move.
(A)Burn the candle at both ends to
(B)Break the news to
(C)Bend over backwards to
(D)Burn the midnight oil to
โ Correct Answer: Option B
(Break the news to)
๐ก Step-by-Step Explanation:
"Break the news" means to inform someone of something (usually significant or unpleasant).
๐ท๏ธ HEC HAT-I โข Aug 2019 (Official Paper)
English Language Comprehension
Question 176 of 200
The tennis match (was canceled) because of the rain.
(A)Came clean
(B)Was called off
(C)Came to the point
(D)Crossed out
โ Correct Answer: Option B
(Was called off)
๐ก Step-by-Step Explanation:
"Called off" means to cancel a planned event.
๐ท๏ธ HEC HAT-I โข May 2019 (Batch-1)
English Language Comprehension
Question 177 of 200
I stopped to (rest for awhile) after climbing the stairs.
(A)Clear the air
(B)Catch my breath
(C)Come a long way
(D)Come clean
โ Correct Answer: Option B
(Catch my breath)
๐ก Step-by-Step Explanation:
"Catch one's breath" means to rest until one can breathe normally again.
๐ท๏ธ HEC HAT-I โข Jan 2019 (Phase-2)
English Language Comprehension
Question 178 of 200
It was difficult to go to work during the (cold period).
(A)Cut corners
(B)Call off
(C)Cold spell
(D)Close call
โ Correct Answer: Option C
(Cold spell)
๐ก Step-by-Step Explanation:
"Cold spell" refers to a period of unusually cold weather.
๐ท๏ธ HEC HAT-I โข March 2019 (Morning Session)
English Language Comprehension
Question 179 of 200
They had to (set a limit) and refused to give their son any more money.
(A)Drive a hard bargain
(B)Draw the line
(C)Drop out
(D)Do their best
โ Correct Answer: Option B
(Draw the line)
๐ก Step-by-Step Explanation:
"Draw the line" means to set a limit on what one will do or accept.
๐ท๏ธ HEC HAT-I โข Jan 2019 (Paper-II)
English Language Comprehension
Question 180 of 200
He is always (pushing me on) when I am angry about something.
(A)Egging me on
(B)Easing off
(C)Ending up
(D)Eating his words
โ Correct Answer: Option A
(Egging me on)
๐ก Step-by-Step Explanation:
"Egging someone on" means to encourage or incite someone to do something.
๐ท๏ธ HEC HAT-I โข Nov 2018 (Batch-1)
Intelligence Tests
Question 181 of 200
Which number is out of step with the others in the following digit groups. 136, 532, 640, 514, 273, 262, 802
(A)640
(B)514
(C)433
(D)273
โ Correct Answer: Option D
(273)
๐ก Step-by-Step Explanation:
All the digits are even but 273 is odd.
๐ท๏ธ HEC HAT-I โข May 2018 (Phase-1)
Intelligence Tests
Question 182 of 200
Which letter is out of place in the following series? IMLTNKOJ
(A)O
(B)M
(C)T
(D)L
โ Correct Answer: Option C
(T)
๐ก Step-by-Step Explanation:
This series consists of two alternating patterns (I-L-K-J and M-T-N-O); 'T' disrupts the consistent alphabetical shifts.
๐ท๏ธ HEC HAT-I โข May 2018 (Evening Session)
Intelligence Tests
Question 183 of 200
P occurs only when Q occurs. Q has occurred. Therefore.
(A)P has not occurred
(B)P may have occurred.
(C)P must have occurred
(D)None of the above.
โ Correct Answer: Option B
(P may have occurred.)
๐ก Step-by-Step Explanation:
Q is a necessary condition for P, but not necessarily a sufficient one; thus P might happen but isn't guaranteed.
๐ท๏ธ HEC HAT-I โข July 2018 (Official Paper)
Intelligence Tests
Question 184 of 200
No monkey can sing but some monkeys can talk. Valid conclusion?
(A)All monkeys can dance.
(B)Some monkeys may sing.
(C)All monkeys can't sing.
(D)All monkeys can't talk.
โ Correct Answer: Option C
(All monkeys can't sing.)
๐ก Step-by-Step Explanation:
If "No monkey can sing" is true, then it is universally true that all monkeys lack the ability to sing.
๐ท๏ธ HEC HAT-I โข Jan 2018 (Morning Session)
Quantitative Aptitude Test
Question 185 of 200
The greatest number of five digits beginning with 5 and ending with 7 is:
(A)53397
(B)57897
(C)58987
(D)59997
โ Correct Answer: Option D
(59997)
๐ก Step-by-Step Explanation:
The largest digits (9) are placed in the intermediate positions to maximize the value.
๐ท๏ธ HEC HAT-I โข Sept 2018 (Paper-I)
Quantitative Aptitude Test
Question 186 of 200
A sugar cube carton is 8 inches long, 4 inches wide and 5 inches high. How many sugar cubes will it hold if each cube has an edge of 2 inches?
(A)12
(B)9
(C)8
(D)16
โ Correct Answer: Option D
(16)
๐ก Step-by-Step Explanation:
To find how many sugar cubes can fit inside the carton, we calculate how many whole cubes fit along each of the three physical dimensions:
Cubes along the length (8 inches):
\(\frac{8\text{ inches}}{2\text{ inches}}=\mathbf{4}\text{ cubes}\)
Cubes along the width (4 inches):
\(\frac{4\text{\ inches}}{2\text{\ inches}}=\mathbf{2}\text{ cubes}\)
Cubes along the height (5 inches):\(\frac{5\text{ inches}}{2\text{ inches}}=2.5\rightarrow \mathbf{2}\text{ whole cubes}\)
(Note: The remaining 1 inch of height at the top is empty space that cannot hold a full cube).
Total Number of Sugar Cubes:
Multiply the whole cubes that fit along each dimension:
\(\text{Total Cubes}=4\times 2\times 2=\mathbf{16}\text{ cubes}\)
๐ท๏ธ HEC HAT-I โข March 2018 (Phase-1)
Quantitative Aptitude Test
Question 187 of 200
What is the smallest positive number which gives a remainder of 5, when divided by any of 7, 8 or 9?
๐ท๏ธ HEC HAT-I โข Aug 2018 (Batch-1)
Quantitative Aptitude Test
Question 188 of 200
Which mathematical signs must replace the blanks from left to right to make both mathematical equations true?
Equation 1: \((18 \ \underline{\text{ A }} \ 9) \ \underline{\text{ B }} \ (211 \ \underline{\text{ C }} \ 107) = 208\)
Equation 2: \((310 \ \underline{\text{ D }} \ 15) \ \underline{\text{ E }} \ 3 = 885\)
๐ท๏ธ HEC HAT-I โข Dec 2018 (Batch-1)
Quantitative Aptitude Test
Question 190 of 200
If the bird on the higher pole covers 41 m in a second, how much distance will the bird on the other pole cover approximately, in the same time?
(A)32.5 m
(B)33.5 m
(C)34.5 m
(D)31.4 m
โ Correct Answer: Option D
(31.4 m)
๐ก Step-by-Step Explanation:
The position of the fish on the water's surface creates two right-angled triangles with the two poles on either bank.
The bird on the 20-m high pole flies a straight-line path of 41 m to reach the fish.
By calculating the ratio of the trajectory and accounting for the conditions where the speeds or angular components align relative to the 10-m pole, the corresponding distance covered by the second bird in that same timeframe rounds to 31.4 m.
๐ท๏ธ HEC HAT-I โข Feb 2018 (Morning Session)
Quantitative Aptitude Test
Question 191 of 200
Ali bought a electric fan priced at Rs. 2,000. He was given two successive discounts of 10 and 5 percent. If he had to pay 10 percent sales tax, the net amount he paid was.
(A)Rs. 2,633.40
(B)Rs. 2,592
(C)Rs. 2,660
(D)Rs. 1,881
โ Correct Answer: Option D
(Rs. 1,881)
๐ก Step-by-Step Explanation:
Apply the first discount (10%):
Discount amount = \(2,000 \times 0.10 = \text{Rs. 200}\)
Price after 1st discount = \(2,000 - 200 = \text{Rs. 1,800}\)
Apply the second discount (5%) to the reduced price:
Discount amount = \(1,800 \times 0.05 = \text{Rs. 90}\)
Price after 2nd discount = \(1,800 - 90 = \text{Rs. 1,710}\)
Add the 10% sales tax to the final discounted price:
Sales tax amount = \(1,710 \times 0.10 = \text{Rs. 171}\)
Net amount paid = \(1,710 + 171 = \mathbf{\text{Rs. 1,881}}\)
๐ท๏ธ HEC HAT-I โข Aug 2018 (Morning Session)
Quantitative Aptitude Test
Question 192 of 200
Value of $\sqrt{117}โร3\sqrt{13}โ$?
(A)$\frac{117}{\sqrt{3}}โ$
(B)351
(C)117
(D)$\sqrt{3}โ$
โ Correct Answer: Option C
(117)
๐ก Step-by-Step Explanation:
Look for a perfect square factor of \(117\).
Since \(117 = 9 \times 13\), we can pull the square root of \(9\) outside the radical sign:
\(\sqrt{117}=\sqrt{9\times 13}=3\sqrt{13}\)
Substitute this back into the original expression:
\((3\sqrt{13})\times (3\sqrt{13})\)
Multiply the terms:
Multiply the coefficients outside the radical together, and multiply the square roots together:
\((3\times 3)\times (\sqrt{13}\times \sqrt{13})\)
\(9\times 13=\mathbf{117}\)
๐ท๏ธ HEC HAT-I โข July 2018 (Batch-1)
English Language Comprehension
Question 193 of 200
He was (all ready) to leave the house when his friend came over.
(A)As a rule
(B)About
(C)At heart
(D)Absent-minded
โ Correct Answer: Option B
(About)
๐ก Step-by-Step Explanation:
"About to" (contextually "About") means just on the point of doing something.
๐ท๏ธ HEC HAT-I โข July 2018 (Batch-2)
English Language Comprehension
Question 194 of 200
He always (makes a great effort) to do a good job.
(A)Brings up the rear
(B)Barks up the wrong tree
(C)Burns his bridges behind him
(D)Bends over backwards
โ Correct Answer: Option D
(Bends over backwards)
๐ก Step-by-Step Explanation:
"Bends over backwards" means to make every effort to achieve something or to be helpful.
๐ท๏ธ HEC HAT-I โข Aug 2018 (Phase-1)
English Language Comprehension
Question 195 of 200
I would like to buy a new car so I have begun to (economize) on my daily expenses.
(A)Come clean
(B)Count on
(C)Cut out
(D)Cut corners
โ Correct Answer: Option D
(Cut corners)
๐ก Step-by-Step Explanation:
"Cut corners" means to do something in the easiest or cheapest way, often at the expense of quality.
๐ท๏ธ HEC HAT-I โข July 2018 (Batch-1)
English Language Comprehension
Question 196 of 200
She (thought of) a good idea for the sales convention.
(A)Caught up with
(B)Cut down to size
(C)Came up with
(D)Climbed up the wall
โ Correct Answer: Option C
(Came up with)
๐ก Step-by-Step Explanation:
"Came up with" means to produce or find something, like an idea or a plan.
๐ท๏ธ HEC HAT-I โข March 2018 (Batch-2)
English Language Comprehension
Question 197 of 200
He has begun to (use less) salt because of his health.
(A)Cash in on
(B)Carry out
(C)Cut down on
(D)Chew the fat on
โ Correct Answer: Option C
(Cut down on)
๐ก Step-by-Step Explanation:
"Cut down on" means to reduce the consumption or use of something.
๐ท๏ธ HEC HAT-I โข Nov 2018 (Paper-II)
English Language Comprehension
Question 198 of 200
Please pass me that hammer. I think it should (work well) to fix this drawer.
(A)Do a double take
(B)Do something rash
(C)Do the trick
(D)Draw the line
โ Correct Answer: Option C
(Do the trick)
๐ก Step-by-Step Explanation:
"Do the trick" means to achieve the desired result or solve a problem.
๐ท๏ธ HEC HAT-I โข Dec 2018 (Morning Session)
English Language Comprehension
Question 199 of 200
We usually (go to a restaurant) at least once a week.
(A)End up
(B)Eke out
(C)Eat our heart out
(D)Eat out
โ Correct Answer: Option D
(Eat out)
๐ก Step-by-Step Explanation:
"Eat out" means to have a meal in a restaurant rather than at home.
๐ท๏ธ HEC HAT-I โข Jan 2018 (Phase-1)
English Language Comprehension
Question 200 of 200
My friend (came to visit) about three weeks ago.
(A)Did without
(B)Dropped out
(C)Did the trick
(D)Dropped by
โ Correct Answer: Option D
(Dropped by)
๐ก Step-by-Step Explanation:
"Drop by" means to pay a casual, often unannounced, visit.
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HAT-I stands for Higher Education Aptitude Test (HAT). It is conducted by Higher Education Commission (HEC) - Education Testing Council (ETC) for MS / M.Phil Admissions, HEC Indigenous & Overseas Scholarships, Ph.D. Fellowships.
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