GATE AE Numerical Ability: Previous Year Questions

GATE AE (Aerospace Engineering) Numerical Ability previous year questions from the General Aptitude section, with figures and the official answer key where available.

All GATE AE papers

GATE AE 2026, Question 3 (1 mark, MCQ)

General Aptitude - Numerical Ability

A school has 100 students distributed among $1^{\text{st}}$ to $10^{\text{th}}$ standards. Based on this, which one of the following statements is always correct?

  1. There are at least 10 students who belong to the same standard.
  2. There is at least one student in each standard.
  3. There are at most 10 students in $10^{\text{th}}$ standard.
  4. The total number of students from $1^{\text{st}}$ to $5^{\text{th}}$ standards is at least 50.

Official answer: A

GATE AE 2026, Question 4 (1 mark, MCQ)

General Aptitude - Numerical Ability

How many 3-digit numbers can be formed using three distinct single digit prime numbers?

  1. 64
  2. 24
  3. 12
  4. 4

Official answer: B

GATE AE 2026, Question 5 (1 mark, MCQ)

General Aptitude - Numerical Ability

In a group of students, 10 students like Mathematics, 12 students like English, 4 students like both Mathematics and English, and 6 students like neither Mathematics nor English. The number of students in the group is ____

  1. 18
  2. 20
  3. 24
  4. 32

Official answer: C

GATE AE 2025, Question 4 (1 mark, MCQ)

General Aptitude - Numerical Ability

In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of P, Q, and R ?

  1. P = 6; Q = 5; R = 3
  2. P = 5; Q = 6; R = 3
  3. P = 3; Q = 6; R = 6
  4. P = 5; Q = 3; R = 6

Official answer: A

GATE AE 2025, Question 5 (1 mark, MCQ)

General Aptitude - Numerical Ability

A rectangle has a length L and a width W, where L > W. If the width, W, is increased by 10%, which one of the following statements is correct for all values of L and W?

  1. Perimeter increases by 10%.
  2. Length of the diagonals increases by 10%.
  3. Area increases by 10%.
  4. The rectangle becomes a square.

Official answer: C

GATE AE 2025, Question 7 (2 marks, MCQ)

General Aptitude - Numerical Ability

Weight of a person can be expressed as a function of their age. The function varies from person to person. Suppose this function is identical for two brothers, and it monotonically increases till the age of 50 years and then it monotonically decreases. Let $a_1$ and $a_2$ (in years) denote the ages of the brothers and $a_1 < a_2$. Which one of the following statements is correct about their age on the day when they attain the same weight?

  1. $a_1 < a_2 < 50$
  2. $a_1 < 50 < a_2$
  3. $50 < a_1 < a_2$
  4. Either $a_1 = 50$ or $a_2 = 50$

Official answer: B

GATE AE 2025, Question 9 (2 marks, MCQ)

General Aptitude - Numerical Ability

If a real variable $x$ satisfies $3^{x^2} = 27 \times 9^x$, then the value of $\dfrac{2^{x^2}}{(2^x)^2}$ is:

  1. $2^{-1}$
  2. $2^{0}$
  3. $2^{3}$
  4. $2^{15}$

Official answer: C

GATE AE 2025, Question 10 (2 marks, MCQ)

General Aptitude - Numerical Ability

The number of patients per shift ($X$) consulting Dr. Gita in her past 100 shifts is shown in the figure. If the amount she earns is ₹ $1000(X - 0.2)$, what is the average amount (in ₹) she has earned per shift in the past 100 shifts? Note: The figure shown is representative.

  1. 6,100
  2. 6,300
  3. 6,000
  4. 6,500

Official answer: A

GATE AE 2024, Question 2 (1 mark, MCQ)

General Aptitude - Numerical Ability

If two distinct non-zero real variables $x$ and $y$ are such that $(x+y)$ is proportional to $(x-y)$ then the value of $\dfrac{x}{y}$

  1. depends on $xy$
  2. depends only on $x$ and not on $y$
  3. depends only on $y$ and not on $x$
  4. is a constant

Official answer: D

GATE AE 2024, Question 3 (1 mark, MCQ)

General Aptitude - Numerical Ability

Consider the following sample of numbers: 9, 18, 11, 14, 15, 17, 10, 69, 11, 13 The median of the sample is

  1. 13.5
  2. 14
  3. 11
  4. 18.7

Official answer: A

GATE AE 2024, Question 4 (1 mark, MCQ)

General Aptitude - Numerical Ability

The number of coins of ₹1, ₹5, and ₹10 denominations that a person has are in the ratio 5:3:13. Of the total amount, the percentage of money in ₹5 coins is

  1. 21%
  2. $14\frac{2}{7}\%$
  3. 10%
  4. 30%

Official answer: C

GATE AE 2024, Question 5 (1 mark, MCQ)

General Aptitude - Numerical Ability

For positive non-zero real variables $p$ and $q$, if $$\log(p^2 + q^2) = \log p + \log q + 2\log 3,$$ then, the value of $\dfrac{p^4+q^4}{p^2q^2}$ is

  1. 79
  2. 81
  3. 9
  4. 83

Official answer: A

GATE AE 2024, Question 7 (2 marks, MCQ)

General Aptitude - Numerical Ability

A rectangular paper sheet of dimensions 54 cm × 4 cm is taken. The two longer edges of the sheet are joined together to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken. Then, the ratio of the volume of the cylindrical tube to the volume of the cube is

  1. $1/\pi$
  2. $2/\pi$
  3. $3/\pi$
  4. $4/\pi$

Official answer: A

GATE AE 2024, Question 9 (2 marks, MCQ)

General Aptitude - Numerical Ability

A rectangular paper of 20 cm × 8 cm is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The perimeter of the final folded sheet (in cm) is

  1. 18
  2. 24
  3. 20
  4. 21

Official answer: A

GATE AE 2023, Question 1 (1 mark, MCQ)

General Aptitude - Numerical Ability

“You are delaying the completion of the task. Send _______ contributions at the earliest.”

  1. you are
  2. your
  3. you’re
  4. yore

Official answer: B

GATE AE 2023, Question 7 (2 marks, MCQ)

General Aptitude - Numerical Ability

To construct a wall, sand and cement are mixed in the ratio of 3:1. The cost of sand and that of cement are in the ratio of 1:2. If the total cost of sand and cement to construct the wall is 1000 rupees, then what is the cost (in rupees) of cement used?

  1. 400
  2. 600
  3. 800
  4. 200

Official answer: A

GATE AE 2023, Question 9 (2 marks, MCQ)

General Aptitude - Numerical Ability

The coefficient of $x^4$ in the polynomial $(x-1)^3(x-2)^3$ is equal to ______.

  1. 33
  2. $-3$
  3. 30
  4. 21

Official answer: A

GATE AE 2023, Question 10 (2 marks, MCQ)

General Aptitude - Numerical Ability

Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and are not allowed to overlap.

  1. circle
  2. regular octagon
  3. regular pentagon
  4. rhombus

Official answer: D

GATE AE 2022, Question 1 (1 mark, MCQ)

General Aptitude - Numerical Ability

Writing too many things on the ________ while teaching could make the students get _________.

  1. bored / board
  2. board / bored
  3. board / board
  4. bored / bored

Official answer: B

GATE AE 2022, Question 3 (1 mark, MCQ)

General Aptitude - Numerical Ability

If $f(x) = 2\ln\left(\sqrt{e^x}\right)$, what is the area bounded by $f(x)$ for the interval $[0, 2]$ on the $x$-axis?

  1. $\dfrac{1}{2}$
  2. 1
  3. 2
  4. 4

Official answer: C

GATE AE 2022, Question 4 (1 mark, MCQ)

General Aptitude - Numerical Ability

A person was born on the fifth Monday of February in a particular year. Which one of the following statements is correct based on the above information?

  1. The $2^{\text{nd}}$ February of that year is a Tuesday
  2. There will be five Sundays in the month of February in that year
  3. The $1^{\text{st}}$ February of that year is a Sunday
  4. All Mondays of February in that year have even dates

Official answer: A

GATE AE 2022, Question 7 (2 marks, MCQ)

General Aptitude - Numerical Ability

For the past $m$ days, the average daily production at a company was 100 units per day. If today's production of 180 units changes the average to 110 units per day, what is the value of $m$?

  1. 18
  2. 10
  3. 7
  4. 5

Official answer: C

GATE AE 2022, Question 8 (2 marks, MCQ)

General Aptitude - Numerical Ability

Consider the following functions for non-zero positive integers, $p$ and $q$. $$f(p,q) = \underbrace{p \times p \times p \times \dots \times p}_{q\ \text{terms}} = p^q;\quad f(p,1) = p$$ $$g(p,q) = p^{p^{p^{\cdot^{\cdot^{p}}}}}\ (\text{up to } q \text{ terms});\quad g(p,1) = p$$ Which one of the following options is correct based on the above?

  1. $f(2,2) = g(2,2)$
  2. $f(g(2,2),2) < f(2,g(2,2))$
  3. $g(2,1) \neq f(2,1)$
  4. $f(3,2) > g(3,2)$

Official answer: A

GATE AE 2018, Question 3 (1 mark, MCQ)

General Aptitude - Numerical Ability

Find the missing group of letters in the following series: BC, FGH, LMNO, _____

  1. UVWXY
  2. TUVWX
  3. STUVW
  4. RSTUV

Official answer: B

GATE AE 2018, Question 4 (1 mark, MCQ)

General Aptitude - Numerical Ability

The perimeters of a circle, a square and an equilateral triangle are equal. Which one of the following statements is true?

  1. The circle has the largest area.
  2. The square has the largest area.
  3. The equilateral triangle has the largest area.
  4. All the three shapes have the same area.

Official answer: A

GATE AE 2018, Question 5 (1 mark, MCQ)

General Aptitude - Numerical Ability

The value of the expression $\dfrac{1}{1+\log_u vw} + \dfrac{1}{1+\log_v wu} + \dfrac{1}{1+\log_w uv}$ is ________.

  1. -1
  2. 0
  3. 1
  4. 3

Official answer: C

GATE AE 2018, Question 6 (2 marks, MCQ)

General Aptitude - Numerical Ability

Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films?

  1. 0
  2. 2
  3. 4
  4. 8

Official answer: C

GATE AE 2018, Question 7 (2 marks, MCQ)

General Aptitude - Numerical Ability

A wire would enclose an area of 1936 m$^2$, if it is bent into a square. The wire is cut into two pieces. The longer piece is thrice as long as the shorter piece. The long and the short pieces are bent into a square and a circle, respectively. Which of the following choices is closest to the sum of the areas enclosed by the two pieces in square meters?

  1. 1096
  2. 1111
  3. 1243
  4. 2486

Official answer: C

GATE AE 2018, Question 8 (2 marks, MCQ)

General Aptitude - Numerical Ability

A contract is to be completed in 52 days and 125 identical robots were employed, each operational for 7 hours a day. After 39 days, five-seventh of the work was completed. How many additional robots would be required to complete the work on time, if each robot is now operational for 8 hours a day?

  1. 50
  2. 89
  3. 146
  4. 175

GATE AE 2018, Question 9 (2 marks, MCQ)

General Aptitude - Numerical Ability

A house has a number which needs to be identified. The following three statements are given that can help in identifying the house number. i. If the house number is a multiple of 3, then it is a number from 50 to 59. ii. If the house number is NOT a multiple of 4, then it is a number from 60 to 69. iii. If the house number is NOT a multiple of 6, then it is a number from 70 to 79. What is the house number?

  1. 54
  2. 65
  3. 66
  4. 76

Official answer: D

GATE AE 2016, Question 1 (1 mark, MCQ)

General Aptitude - Numerical Ability

The chairman requested the aggrieved shareholders to _________________ him.

  1. bare with
  2. bore with
  3. bear with
  4. bare

Official answer: C

GATE AE 2016, Question 2 (1 mark, MCQ)

General Aptitude - Numerical Ability

Identify the correct spelling out of the given options:

  1. Managable
  2. Manageable
  3. Mangaeble
  4. Managible

Official answer: B

GATE AE 2016, Question 3 (1 mark, MCQ)

General Aptitude - Numerical Ability

Pick the odd one out in the following: 13, 23, 33, 43, 53

  1. 23
  2. 33
  3. 43
  4. 53

Official answer: B

GATE AE 2016, Question 5 (1 mark, MCQ)

General Aptitude - Numerical Ability

If $|9y - 6| = 3$, then $y^2 - 4y/3$ is _______.

  1. 0
  2. +1/3
  3. -1/3
  4. undefined

Official answer: C

GATE AE 2016, Question 9 (2 marks, MCQ)

General Aptitude - Numerical Ability

Shaquille O' Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free throws out of 100 attempts on average. What is the probability that he will successfully make exactly 6 free throws in 10 attempts?

  1. 0.2508
  2. 0.2816
  3. 0.2934
  4. 0.6000

Official answer: A

GATE AE 2016, Question 10 (2 marks, NAT)

General Aptitude - Numerical Ability

The numeral in the units position of $211^{870} + 146^{127} \times 3^{424}$ is _____.

Official answer: 7

GATE AE 2014, Question 4 (1 mark, MCQ)

General Aptitude - Numerical Ability

If $y = 5x^2 + 3$, then the tangent at $x = 0$, $y = 3$

  1. passes through $x = 0$, $y = 0$
  2. has a slope of $+1$
  3. is parallel to the $x$-axis
  4. has a slope of $-1$

Official answer: C

GATE AE 2014, Question 5 (1 mark, NAT)

General Aptitude - Numerical Ability

A foundry has a fixed daily cost of Rs 50,000 whenever it operates and a variable cost of Rs $800Q$, where $Q$ is the daily production in tonnes. What is the cost of production in Rs per tonne for a daily production of 100 tonnes?

Official answer: 1300

GATE AE 2014, Question 6 (2 marks, MCQ)

General Aptitude - Numerical Ability

Find the odd one in the following group: ALRVX, EPVZB, ITZDF, OYEIK

  1. ALRVX
  2. EPVZB
  3. ITZDF
  4. OYEIK

Official answer: D

GATE AE 2014, Question 8 (2 marks, NAT)

General Aptitude - Numerical Ability

The smallest angle of a triangle is equal to two thirds of the smallest angle of a quadrilateral. The ratio between the angles of the quadrilateral is 3:4:5:6. The largest angle of the triangle is twice its smallest angle. What is the sum, in degrees, of the second largest angle of the triangle and the largest angle of the quadrilateral?

Official answer: 180

GATE AE 2014, Question 9 (2 marks, MCQ)

General Aptitude - Numerical Ability

One percent of the people of country X are taller than 6 ft. Two percent of the people of country Y are taller than 6 ft. There are thrice as many people in country X as in country Y. Taking both countries together, what is the percentage of people taller than 6 ft?

  1. 3.0
  2. 2.5
  3. 1.5
  4. 1.25

Official answer: D