Quantitative Aptitude Notes for GATE DA

GATE DA Quantitative Aptitude: 2 units and 7 chapters, weightage from 15 previous year questions across 3 papers, a study order by exam weight and 843 practice questions.

About Quantitative Aptitude Notes

Full study notes for Quantitative Aptitude in GATE DA, organised across 7 chapters. Each chapter page explains concepts from the basics with worked examples and the formulas you need.

GATE DA Quantitative Aptitude Unit-wise Weightage from Past Papers

We counted every GATE DA Quantitative Aptitude previous year question in our bank (15 questions from 3 papers) and grouped them by unit.

Unit	Chapters	PYQs	Share of section	Avg per paper
Numerical Computation & Estimation	6	12	80%	4
Data Interpretation	1	3	20%	1

Suggested Quantitative Aptitude Study Order for GATE DA

Numerical Computation & Estimation: 80% of past Quantitative Aptitude questions, about 4 per paper.
Data Interpretation: 20% of past Quantitative Aptitude questions, about 1 per paper.

Start where the marks are. Units at the top of this list have appeared most often in past GATE DA papers.

Units in GATE DA Quantitative Aptitude

All Quantitative Aptitude chapters

One Solved Question from Each Quantitative Aptitude Chapter

Question 1 · Number Systems, Digit Problems and Divisibility MCQ

Consider the formation of 4-digit numbers using the digits ${0, 1, 2, 3, 4, 5}$ without repetition. Which of the following statements is TRUE?

A.
The thousands place has 6 possible choices.
B.
The total number of such 4-digit numbers is 360.
C.
If the number must be divisible by 5, the units digit must be 0 or 5.
D.
The total number of such 4-digit numbers with repetition allowed is 625.

Correct Answer:

Step-by-Step Solution

Key idea: Evaluate each statement by applying the fundamental rules of number formation, especially the leading zero constraint.

Step 1: Statement A: The thousands place cannot be 0, so it has only 5 choices (1, 2, 3, 4, 5), not 6. False.

Step 2: Statement B: Total numbers = $5 \times 5 \times 4 \times 3 = 300$ , not 360. (360 would be $6 \times 5 \times 4 \times 3$ , ignoring the leading zero constraint). False.

Step 3: Statement C: A number is divisible by 5 if its units digit is 0 or 5. This is a standard divisibility rule. True.

Step 4: Statement D: With repetition allowed, total numbers = $5 \times 6 \times 6 \times 6 = 1080$ (thousands has 5 choices, others have 6). 625 is $5^{4}$ , which is incorrect. False.

Answer: C

Question 2 · Exponents, Logarithms and Infinite Series MCQ

For $x > 0$ , let $f (x) = x^{0} + x^{1}$ . What is the maximum value of $f (x)$ on the interval $[1, 3]$ ?

A.
4
B.
3
C.
2
D.
5

Correct Answer:

Step-by-Step Solution

Key idea: This tests the zero exponent rule ( $x^{0} = 1$ for $x > 0$ ) and evaluating a function on a closed interval.

Step 1: Simplify $f (x)$ . Since $x > 0$ , $x^{0} = 1$ . So $f (x) = 1 + x^{1} = 1 + x$ .

Step 2: Find the maximum on $[1, 3]$ . Since $f (x) = 1 + x$ is a linear increasing function, the maximum occurs at the right endpoint $x = 3$ .

Step 3: Evaluate $f (3) = 1 + 3 = 4$ .

Answer: 4

Common trap: Forgetting that $x^{0} = 1$ and treating it as $x^{0} = 0$ or $x^{0} = x$ , leading to wrong simplification.

Question 3 · Percentages, Ratios and Financial Computation MCQ

Person 1 and Person 2 invest in two funds, A and B. Person 1 invests ₹ $10, 000$ in A and ₹ $20, 000$ in B. Person 2 invests ₹ $20, 000$ in A and ₹ $10, 000$ in B. If Person 1 gets ₹ $500$ more than Person 2, and the rate of B is $10%$ , which of the following statements must be true?

A.
The rate of A is $5%$ .
B.
The rate of A is $10%$ .
C.
The rate of A is $15%$ .
D.
The rate of A cannot be determined.

Correct Answer:

Step-by-Step Solution

Key idea: Use the difference in returns to find the unknown rate.

Step 1: Person 1's return = $10, 000 a + 20, 000 (0.10) = 10, 000 a + 2, 000$ .

Step 2: Person 2's return = $20, 000 a + 10, 000 (0.10) = 20, 000 a + 1, 000$ .

Step 3: Difference = $(10, 000 a + 2, 000) - (20, 000 a + 1, 000) = - 10, 000 a + 1, 000$ .

Step 4: We are given this difference is ₹ $500$ .

Step 5: $- 10, 000 a + 1, 000 = 500 ⟹ 10, 000 a = 500 ⟹ a = 0.05 = 5%$ .

Answer: The rate of A is $5%$ .

Question 4 · Descriptive Statistics and Data Normalization MCQ

For a sorted data set of 7 numbers represented as $x_{1} \leq x_{2} \leq x_{3} \leq x_{4} \leq x_{5} \leq x_{6} \leq x_{7}$ , which position corresponds to the median?

A.
3rd
B.
4th
C.
5th
D.
Average of 3rd and 5th

Correct Answer:

Step-by-Step Solution

Key idea: This is a definition recall question, recognisable because it asks for the position of the median in a sorted list of a specific size.

Step 1: Recall the definition of the median. The median is the middle value of a sorted data set.

Step 2: Determine the middle position for an odd number of elements $n$ . The formula for the middle position is $\frac{n + 1}{2}$ .

Step 3: Substitute $n = 7$ into the formula: $\frac{7 + 1}{2} = \frac{8}{2} = 4$ .

Step 4: The 4th position corresponds to the variable $x_{4}$ .

Answer: B

Question 5 · Combinatorial Counting and Bijections MCQ

Which of the following sets of three digits has a sum that is exactly divisible by 3?

A.
{1, 2, 4}
B.
{1, 3, 5}
C.
{2, 3, 5}
D.
{2, 4, 5}

Correct Answer:

Step-by-Step Solution

Key idea: Direct application of the digit sum rule for divisibility by 3.

Step 1: Calculate the sum of digits for each option.

Option A: 1 + 2 + 4 = 7 (Not divisible by 3)
Option B: 1 + 3 + 5 = 9 (Divisible by 3)
Option C: 2 + 3 + 5 = 10 (Not divisible by 3)
Option D: 2 + 4 + 5 = 11 (Not divisible by 3)

Step 2: Identify the set with a sum divisible by 3.

Answer: {1, 3, 5}

Question 6 · Geometry and Mensuration MCQ

If an arc subtends an angle of $3 5^{\circ}$ at a point on the remaining part of the circumference, what is the angle subtended by the same arc at the center of the circle?

A.
$3 5^{\circ}$
B.
$5 5^{\circ}$
C.
$7 0^{\circ}$
D.
$10 5^{\circ}$

Correct Answer:

Step-by-Step Solution

Insight: The central angle is always exactly double the angle at the circumference for the same arc.

Exam route: Multiply the given circumference angle by 2: $3 5^{\circ} \times 2 = 7 0^{\circ}$ .

Learning route: By the Central Angle Theorem, the angle subtended by an arc at the center ( $∠ A O B$ ) is double the angle subtended by the same arc at any point on the remaining circumference ( $∠ A P B$ ). Therefore, $∠ A O B = 2 \times 3 5^{\circ} = 7 0^{\circ}$ .

Answer: C

Question 7 · Data Interpretation: Tables, Charts and Graphs MCQ

If the average value of a dataset $X$ is 10, and a new dataset $Y$ is created using the linear transformation $Y = 2 X + 3$ , what is the average value of $Y$ ?

A.
20
B.
13
C.
26
D.
23

Correct Answer:

Step-by-Step Solution

Key idea: This is a direct substitution question, recognisable because it gives the average of a variable and asks for the average after a linear transformation.

Step 1: Recall the property of linear transformation of averages. If $Y = a X + b$ , then the average of $Y$ is $\overset{ˉ}{Y} = a \overset{ˉ}{X} + b$ .

Step 2: Identify the given values. $\overset{ˉ}{X} = 10$ , $a = 2$ , and $b = 3$ .

Step 3: Substitute these values into the formula: $\overset{ˉ}{Y} = 2 (10) + 3$ .

Step 4: Calculate the result: $20 + 3 = 23$ .

Answer: D

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Quantitative Aptitude Notes for GATE DA

About Quantitative Aptitude Notes

GATE DA Quantitative Aptitude Unit-wise Weightage from Past Papers

Suggested Quantitative Aptitude Study Order for GATE DA

Units in GATE DA Quantitative Aptitude

All Quantitative Aptitude chapters

One Solved Question from Each Quantitative Aptitude Chapter

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution

Step-by-Step Solution