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Quantitative Aptitude Notes for GATE CS

GATE CS Quantitative Aptitude: 2 units and 6 chapters, weightage from 33 previous year questions across 10 papers, a study order by exam weight and 540 practi

A question from this chapter

Question 1

Level 1: Warm-up

Using the deviation shortcut, if the assumed mean is 100 and the sum of deviations for 5 observations is -25, what is the actual mean?

Question 2

Level 1: Warm-up

How many pairs of positive integers (x, y) satisfy the equation lo g_{10} (\frac{x + y}{2}) = \frac{1}{2} (lo g_{10} x + lo g_{10} y) and the condition x + y \leq 12 ?

Question 3

Level 1: Warm-up

Assertion (A): If a triangle is half the area of a square and also half the area of a rectangle, then the square and rectangle have equal areas. Reason (R): The area of a triangle is always measured in cubic units. Choose the correct option:

Question 4

Level 1: Warm-up

In a group of 50 people, 30 like tea and 25 like coffee. What is the minimum number of people who like both tea and coffee?

Question 5

Level 1: Warm-up

An item has a fixed Selling Price of ₹500. Which of the following Marked Prices yields the minimum non-negative Discount Percentage, assuming the standard constraint M P \geq S P is strictly enforced?

Question 6

Level 1: Warm-up

A component's share in a pie chart was 20% of a total value of 500 . In the next year, its share became 25% of a total value of 600 . What is the percentage change in the absolute value of this component?

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Quantitative Aptitude Notes for GATE CS

GATE CS Quantitative Aptitude: 2 units and 6 chapters, weightage from 33 previous year questions across 10 papers, a study order by exam weight and 540 practice questions.

About Quantitative Aptitude Notes

Full study notes for Quantitative Aptitude in GATE CS, organised across 6 chapters. Each chapter page explains concepts from the basics with worked examples and the formulas you need.

GATE CS Quantitative Aptitude Unit-wise Weightage from Past Papers

We counted every GATE CS Quantitative Aptitude previous year question in our bank (33 questions from 10 papers) and grouped them by unit.

Unit	Chapters	PYQs	Share of section	Avg per paper
Numerical computation and estimation	4	28	85%	2.8
Data interpretation	2	5	15%	0.5

Suggested Quantitative Aptitude Study Order for GATE CS

Numerical computation and estimation: 85% of past Quantitative Aptitude questions, about 2.8 per paper.
Data interpretation: 15% of past Quantitative Aptitude questions, about 0.5 per paper.

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

Units in GATE CS Quantitative Aptitude

All Quantitative Aptitude chapters

One Solved Question from Each Quantitative Aptitude Chapter

Question 1 · Arithmetic, Ratios, Percentages and Commercial Mathematics MCQ

Using the deviation shortcut, if the assumed mean is 100 and the sum of deviations for 5 observations is -25, what is the actual mean?

A.
90
B.
95
C.
105
D.
125

Correct Answer:

Step-by-Step Solution

Key idea: This is a direct application of the deviation shortcut formula, recognizable because it provides the assumed mean, the sum of deviations, and the count.

Step 1: Identify the given values: Assumed mean $A = 100$ , Sum of deviations $\sum d_{i} = - 25$ , Number of observations $n = 5$ .

Step 2: Apply the formula: $Actual Mean = A + \frac{\sum d _{i}}{n}$ .

Step 3: Calculate: $100 + \frac{- 25}{5} = 100 - 5 = 95$ .

Answer: B

Question 2 · Algebra, Equations, Functions and Sequences MCQ

How many pairs of positive integers $(x, y)$ satisfy the equation $lo g_{10} (\frac{x + y}{2}) = \frac{1}{2} (lo g_{10} x + lo g_{10} y)$ and the condition $x + y \leq 12$ ?

A.
4
B.
5
C.
6
D.
11

Correct Answer:

Step-by-Step Solution

Key idea: Simplify the right side to recognize the AM-GM equality condition.

Step 1: Simplify the right side using log rules.

$\frac{1}{2} (lo g_{10} x + lo g_{10} y) = \frac{1}{2} lo g_{10} (x y) = lo g_{10} ((x y)^{1/2}) = lo g_{10} (x y)$

Step 2: Equate the arguments since the logs are equal.

$\frac{x + y}{2} = x y$

Step 3: Recognize this as the Arithmetic Mean (AM) equals Geometric Mean (GM) condition.

For positive real numbers, AM = GM if and only if $x = y$ .

Step 4: Apply the condition $x + y \leq 12$ .

Since $x = y$ , we have $2 x \leq 12 ⟹ x \leq 6$ .

Step 5: Count the positive integer pairs.

$x$ can be $1, 2, 3, 4, 5, 6$ . Since $y = x$ , the pairs are $(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)$ .

There are 6 such pairs.

Answer: 6

Question 3 · Geometry, Mensuration and Area MCQ

Assertion (A): If a triangle is half the area of a square and also half the area of a rectangle, then the square and rectangle have equal areas.

Reason (R): The area of a triangle is always measured in cubic units.

Choose the correct option:

A.
Both A and R are true and R is the correct explanation of A
B.
Both A and R are true but R is NOT the correct explanation of A
C.
A is true but R is false
D.
A is false but R is true

Correct Answer:

Step-by-Step Solution

Key idea: This is a geometric invariance problem combined with a units check. Step 1: Analyze Assertion (A). - Let the triangle's area be

T

. - Triangle is half the square:

T = \frac{1}{2} \times Area_{square}

, so

Area_{square} = 2 T

. - Triangle is half the rectangle:

T = \frac{1}{2} \times Area_{rectangle}

, so

Area_{rectangle} = 2 T

. - Therefore,

Area_{square} = Area_{rectangle} = 2 T

. - Assertion (A) is true. Step 2: Analyze Reason (R). - Area is a two-dimensional measurement. - Area is measured in square units (e.g., cm², m²), not cubic units. - Cubic units are for volume (three-dimensional). - Reason (R) is false. Answer: A is true but R is false

Question 4 · Counting, Sets and Elementary Probability MCQ

In a group of 50 people, 30 like tea and 25 like coffee. What is the minimum number of people who like both tea and coffee?

A.
5
B.
15
C.
25
D.
55

Correct Answer:

Step-by-Step Solution

Key idea: Use the inclusion-exclusion principle and the fact that the union cannot exceed the total population.

Step 1: Let $T$ be the set of tea lovers and $C$ be the set of coffee lovers. We have $n (T) = 30$ , $n (C) = 25$ , and the total population $n (U) = 50$ .

Step 2: The inclusion-exclusion formula is $n (T \cup C) = n (T) + n (C) - n (T \cap C)$ .

Step 3: Since $n (T \cup C) \leq n (U)$ , we have $30 + 25 - n (T \cap C) \leq 50$ .

Step 4: Simplify the inequality: $55 - n (T \cap C) \leq 50 ⟹ n (T \cap C) \geq 5$ .

Answer: 5

Question 5 · Tables and Structured Data MCQ

An item has a fixed Selling Price of ₹500. Which of the following Marked Prices yields the minimum non-negative Discount Percentage, assuming the standard constraint $M P \geq S P$ is strictly enforced?

A.
₹450
B.
₹550
C.
₹500
D.
₹600

Correct Answer:

Step-by-Step Solution

Key idea: The constraint $M P \geq S P$ ensures that the Discount Percentage is non-negative.

Step 1: Recall the formula for Discount Percentage: $Discount % = \frac{M P - S P}{M P} \times 100$ .

Step 2: To minimize the non-negative discount, we need $M P - S P$ to be as small as possible, which means $M P$ should be as close to $S P$ as possible.

Step 3: Given the constraint $M P \geq S P$ , the minimum valid value for $M P$ is exactly $S P$ , i.e., $M P = 500$ .

Step 4: If $M P = 500$ , then $Discount % = \frac{500 - 500}{500} \times 100 = 0%$ .

Answer: ₹500

Question 6 · Charts and Graphical Data Interpretation MCQ

A component's share in a pie chart was $20%$ of a total value of $500$ . In the next year, its share became $25%$ of a total value of $600$ . What is the percentage change in the absolute value of this component?

A.
25%
B.
50%
C.
75%
D.
100%

Correct Answer:

Step-by-Step Solution

Key idea: calculate absolute values for both years first, then apply the percentage change formula.

Step 1: Old absolute value = $20%$ of $500 = 100$ .

Step 2: New absolute value = $25%$ of $600 = 150$ .

Step 3: Percentage change = $\frac{150 - 100}{100} \times 100 = 50%$ .

Answer: 50%.