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Data interpretation Notes for GATE CS

GATE CS Data interpretation: 2 chapters, 5 previous year questions (15% of Quantitative Aptitude), 79 practice questions and one solved question from each cha

A question from this chapter

Question 1

Level 3: Exam Standard

The table below shows the partial pricing details for two items, M and N. The ratio of the Cost Price (CP) of M to the CP of N is 3:4. The Marked Price (MP) of M is \frac{4}{3} times its CP. The Marked Price of N is m times its CP. Both items are sold at the same discount percentage d % on their respective Marked Prices. If the overall profit percentage for the two items combined is exactly 20%, and the profit percentage on item N does not exceed 50%, what is the maximum possible value of d ?

Question 2

Level 3: Exam Standard

The central angle for Engineering in a pie chart of total research publications was 12 0^{\circ} in 2020 and 9 6^{\circ} in 2024. The total number of publications in 2024 was 30% more than in 2020. Assertion (A): The number of engineering publications increased by approximately 4% from 2020 to 2024. Reason (R): A 20% decrease in the central angle of a sector implies a 20% decrease in the number of items in that sector. Which one of the following is correct?

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Data interpretation Notes for GATE CS

GATE CS Data interpretation: 2 chapters, 5 previous year questions (15% of Quantitative Aptitude), 79 practice questions and one solved question from each chapter.

About Data interpretation Notes

Full study notes for Data interpretation in GATE CS, organised across 2 chapters. Each chapter page explains concepts from the basics with worked examples and the formulas you need.

Data interpretation Weightage in GATE CS

Data interpretation accounts for 5 of 33 Quantitative Aptitude previous year questions in our bank (15%), about 1 per paper across 5 papers.

Data interpretation Chapter Matrix

Chapter	Topics	PYQs	Share of unit PYQs	Practice questions
Tables and Structured Data	Commercial Tables and Percentage Calculations, Recurrence Patterns in Tabular Data	2	40%	32
Charts and Graphical Data Interpretation	Pie Chart Interpretation and Percentage Change, Bar Charts and Ratio Comparison	3	60%	47

One Solved Question from Each Data interpretation Chapter

Question 1 · Tables and Structured Data MCQ

The table below shows the partial pricing details for two items, M and N. The ratio of the Cost Price (CP) of M to the CP of N is 3:4. The Marked Price (MP) of M is $\frac{4}{3}$ times its CP. The Marked Price of N is $m$ times its CP. Both items are sold at the same discount percentage $d %$ on their respective Marked Prices.

If the overall profit percentage for the two items combined is exactly 20%, and the profit percentage on item N does not exceed 50%, what is the maximum possible value of $d$ ?

A.
30
B.
40
C.
45
D.
50

Correct Answer:

Step-by-Step Solution

Key idea: This is an observation and maximization question involving ratios and boundary conditions. The trap is ignoring the constraint on the profit percentage of item N.

Step 1: Let CP of M = $3 x$ and CP of N = $4 x$ . Total CP = $7 x$ .

Step 2: Overall profit is 20%, so Total SP = $7 x \times 1.20 = 8.4 x$ .

Step 3: MP of M = $\frac{4}{3} \times 3 x = 4 x$ . MP of N = $m \times 4 x = 4 m x$ .

Step 4: Both are sold at $d %$ discount.

$SP_{M} = 4 x (1 - \frac{d}{100})$

$SP_{N} = 4 m x (1 - \frac{d}{100})$

Step 5: Total SP = $SP_{M} + SP_{N} = 4 x (1 - \frac{d}{100}) (1 + m) = 8.4 x$ .

Simplifying: $(1 - \frac{d}{100}) (1 + m) = 2.1$ .

Step 6: To maximize $d$ , we must minimize $(1 - \frac{d}{100})$ , which means we must maximize $m$ .

Step 7: Apply the boundary condition: Profit % on N $\leq 50%$ .

$Profit on N = SP_{N} - CP_{N} = 4 m x (1 - \frac{d}{100}) - 4 x$ .

$Profit % on N = \frac{4 m x ( 1 - \frac{d}{100} ) - 4 x}{4 x} = m (1 - \frac{d}{100}) - 1 \leq 0.5$ .

So, $m (1 - \frac{d}{100}) \leq 1.5$ .

Step 8: Substitute $(1 - \frac{d}{100}) = \frac{2.1}{1 + m}$ into the inequality:

$m (\frac{2.1}{1 + m}) \leq 1.5 ⟹ 2.1 m \leq 1.5 + 1.5 m ⟹ 0.6 m \leq 1.5 ⟹ m \leq 2.5$ .

Step 9: The maximum value of $m$ is 2.5. Substitute back to find $d$ :

$1 - \frac{d}{100} = \frac{2.1}{1 + 2.5} = \frac{2.1}{3.5} = 0.6$ .

$\frac{d}{100} = 0.4 ⟹ d = 40$ .

Answer: 40

Question 2 · Charts and Graphical Data Interpretation MCQ

The central angle for Engineering in a pie chart of total research publications was $12 0^{\circ}$ in 2020 and $9 6^{\circ}$ in 2024. The total number of publications in 2024 was 30% more than in 2020.

Assertion (A): The number of engineering publications increased by approximately 4% from 2020 to 2024.

Reason (R): A 20% decrease in the central angle of a sector implies a 20% decrease in the number of items in that sector.

Which one of the following is correct?

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 an assertion-reason question about sector angles and changing totals. A central angle measures share of the whole, not the underlying quantity, unless the whole is unchanged.

Insight: quantity ratio = angle ratio × total ratio.

Exam route:

The angle ratio for Engineering is

$\frac{96}{120} = \frac{4}{5} = 0.8.$

The total ratio is

$1 + 0.30 = 1.30 = \frac{13}{10} .$

Therefore the quantity ratio is

$\frac{4}{5} \times \frac{13}{10} = \frac{52}{50} = 1.04.$

So engineering publications increased by $4%$ . Assertion A is true.

Reason R says that a decrease in angle directly implies the same decrease in count. That is false in general because the total may change. Here the total increased by 30%, which more than offset the 20% fall in angle share.

Learning route:

Take a convenient base total. Let the 2020 total be $300$ .

$E_{2020} = \frac{120}{360} \times 300 = 100.$

The 2024 total is $390$ .

$E_{2024} = \frac{96}{360} \times 390 = 104.$

The increase is $4$ on $100$ , i.e. $4%$ .

Tempting wrong path: follow Reason R and reduce the 2020 count by 20%. That gives a decrease and makes Assertion A appear false, pointing to the last option. The break occurs at treating angle change as quantity change without checking the total.

Generalization: angle ratio gives share ratio; quantity ratio requires multiplying by total ratio.

Verification: using $300$ and $390$ gives $100$ and $104$ , confirming a 4% increase.

Answer: C

A question from this chapter

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Data interpretation Notes for GATE CS

About Data interpretation Notes

Data interpretation Weightage in GATE CS

Data interpretation Chapter Matrix

More from Quantitative Aptitude

One Solved Question from Each Data interpretation Chapter

Step-by-Step Solution

Step-by-Step Solution