GATE Numerical Ability and Data Interpretation
Data interpretation is a distinct skill from a single stand-alone numerical: instead of one question with one answer, you are handed one dataset — a table, a pie chart, a bar or line graph — and asked several questions that all draw on the same numbers. This guide works through how to read each chart type correctly, then covers four numerical patterns (simple and compound interest, ratio and proportion, and permutations/combinations) that are common in the quantitative half of GATE's General Aptitude section but are not themselves chart-reading.
Worked example — a data table with several derived questions
Runs scored by four batsmen across three matches:
| Player | Match 1 | Match 2 | Match 3 | Total |
|---|---|---|---|---|
| A | 45 | 60 | 30 | 135 |
| B | 52 | 48 | 70 | 170 |
| C | 38 | 55 | 42 | 135 |
| D | 60 | 65 | 55 | 180 |
(a) Who has the highest average? Average = total ÷ 3 matches. D: 180 ÷ 3 = 60, the highest of the four (A = 45, B ≈ 56.67, C = 45).
(b) What is the overall average across all twelve innings? Sum of totals = 135 + 170 + 135 + 180 = 620. Average = 620 ÷ 12 = 51.67.
(c) What percentage of D's total came from Match 3? 55 ÷ 180 × 100 = 30.56 %.
Notice all three questions reuse the same table — this is the defining feature of a DI set: read the table once, carefully, before touching any individual question.
Worked example — a pie chart
A company's total expenditure of ₹40,00,000 is shown as a pie chart. The "Rent" sector subtends 54° at the centre; the "Salaries" sector subtends 144°.
Percentage rule for a pie chart: % share = (sector angle ÷ 360°) × 100.
Rent: (54 ÷ 360) × 100 = 15 %. Rent expenditure = 15 % of 40,00,000 =
₹6,00,000.
Salaries: (144 ÷ 360) × 100 = 40 %. Salary expenditure = 40 % of 40,00,000 =
₹16,00,000.
Ratio of salary to rent expenditure: 16,00,000 : 6,00,000 = 16 : 6 = 8 : 3 — always simplify a ratio question fully; leaving it as 16 : 6 is an unfinished answer.
Worked example — a line graph, and a trap that connects to percentage change
A company's revenue (₹ crore) over three years: 2023 = 80, 2024 = 100, 2025 = 115. Find the percentage change year to year, and the overall percentage change from 2023 to 2025.
2023 → 2024: (100 − 80) ÷ 80 × 100 = 25 % increase.
2024 → 2025: (115 − 100) ÷ 100 × 100 = 15 % increase.
2023 → 2025 (overall, computed directly): (115 − 80) ÷ 80 × 100 = 35 ÷ 80 × 100 =
43.75 %.
Notice 43.75 % is not 25 % + 15 % = 40 %. Successive percentage changes never add directly — each one is taken on a different base — so a line-graph question asking for total change across several years must always be computed from the first and last values directly, never by summing the intermediate year-on-year changes.
Simple interest vs compound interest
₹10,000 is invested at 10 % per annum for 2 years. Compare simple and compound interest.
SI = (10000 × 10 × 2) / 100 = ₹2,000 (amount = ₹12,000)
CI = 10000 × (1.10)² − 10000 = 10000 × 1.21 − 10000 = 12,100 − 10,000 =
₹2,100 (amount = ₹12,100)
The gap, ₹100, is not a coincidence — for exactly 2 years, CI − SI = P × (R/100)² =
10000 × 0.01 = ₹100, a shortcut worth keeping for any "difference between CI and SI over 2
years" question, though computing both directly and subtracting is just as reliable a
cross-check.
Ratio and proportion
The ratio of the present ages of A and B is 3 : 4. After 6 years, the ratio becomes 4 : 5.
Find their present ages.
Let the ages be 3x and 4x. After 6 years: (3x + 6) / (4x + 6) = 4/5.
Cross-multiply: 5(3x + 6) = 4(4x + 6) → 15x + 30 = 16x + 24 → x = 6.
Present ages: A = 3(6) = 18, B = 4(6) = 24.
Check: after 6 years, A = 24, B = 30, and 24 : 30 = 4 : 5. ✓
Permutations and combinations, directly
A committee of 3 is to be selected from 5 men and 4 women, with exactly 2 men and 1 woman.
In how many ways can this be done?
Number of ways = C(5,2) × C(4,1)
C(5,2) = 5! / (2! × 3!) = 120 / 12 = 10
C(4,1) = 4
Total = 10 × 4 = 40 ways
The key idea: when a selection has two independent conditions (a fixed number of men AND a
fixed number of women), multiply the separate combination counts rather than adding them.
Reading traps specific to data interpretation
- Skipping the axis labels and units. A bar graph in "₹ lakh" read as "₹ crore" is wrong by a factor of 100 before any arithmetic even starts.
- Answering from memory of a similar-looking chart instead of the specific numbers given — DI options are usually close together precisely to catch this.
- Leaving a ratio unsimplified. 16 : 6 and 8 : 3 are the same ratio, but only one matches the answer option in most cases.
- Adding successive percentage changes. As shown above, they must be multiplied as growth factors, or the total computed directly from first and last values.
- Forgetting compound interest compounds on the growing amount, not on the original principal each year — using SI-style thinking for a CI question is the single most common error in this pattern.
Quick reference
| Pattern | The one thing to get right |
|---|---|
| Table / DI set | Read the whole dataset once before answering any sub-question |
| Pie chart | % = (angle ÷ 360) × 100, then apply to the stated total |
| Line/bar graph | Overall % change from first and last values, never summed from intermediate steps |
| SI vs CI | CI compounds on the growing amount; the two diverge more with each extra year |
| Ratio and proportion | Set up algebraically, cross-multiply, then verify by substitution |
| Permutations/combinations | Independent conditions multiply; do not add combination counts |
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