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CAT (Common Admission Test) · Data Interpretation & Logical Puzzles

Data Interpretation: Tables

Extracting and computing values from tabular data sets and multi-row tables.

Table DI is arithmetic against a grid: read the headers and units, compute each needed total once, then answer with the exact quantity the stem names — share, percentage change, average or ratio — not the absolute difference that sits next to it.

  • CAT (Common Admission Test)
  • Medium level
  • 6 concepts
  • 17 practice questions

1Read headers and units before any cell

Every table DI set opens with a unit annotation in a header — "in '000 tonnes", "₹ crore", "in lakhs". The cell you see is not the quantity the question uses until that unit has been applied. Misreading thousands as ones, or crores as rupees, is the single most common way a clean calculation lands on the wrong option.

Underline the unit once, convert every cell you will touch into the unit the stem asks for, and only then add or divide. A total of 84 in a column headed "in '000" is 84,000 of the underlying unit — treating 84 as the answer is not a rounding error, it is a scale error.

Figure. Cells 48 and 36 sum to 84 — the scale-trap option. The header unit ('000 tonnes) multiplies that sum to 84,000 tonnes.

How it works

  1. Name the unitRead the column and row headers for the unit annotation before looking at any number.
  2. Match the stemIf the stem asks for tonnes and the table is in '000 tonnes, multiply every used cell by 1,000 first.
  3. Then computeOnly after the scale is fixed do you form totals, shares or ratios.

A miniature of the trap: the numbers are small; the unit is not.

The header that must be read
RegionProduction (in '000 tonnes)
East48
West36

Thousands are not ones

A table of regional production is headed "Production (in '000 tonnes)". Region East shows 48 and Region West shows 36. What is the combined production in tonnes?

  • East cell as written48
  • West cell as written36
  • Sum of cells = 48 + 3684
  • Apply the header unit: 84 × 1,00084,000 tonnes

Pro tip. If an option equals the sum of the cells with no unit applied, it is the scale-trap answer — written for candidates who never read the header.

A column is headed "Sales (₹ lakh)". One cell reads 25. The stem asks for sales in rupees. The value to use is
  1. 25
  2. 2,500
  3. 2,500,000

One lakh is 100,000, so 25 lakh = 25 × 100,000 = 2,500,000 rupees. 25 is the cell as printed with the unit ignored; 2,500 treats a lakh as 100.

2Compute each needed total once

Most table sets ask three or four questions against the same column or row. The column total (or the row total) is the denominator of every share and the base of every "of the total" stem. Compute that total once, write it above the set, and reuse it — recomputing 40 + 30 + 20 + 10 on every sub-question is how time and arithmetic errors enter.

When a later question asks for a subtotal — "the bottom two products" — form that subtotal from the cells and divide by the same written total. Do not re-add the whole column to get a second copy of a number you already have.

Figure. One bar, four segments: the whole length is the total you park once.

How it works

  1. Add the columnSum every cell in the column (or row) the set will keep returning to.
  2. Park the totalWrite the total once beside the table; every share question divides by that same number.
  3. Form subtotals from cellsA "bottom two" or "A and B together" stem adds only those cells, then divides by the parked total.

One total, two share questions

In 2023 four products earned ₹40, ₹30, ₹20 and ₹10 crore. What percentage of total revenue came from the top product, and what percentage came from the bottom two products combined?

  • Column total = 40 + 30 + 20 + 10100 crore
  • Top share = 40 / 100 × 10040%
  • Bottom-two subtotal = 20 + 1030 crore
  • Bottom-two share = 30 / 100 × 10030%

Pro tip. Both answers used the same 100. If a later question in the set asks for the share of products 2 and 3, it is (30 + 20) / 100 = 50% — still the same denominator.

Five regions report sales 12, 18, 15, 10 and 25 (same units). The share of the largest region is
  1. 25%
  2. 31.25%
  3. 20%

Total = 12 + 18 + 15 + 10 + 25 = 80; largest share = 25/80 × 100 = 31.25%. 25% treats the cell as already a percentage; 20% is 1/5 of five regions with equal weight, which this column is not.

3Percentage change uses the earlier column as base

Year-on-year growth from a table is (new − old) / old × 100, and old is the earlier year — never the later one, never the larger of the two. From 2022 sales of 100 to 2023 sales of 130 the growth is 30%, because 100 sits in the denominator.

Overall growth across several years compares the first value to the last value of the span. Adding the yearly percentage changes does not recover that overall figure: 25% then 30% sums to 55%, but 80 → 130 is a 62.5% rise. When options are widely spaced, rounding the cells before dividing is enough; when they are close, keep the exact values.

Figure. 2022→2023 growth divides the rise by 100, not by 130.

How it works

  1. Name old and newThe earlier column is old; the later column is new. Underline both before subtracting.
  2. Divide by oldDifference over the earlier value, then × 100.
  3. For a multi-year spanCompare the first and last values of the span — do not sum the year-by-year percentages.
  4. Round only when options allowIf options are far apart, round cells to convenient figures; if they are close, keep the exact values.

Year-on-year and overall are different questions

A company's sales (₹ crore) were 2021: 80, 2022: 100, 2023: 130. What was the percentage growth from 2022 to 2023, and what was the overall growth from 2021 to 2023?

  • 2022 → 2023: (130 − 100) / 100 × 10030%
  • 2021 → 2023: (130 − 80) / 80 × 10062.5%
  • Yearly pieces: (100 − 80) / 80 × 10025%
  • 25% + 30% (sum of yearly changes)55% ≠ 62.5%

Pro tip. Always use the earlier year as the base for year-on-year growth. For a span, first-to-last is the overall figure; the sum of yearly percentages is a different number and a common wrong option.

Sales rise from 72 to 90. The percentage growth is
  1. 18%
  2. 20%
  3. 25%

(90 − 72) / 72 × 100 = 18/72 × 100 = 25%. 18% is the raw difference read as a percentage of 100; 20% divides 18 by 90 — the later year wrongly used as the base.

4A category's share is the cell over the column total

Share of a category is (category value) / (column total) × 100. Once the column total is parked from the previous idea, every share question is one division. The trap is answering with the cell itself when the stem asked for a percentage of the total, or answering with a percentage of a different column's total.

When the stem asks for the share of two categories combined, add those cells first and then divide by the same column total — do not average their separate shares unless the stem asks for that.

Figure. The top segment is 40 of the 100 — that length is the share.

How it works

  1. Park the totalUse the column total already computed for the set.
  2. Take the category cellOr the sum of the cells the stem names.
  3. Divide and × 100Category over total, as a percentage.

Top product as a share of revenue

In 2023, four products earned ₹40, ₹30, ₹20 and ₹10 crore respectively. What percentage of total revenue came from the top product?

  • Total revenue = 40 + 30 + 20 + 10100 crore
  • Top product40 crore
  • Share = 40 / 100 × 10040%
  • Match stem: percentage of total, not the cell40%

Pro tip. Compute the column total once, then every share question is a quick division by that total.

Three segments are 25, 35 and 40. The middle segment's share of the total is
  1. 35%
  2. 30%
  3. 46.7%

Total = 100; middle share = 35/100 × 100 = 35%. 30% averages the three shares as if they were equal weights on something else; 46.7% is 35/75 — the middle as a share of the other two, not of the whole.

5Row averages and cell ratios

The average of a row is the sum of its entries divided by how many entries you summed. Empty or "n.a." cells are not zeroes unless the stem says so — dropping a missing year and dividing by the years that exist is the usual move.

A ratio of two cells is cell₁ : cell₂, simplified before any comparison. Reducing 84 : 56 to 3 : 2 is what lets you match options quickly; leaving the unsimplified form invites multiplying both sides by the wrong factor when the next question asks for a related quantity.

Figure. The dashed rule sits at the row average 103.33 — above Y1 and Y2, below Y3.

How it works

  1. Sum the entries you meanInclude every cell the stem counts; exclude blanks the stem does not treat as zero.
  2. Divide by the countAverage = sum / number of included entries.
  3. For a ratio, simplify firstCancel the greatest common factor before comparing with options or chaining a further step.
Two derived reads from the same grid
QuantityRule
Row averagesum of included entries ÷ count of those entries
Cell ratiocell₁ : cell₂, then cancel the common factor
Missing cellomit from the count unless the stem treats it as zero

Average across three years, then a simplified ratio

Sales (₹ crore) were 80, 100 and 130 across three years. What is the average annual sales? Separately, two cells in another column are 84 and 56; simplify their ratio.

  • Sum of row = 80 + 100 + 130310
  • Average = 310 / 3103.33 crore (repeating)
  • Ratio cells 84 : 56; gcd = 28divide both by 28
  • Simplified ratio3 : 2

Pro tip. Write the average with enough decimals to separate close options — 103.3 and 103⅓ are the same number, and an option of 103 is a truncated trap.

Four quarterly figures are 45, 55, 50 and 70. Their average is
  1. 55
  2. 50
  3. 220

(45 + 55 + 50 + 70) / 4 = 220 / 4 = 55. 50 is the median-looking middle value, not the mean; 220 is the sum with the division forgotten.

6Highest growth is a ratio, not a raw difference

When the stem asks which category grew the most in percentage terms, compare (new − old) / old for each row — not the raw differences new − old. A rise of 20 on a base of 100 is 20%; a rise of 15 on a base of 40 is 37.5%. The larger absolute jump is not the larger percentage growth.

The mirror trap is answering a "by how many units" stem with a percentage. Match the calculation to the exact quantity asked: absolute when the stem says absolute, percentage or ratio when it says percentage or ratio.

Figure. B's rise looks taller; A's rise is a larger fraction of its own base.

How it works

  1. Read the quantity named"Highest percentage growth" and "largest increase" are different questions.
  2. For percentage growthForm (new − old) / old for every candidate row; rank those ratios.
  3. For absolute increaseRank the raw differences only — and do not convert them to percentages afterwards.

Larger jump, smaller growth rate

Product A rises from 40 to 55 units; Product B rises from 100 to 120 units. Which product has the higher percentage growth?

  • A absolute change = 55 − 4015
  • A percentage growth = 15 / 40 × 10037.5%
  • B absolute change = 120 − 10020
  • B percentage growth = 20 / 100 × 10020%

Pro tip. B's absolute increase is larger (20 > 15), but A's percentage growth is larger (37.5% > 20%). For "highest percentage growth", compare the ratios of change to base, not the raw differences.

Region X goes from 200 to 240; Region Y goes from 50 to 70. Which has the higher percentage growth?
  1. X, because it rose by 40
  2. Y, at 40%
  3. Both equal at 20%

X: 40/200 = 20%. Y: 20/50 = 40%. Y wins on percentage growth even though X's absolute rise is larger. "Both equal at 20%" copies X's rate onto Y; the first option ranks by absolute change.

Notes

  • Table DI - Read Headers First: Identify what each row and column represents and the units before calculating; misreading a header (units in thousands vs lakhs) is the top cause of errors.
  • Row/Column Totals: Many questions hinge on totals or subtotals; compute the relevant total once and reuse it for percentage and ratio parts rather than recomputing.
  • Percentage Change and Share: Growth from one column to the next uses (new-old)/old; a category's share of the total uses that category divided by the column total.
  • Approximation for Speed: Round values to convenient figures when the options are far apart; exact computation is only needed when options are close.
  • Common trap: Comparing absolute values when the question asks for percentage/ratio (or vice versa) - always match your calculation to the exact quantity asked.

Formulas

  • Percentage change = \dfrac{\text{new}-\text{old}}{\text{old}}\times 100.
  • Share of a category = \dfrac{\text{category value}}{\text{column total}}\times 100.
  • Average of a row = \dfrac{\text{sum of row entries}}{\text{number of entries}}.
  • Ratio of two cells = \dfrac{\text{cell}_1}{\text{cell}_2} (simplify before comparing).
  • Overall growth over years: compare first and last values, not the sum of yearly changes.

Exam traps & shortcuts

  • Underline units and headers before touching any numbers to avoid scale errors.
  • Compute a needed total once and reuse it across all sub-questions of the set.
  • Round aggressively when answer options are widely spaced to save time.
  • For 'highest percentage growth', compare ratios of change to base, not raw differences.

Reference tables

The five reads a table stem usually wants.

Table DI formula sheet
QuantityFormula
Percentage change\dfrac{\mathrm{new}-\mathrm{old}}{\mathrm{old}}\times 100
Category share\dfrac{\mathrm{category\ value}}{\mathrm{column\ total}}\times 100
Row average\dfrac{\mathrm{sum\ of\ included\ entries}}{\mathrm{count}}
Cell ratio\mathrm{cell}_1:\mathrm{cell}_2 (simplify first)
Overall growth over yearsfirst value to last value of the span — not the sum of yearly % changes

Same moves on the grid; different rankings.

Absolute change versus percentage growth
Stem asks forCompareDo not
Largest increase (units)raw new − oldconvert to % and re-rank
Highest percentage growth(new − old) / oldrank by the raw difference
Share of totalcell / column totalreport the cell as if it were already a %

Recap

Read only this the night before.

Headers
Unit annotation first. A cell of 48 under "in '000" is 48,000 of the underlying unit.
Totals
Add the column once, park it, reuse it for every share in the set.
Change
Growth divides by the earlier year. Overall span is first-to-last, not the sum of yearly percentages (25% + 30% ≠ 62.5%).
Share
Category over column total. The cell alone is not a percentage of anything.
Rank
Highest percentage growth ranks (new−old)/old. A bigger absolute jump can still be a smaller rate.
Speed
Round when options are far apart; keep exact values when they are close.

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