🧩 DILR

Quantitative Reasoning

Data-driven sets needing arithmetic on tables, ratios, and growth.

of DILR

Why This Topic Matters

Total PYQs📊

of 1002 · 2021–2025

Years featured📅

2/5

of recent CAT years

% of DILR📈

~3%

of section questions

Est. hours⏱️

~6h

to master

2021

2022

2023

~2/22

2024

~2/22

2025

Quantitative Reasoning Sets

The DILR sets where the logic is arithmetic: a defined quantity (an index, a weighted average, an occupancy factor, a vote share), a part-filled table, and questions that make you run the definition forwards and backwards. No exotic math — the challenge is bookkeeping under time pressure.

The tested form	Year	What it looked like
Weighted-average / factor set	2025	An "occupancy factor" defined per train segment; compute and invert it
Geometry-flavoured DI	2024	Quantities tied to areas/lengths read off a figure
Scenario-payoff set	2024	An election where vote shares followed stated formulas, case by case

🎯PYQ Evidence

The occupancy-factor template. : The set defines a quantity (occupancy per segment), gives partial data, and asks things like "what was the factor for segment D–E?" — pure definition-application — and then harder ones that require inverting the definition (given the factor, recover the missing count). The CAT 2024 worked the same way: the rules were formulas ("percentage voting = 20 × sum of levels"), and every question was a disciplined case-evaluation of those formulas. When a set defines a quantity, write the formula once at the top of your rough work — every question reuses it.

The method

Extract the definition. Write the defining formula in symbols before reading question 1. E.g. $\text{factor} = \dfrac{\text{actual}}{\text{capacity}}$ , $\text{index} = \sum w_i x_i$ .
Map the data to the symbols. Mark which cells of the table are given and which are unknown.
Use totals as equations. Row sums, column sums, and "overall average" statements are linear equations — often enough to pin every blank.
Forwards, then backwards. Early questions apply the definition; later ones invert it ("what must X have been so that…"). Inverting is the same formula, solved for a different symbol.
Keep units honest. Thousands vs units, percentages vs counts — every recent set mixes them deliberately.

A worked mini-set

✏️Worked Example

A metro line has segments P–Q, Q–R, R–S with capacities 200, 250, 200. The occupancy factor of a segment = passengers carried ÷ capacity. Given: factor(P–Q) = 0.70, passengers(Q–R) = 200, factor(R–S) = 0.55.

Apply forwards: passengers(P–Q) $= 0.70 × 200 = 140$ ; factor(Q–R) $= 200/250 = 0.80$ ; passengers(R–S) $= 0.55 × 200 = 110$ .
Invert: "What would R–S's factor be if 30 more passengers boarded?" → $(110+30)/200 = 0.70$ .
Totals as equations: "Across all three segments the line carried…" → $140 + 200 + 110 = 450$ — one addition, three questions' worth of value.

🎯PYQ Evidence

Quant-flavoured sets reward turning the rules into an expression and fixing the underlying number-set first. : treat it as algebra, not casework — turnout is 20 x (sum of levels)% split by level, and each attack moves a fixed fraction (Ramya's attack hands 20% of her would-be votes to Amiya), so maximising Amiya means picking both-vigorous (80% base) with Ramya attacking, giving 40 + 8 = 48%. : the nine PMs are the fixed set {10,20,...,90}, and the single "one NUR exceeds one city, both in Humbleset" rule forces NURs = {10, 20, 40}; from there each PI is just 0.5 x NUR + 0.25 x city + 0.25 x city. Lock the value-set and the formula, and the arithmetic answers itself.

Common traps

⚠️CAT Trap

Dividing by the wrong base. Weighted-average sets live and die on the denominator: occupancy uses capacity of that segment, vote share uses votes cast, not electorate, an index uses its own weights. Before computing, say the denominator out loud. CAT writes the definition precisely — the trap options are what you get with the plausible but wrong base.

Mixing units — thousands in one table, raw counts in another.
Recomputing instead of reusing — the definition and the totals you've already derived answer most later questions in one step.

Checklist

Write the defining formula in symbols first
Mark given vs unknown cells; turn totals into equations
Say the denominator before every division
Reuse earlier results — later questions build on them
Watch units (thousands, %, counts) on every figure

Sample Questions

15 practice questions

Context

PQR 2022 Exam aspirants from 5 states.

State	Applicants	Appeared	Boys:Girls
Haryana	48000	32000	3:5
Punjab	45000	—	4:3
Maharashtra	55000	—	5:4
Uttarakhand	32000	12000	—
Himachal	24000	—	2:3

From Punjab, Maharashtra, and Haryana together 30000 boys appeared. Boys from Punjab = girls from Maharashtra.

Hard

Approximately what % of applicants appeared from Maharashtra?

Context

Classes 7-10 student activity data (each student does exactly one of dancing, painting or singing).

Class	Total students	Dancing %	Painting %
7	120	25	40
8	160	20	50
9	90	40	10
10	150	50	40

Medium

Standard 9 dancing students are what % of all-class singing students?

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CAT PYQ Spotlight

Actual CAT questions on this topic

Context

Two students, Amiya and Ramya are the only candidates in an election for the position of class representative. Each campaign is said to have a level of 1 if it is a staid campaign and a level of 2 if it is a vigorous campaign. Campaigns can be of two types: focus on issues, or attack the other candidate.

If both run campaigns focusing on issues: percentage voting = 20 × (sum of levels)%; votes proportional to levels.

If at least one runs an attacking campaign:

• If Amiya attacks and Ramya focuses on issues: 10% of Amiya's would-be votes go to Ramya, another 10% don't vote.

• If Ramya attacks and Amiya focuses on issues: 20% of Ramya's would-be votes go to Amiya, another 5% don't vote.

• If both attack: 10% of each candidate's would-be votes don't vote at all.

CAT 2024 · Slot 1

Medium

If both of them run staid campaigns attacking the other, then what percentage of students will vote in the election?

Context

If both run campaigns focusing on issues: percentage voting = 20 × (sum of levels)%; votes proportional to levels.

If at least one runs an attacking campaign:

• If Amiya attacks and Ramya focuses on issues: 10% of Amiya's would-be votes go to Ramya, another 10% don't vote.

• If Ramya attacks and Amiya focuses on issues: 20% of Ramya's would-be votes go to Amiya, another 5% don't vote.

• If both attack: 10% of each candidate's would-be votes don't vote at all.

CAT 2024 · Slot 1

Hard

What is the minimum percentage of students who will vote in the election?

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