By the end of this chapter you'll be able to…

  • 1Apply the fixed quantity-comparison option key
  • 2Estimate or cancel instead of fully computing both quantities
  • 3Compare fractions/percentages by cross-multiplication and like bases
  • 4Recognise straddling quadratic/range values as 'cannot be established'
  • 5Use ≥/≤ for possible equality and = only for always-equal
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Why this chapter matters in IBPS PO
Quantity comparison packages ordinary arithmetic — percentage, ratio, ages, quadratics — into a fixed 'compare Quantity I and II' key, worth 0–5 Mains marks. The efficiency comes from realising you usually don't need both exact values: estimate, cancel a common factor, or compare like-for-like to decide the relation faster. It also reuses the quadratic 'cannot be established' logic, so mastering that chapter pays off here too.

Quantity Comparison (I vs II) — IBPS PO

Quantity comparison gives you two quantities — Quantity I and Quantity II — each defined by a small problem, and asks for the relation between them. It's a newer Mains format that packages ordinary arithmetic (percentage, ratio, ages, simple equations) into a fixed comparison key. The efficient approach is rarely to compute both quantities fully — often you can estimate, cancel a common factor, or reason about magnitude to decide the relation faster. At 0–5 Mains marks, treating it as "compare, don't fully solve" is the time-saver.


1. What IBPS actually asks

Two quantities and the fixed key:

  1. Quantity I > Quantity II
  2. Quantity I < Quantity II
  3. Quantity I ≥ Quantity II
  4. Quantity I ≤ Quantity II
  5. Quantity I = Quantity II or relation cannot be established

Each quantity is a mini arithmetic problem — a percentage, an average, roots of a quadratic, a probability, a speed. Read the exact option order printed with the set.


2. The method: compute (or estimate) each, then compare

  1. Solve Quantity I to a value (or a range/roots).
  2. Solve Quantity II likewise.
  3. Compare and map to the key — using ≥/≤ if equality is possible, or "cannot be established" if the values interleave (as with quadratic roots).

But before grinding both out fully, look for a shortcut.


3. Estimate and cancel — the speed move

You often don't need exact values:

  • Magnitude estimate: if Quantity I is clearly "around 200" and Quantity II is "around 350", you're done — no exact figures needed.
  • Cancel a common structure: if both are k × something, compare the something.
  • Compare like-for-like: two percentages of the same base, or two fractions by cross-multiplication (a/b vs c/dad vs bc).

Ask "do I actually need the exact values, or just which is bigger?" Usually the latter — and estimation gets you there in half the time.


4. The quadratic / range case (cannot be established)

When a quantity comes from a quadratic (two roots) or a range, the comparison can be ambiguous:

  • Quantity I = roots {2, 3}, Quantity II = 2.5 ⇒ I could be 2 (< II) or 3 (> II) ⇒ relation cannot be established.
  • Only when every value of one quantity is consistently ≥ / ≤ the other is a definite relation possible (this mirrors the Quadratic Equations chapter).

Don't force a > or < when the quantity is a set of values that straddle the other.


5. The equality subtlety

  • Use ≥ / ≤ when the quantities can be equal in some case but one is otherwise larger.
  • Use = only when they are always exactly equal.
  • If a clean single comparison isn't possible and it's not an either–case, it's "cannot be established".

Solved examples

Question 1 of 4

Q1. Quantity I: 25% of 240. Quantity II: ⅓ of 180.

Show explanation

Solution. I = 60; II = 60 ⇒ Quantity I = Quantity II (option 5).

Question 2 of 4

Q2. Quantity I: the average of 12, 18, 30. Quantity II: 25% of 80.

Show explanation

Solution. I = 60/3 = 20; II = 20 ⇒ I = II.

Question 3 of 4

Q3 (estimate). Quantity I: 18% of 449. Quantity II: 21% of 351.

Show explanation

Solution. I ≈ 0.18×450 ≈ 81; II ≈ 0.21×350 ≈ 73.5 ⇒ Quantity I > Quantity II. (No exact computation needed.)

Question 4 of 4

Q4 (quadratic). Quantity I: roots of x² − 5x + 6 = 0. Quantity II: 2.5.

Show explanation

Solution. Roots x = 2, 3. Since 2 < 2.5 < 3, the roots straddle II ⇒ relation cannot be established.


7. The protocol

  1. Read the exact option key.
  2. Before computing, look for an estimate or cancellation — do you need exact values or just the bigger one?
  3. Solve each quantity (or estimate) to a value/range.
  4. Compare and map to the key; use ≥/≤ for possible equality.
  5. If one quantity is a set of values that straddles the other (quadratic/range), the answer is cannot be established.

Key formulas & results

Everything to memorise for the exam hall, in one card. Screenshot this for revision.

Option key
I>II / I<II / I≥II / I≤II / I=II or cannot be established
Read the exact printed order.
Estimate first
Decide if you need exact values or just which is larger
Magnitude estimate often settles it.
Fraction compare
a/b vs c/d ⇒ compare ad and bc
Cross-multiply; no decimals.
Straddle rule
If one quantity's values straddle the other ⇒ cannot be established
Common with quadratic roots.
Equality
≥/≤ if equal in some case; = only if always equal
Otherwise cannot be established.
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Traps IBPS PO sets — and how to dodge them

These are the exact option-traps and misreads that cost marks under negative marking.

WATCH OUT
Fully computing both quantities when an estimate suffices
Ask whether you need the exact values or just the larger. 18% of 449 vs 21% of 351 is decided by rounding to 81 vs 73.5 — no exact arithmetic needed.
WATCH OUT
Forcing a > or < when a quadratic quantity straddles the other
If Quantity I has roots 2 and 3 and Quantity II is 2.5, the values straddle ⇒ relation cannot be established. Don't pick a strict relation.
WATCH OUT
Choosing > when equality is possible
If the quantities can be equal in some case but one is otherwise larger, use ≥ (or ≤), not the strict relation.
WATCH OUT
Dividing twice to compare two fractions
Cross-multiply: a/b vs c/d ⇒ compare ad and bc. One step, no decimals.
WATCH OUT
Ignoring the printed option order
The mapping of options to relations is printed with each set and can vary. Read it before marking.

Exam-pattern practice

PYQ-style questions with full solutions. Work through them as a readiness check — mark yourself honestly and get your gap report at the end.

Readiness check

Are you exam-ready for Quantity Comparison (I vs II)?

6 problems from this chapter. Try each one, reveal the worked solution, mark yourself honestly — get your gap report at the end.

6 questions~4 min worth ~5 marks in IBPS PO exams

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

  • Compare Quantity I and II — arithmetic in a fixed key.
  • Read the exact printed option order.
  • Estimate or cancel before fully computing both.
  • Compare fractions by cross-multiplication; percentages on the same base.
  • Quadratic/range values that straddle ⇒ cannot be established.
  • ≥/≤ for possible equality; = only if always equal.
  • Ask: do I need exact values or just the larger one?

IBPS PO question blueprint

How this topic is asked, tier by tier — so you can prep to the pattern.

Typical weightage: Mains: 0–5 marks (of 60)

Question styleMarks eachTypical countWhat it tests
Arithmetic comparison1 each2–4Percentage, average, ratio, ages as two quantities
Quadratic/range comparison1 each0–2Straddling values and 'cannot be established'
Prep strategy
  • Day 1: the option key and the estimate-first habit.
  • Day 2: fraction/percentage comparison by cross-multiplication.
  • Day 3: quadratic-root straddle cases under a 40-second cap.

Exam-hall strategy

Battle-tested tips from mentors and toppers for this topic under the sectional clock.

  1. Read the option key first.
  2. Estimate or cancel before computing both quantities.
  3. Cross-multiply to compare fractions/percentages.
  4. Use ≥/≤ for possible equality; = only if always equal.
  5. Call it 'cannot be established' when values straddle.

Beyond the exam

Where this skill shows up in the job you're competing for — and in life.

Quick comparisons

Deciding which of two rates, returns or offers is better without exact computation is everyday estimation.

Sanity checks

The estimate-first habit catches errors by confirming the rough magnitude before trusting a precise figure.

Where else this topic is tested

Prepare once, score in every exam that asks it.

SBI PO / RBI Grade BHigh — quantity comparison is a standard Mains set
IBPS Clerk / RRB POMedium — simpler two-quantity comparisons
NABARD / SIDBI Grade AMedium — arithmetic comparison

Questions aspirants ask

Pulled from the Q&A community and mentor sessions.

Usually a Mains set of up to 5. Each quantity is a small arithmetic problem, so the topic is really percentage/ratio/ages/quadratics in a comparison wrapper — quick marks if you estimate rather than fully solve.

Rarely. Often a magnitude estimate, a cancellation, or comparing like-for-like (cross-multiplying fractions) tells you which is larger without exact values. Ask whether you need the numbers or just the relation.

When one quantity is a set of values (e.g. quadratic roots 2 and 3) that straddle the other (2.5). Since the quantity could be smaller or larger depending on the root, no definite relation holds — the same logic as the quadratic-comparison chapter.

Use ≥ (or ≤) when the quantities can be equal in some case but one is otherwise larger; use = only when they are always exactly equal; use strict > / < when one is definitely larger in every case.
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