How to answer quantitative comparison questions
Compare, don't compute
Quantity A against Quantity B, with the same four options every time. The skill is settling the relation with the least arithmetic that actually settles it.
Updated
Two quantities side by side, and always the same four options: A is greater, B is greater, they are equal, or the comparison cannot be determined. The fixed format is the point — it rewards seeing the structural relation between the two sides over grinding both to a number. Full evaluation is the fallback, not the method.
Strip what is shared
When both sides are built from the same pieces, cancel the shared pieces and compare what remains. 17 × 23 against 17 × 24 needs no multiplication. Only compute when the structure refuses to resolve — and then compute the CHEAPER side first; it often bounds the other.
Fractions and percentages travel with their base
A share means nothing without its base: a smaller percentage of a bigger base often wins. Never compare the fractions or the percentages alone — take a tenth of each base, scale up, and compare actual amounts. Roots and powers deserve the same respect: read √m as the whole number that squares to m, and finish the power — the two sides are built to land close.
'Cannot be determined' has one honest meaning
It is correct only when the relation genuinely FLIPS across the allowed values — never because the item looks hard. When a quantity contains n with a stated whole-number range, test the smallest and largest allowed n: if the two ends disagree, the answer is 'cannot be determined'. If they agree, find where the two sides would be EQUAL — a crossing strictly inside the range is the flip; a crossing outside it means the ends have settled the matter. Constant items always resolve to one of the other three options.
The strategy
- Don't re-read the options — they are the same four every time.
- Simplify structurally before any arithmetic.
- Attach every share to its base.
- For n-items: test both ends of the range; if they disagree, it cannot be determined.
- Choose 'equal' only on exact equality, never on 'looks about equal'.
Common traps
- Grinding both sides to a number when two shared factors cancel.
- Comparing percentages without their bases.
- 'Cannot be determined' as a reflex on hard-looking items — it needs a demonstrated flip.
- Calling near-misses equal — these items are engineered to land close.
Speed · ~50s/item: Roughly 30–75 seconds. A structural read settles most items in one pass; the clock punishes only the habit of evaluating everything.
Try it yourself: 4 practice questions
Pick an answer, then reveal it. Nothing is recorded, there is no clock, and none of these questions is ever used in a test.
n is a whole number with 3 < n < 10. Quantity A: 25. Quantity B: 3n.
Reveal the answer
The answer is A — Cannot be determined.
Show why — the worked reasoning
n is a whole number with 6 < n < 17. Quantity A: 3n. Quantity B: 43.
Reveal the answer
The answer is C — Cannot be determined.
Show why — the worked reasoning
Rectangle P measures 6 cm by 19 cm. Triangle Q has sides of 6 cm, 14 cm and 15 cm. Quantity A is the perimeter of P in cm; Quantity B is the perimeter of Q in cm.
Reveal the answer
The answer is B — Quantity A is greater.
Show why — the worked reasoning
Triangle P has a base of 20 cm and a height of 6 cm. Rectangle Q measures 5 cm by 12 cm. Quantity A is the area of P in cm²; Quantity B is the area of Q in cm².
Reveal the answer
The answer is B — They are equal.
Show why — the worked reasoning
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Questions people ask
Will quantitative comparison questions be on the free test?
Maybe. The free test gives numerical reasoning 5 of its 20 questions, spread across 13 different question types, so any one test may or may not include this kind.