Quantitative Comparison Strategy • Topic 1 of 4

The Four Answer Choices

Every Quantitative Comparison question offers the identical four choices in the identical order, so learn them once: (A) Quantity A is greater; (B) Quantity B is greater; (C) the two quantities are equal; (D) the relationship cannot be determined from the information given. The single most useful consequence of this fixed menu is a rule about choice D: if both quantities are specific numbers, the answer can never be D. Two fixed numbers always have a definite relationship — one is bigger, or they are equal — so D is only ever correct when the quantities contain variables that can take more than one relationship. That instantly collapses your options: on a purely numeric QC, you are choosing among A, B and C only. Conversely, the moment a variable appears with no full restriction on its value, D leaps onto your radar. Anchoring to these choices before you compute keeps you comparing rather than needlessly solving.

✅ Solved examples

1. Quantity A: 3² + 4². Quantity B: (3 + 4)². Which choice is correct?
Quantity A = 9 + 16 = 25. Quantity B = 7² = 49. Both are fixed numbers, so D is impossible. 25 < 49, so Choice B (Quantity B is greater).
2. Quantity A: 25% of 80. Quantity B: 80% of 25. Which choice?
A = 0.25 × 80 = 20. B = 0.80 × 25 = 20. Both fixed and equal, so Choice C. (This uses x% of y = y% of x.)
3. x is a real number. Quantity A: x². Quantity B: x. Which choice?
Try x = 2: A = 4 > 2 = B. Try x = 1/2: A = 1/4 < 1/2 = B. The relationship changes with x, and x is unrestricted, so Choice D — cannot be determined.
4. Quantity A: the number of prime numbers between 1 and 10. Quantity B: 4. Which choice?
Primes between 1 and 10 are 2, 3, 5, 7 — that is 4 of them. Both quantities are fixed numbers and equal, so Choice C.

✏️ Practice — try these, take hints as needed

1. Quantity A: 2³. Quantity B: 3². Which choice?
Compute both — they are fixed numbers, so D is out.
8 versus 9.
Which is larger?
B (9 > 8)
2. Quantity A: 1/2 + 1/3. Quantity B: 5/6. Which choice?
Common denominator for A.
3/6 + 2/6 = 5/6.
Compare to B.
C (both equal 5/6)
3. n is any integer. Quantity A: n. Quantity B: n². Can this be pinned down?
Test n = 3, then n = 0, then n = 1.
The order changes across these.
Unrestricted variable.
D
4. Quantity A: 0.2 × 0.2. Quantity B: 0.2. Which choice?
Both are fixed, so not D.
0.04 versus 0.2.
Multiplying by a number below 1 shrinks it.
B (0.2 > 0.04)
5. Quantity A: the average of 10, 20 and 30. Quantity B: 20. Which choice?
Both fixed, so D is impossible.
(10 + 20 + 30)/3.
Compare the result to 20.
C (average is 20)

📝 Topic test — 8 questions

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