Quantitative Comparison — Method
1. Core Idea
Quantitative Comparison (QC) gives you two quantities and asks which is bigger. The answer choices are always the same four:
- 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 critical insight: you usually do not need to compute either quantity. You need to determine the relationship. That is often far less work.
2. Must-Know Rules
The decision rule for D. Choose D if and only if you can find two cases that give different answers. If you find one case where A > B and another where A = B, the answer is D.
When D is impossible. If both quantities are pure numbers with no variables, the answer can never be D — the relationship is fixed even if you cannot see it yet.
Legal operations on both quantities (they preserve the relationship, exactly like inequalities):
| Operation | Safe? |
|---|---|
| Add or subtract the same value | Yes |
| Multiply or divide by the same positive value | Yes |
| Multiply or divide by a negative | No — reverses the relationship |
| Multiply or divide by an expression of unknown sign | No |
| Square both sides | Only if both are known non-negative |
The FROZEN test values. When a variable is unrestricted, test:
- Fractions (0.5)
- Repeats (make variables equal)
- One
- Zero
- Extremes (very large, very small)
- Negatives
If two of these disagree, the answer is D. If all agree, the answer is probably A, B or C — but test at least three.
3. Worked Examples
Example 1 — Simplify rather than compute
Quantity A: 37 x 48. Quantity B: 38 x 47.
Do not multiply. Rewrite:
A = 37 x 48. B = (37 + 1)(48 - 1) = 37x48 - 37 + 48 - 1 = 37x48 + 10.
B is greater. Answer B.
(General pattern: for a fixed sum, the product is larger when the two numbers are closer together.)
Example 2 — Testing for D
x^2 > x. Quantity A: x. Quantity B: 1.
The condition x^2 > x holds when x > 1 or x < 0.
- Try x = 2: A = 2, B = 1 -> A greater.
- Try x = -3: A = -3, B = 1 -> B greater.
Two different outcomes, so the answer is D.
Example 3 — Legal operations
Quantity A: 3x + 7. Quantity B: 2x + 12, given x > 5.
Subtract 2x + 7 from both: A becomes x, B becomes 5.
Since x > 5, A is greater. Answer A.
4. GRE Traps
- Assuming variables are positive integers. Unless stated, x can be negative, zero, or a fraction.
- Choosing D when both quantities are pure numbers. Impossible.
- Testing only one value. One test can never prove A, B or C — it can only rule things out.
- Multiplying both sides by a variable. You do not know its sign.
- Squaring to remove a radical when a quantity might be negative.
- Computing the full value when a comparison would do — this is a time trap more than an accuracy trap.
- Assuming a geometric figure is drawn to scale in a QC question. Many are not.
5. Speed Tricks
- Strip away what is common. Subtract identical terms from both sides; the remainder is usually trivial.
- Look for a shortcut before computing. QC questions are designed to be solvable without arithmetic.
- Test values in this order: 0, 1, a fraction, a negative. Fastest route to D.
- If the two quantities look designed to be equal, suspect C — then test one edge case to be sure.
- Keep an eye on the clock. QC questions should average under 90 seconds. If you are computing large numbers, you have missed the intended route.
- Estimate. If A is clearly above 100 and B is clearly below 50, you are done.
6. Self-Check
Q1. Quantity A: 1/3 + 1/4. Quantity B: 1/2. Which is greater?
Q2. Given x is a non-zero real number. Quantity A: x^2. Quantity B: x^3. Which is greater?
Q3. Quantity A: the average of 10, 20, 30. Quantity B: the median of 10, 20, 30.
Answers
A1. 7/12 vs 6/12. A is greater.
A2. x = 2 gives B greater; x = 0.5 gives A greater. D.
A3. Evenly spaced, so mean = median = 20. C.
7. One-Line Summary for the Board
Compare, don't compute. Strip common terms. If two test values disagree, the answer is D — and D is impossible when both quantities are numbers.