1 · The comparison question
Part of the Middle Level Quantitative Reasoning section shows two quantities, one in Column A and one in Column B. Sometimes there is information above them. The four choices are always the same:
(A) The quantity in Column A is greater. (B) The quantity in Column B is greater. (C) The two quantities are equal. (D) The relationship cannot be determined from the information given.
2 · Plain numbers: never D
If both columns are plain numbers with no letters, one of them must be bigger or they must be equal. The answer can never be D.
Column A: 2⁵. Column B: 5². 2⁵ = 32 and 5² = 25, so the answer is A.
3 · Compare without finishing the work
You often do not need the exact values. Column A: 3/7 of 84. Column B: 84 ÷ 2. You know 3/7 is less than 1/2, so Column A is less than half of 84: the answer is B, with no multiplying.
Do the same thing to both columns to simplify. Adding, subtracting, or multiplying both by a positive number does not change which is bigger.
4 · Letters: try different kinds of numbers
When a column has a variable, test numbers from each kind the information allows: a positive whole number, 0, a negative number, and a fraction between 0 and 1.
Column A: x². Column B: x. If x = 3, A is bigger. If x = 1/2, B is bigger. Two different results mean the answer is D.
5 · Read the information carefully
"x > 1" rules out fractions, 0, and negatives, so x² is always greater than x: the answer becomes A. One small condition can change the answer.
"a + b = 12" alone says nothing about which is bigger. "a + b = 12 and a > b" means a is more than 6.
6 · Common comparison facts
30% of 70 equals 70% of 30. −4² (that is −16) is less than (−4)² (that is 16). A 20% rise then a 20% drop ends below where it started.
Doubling the side of a square multiplies its area by 4, not 2.
7 · Consecutive integers
Five consecutive integers that add to 140 have a mean of 140 ÷ 5 = 28, and the mean is the middle number: 26, 27, 28, 29, 30.
Consecutive odd or even numbers go up by 2.
8 · Ages and averages
Age problems: write each age in t years. Mom is 38 and Jo is 10. In t years, 38 + t = 2(10 + t), so t = 18. Check: 56 and 28.
Averages: use totals. Three tests averaging 80 total 240; to average 84 on four tests the total must be 336, so the fourth score is 96.
9 · Rounding up and cycles
230 people, 50 per bus: 230 ÷ 50 = 4 R30, but the 30 people still need a bus, so 5 buses. Read whether the question wants a full count or what is left over.
Days repeat every 7. 100 days after a Monday: 100 = 14 × 7 + 2, so it is 2 days after Monday, a Wednesday.
10 · Pacing
Comparison questions are usually quicker than word problems. If one is taking too long, try a couple of numbers, make your best choice, and move on; there is no penalty for a wrong answer.
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