For three positive integers m, n and p, the r… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

percent

For three positive integers m, n and p, the ratio of n to p is half the ratio of m to n. Which of the following statements is false?

Correct answer marked below

p is 16% less than m

Correct

p is 2% less than m

m is 28% less than p

m is 62% more than p

m is 28% more than p

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Explanation

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Official Explanation

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According to the question,

\frac{n}{p} = \frac{1}{2} \cdot \frac{m}{n}

which simplifies to

2n^2 = mp

......(1)

For option 1: Let m = 100 and p = 84

Then

n = \sqrt{\frac{mp}{2}} = \sqrt{\frac{100 \times 84}{2}} = \sqrt{4200}

, which is not an integer.

For option 2: Let m = 100 and p = 98

Then

n = \sqrt{\frac{100 \times 98}{2}} = \sqrt{4900} = 70

, which is an integer.

For option 3: Let p = 100 and m = 72

Then

n = \sqrt{\frac{72 \times 100}{2}} = \sqrt{3600} = 60

, which is an integer.…

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What this question tests

Your ability to apply GMAT math concepts to solve a multi-step problem quickly and accurately. At the 705-805 level, accuracy and speed both matter.

Overcomplicating the setup — most GMAT problems reward a direct, organized approach over brute calculation.