In a certain industry, production index x is… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Fractions/Ratios/Decimals

In a certain industry, production index x is directly proportional to the square of efficiency index y, and indirectly proportional to investment index z. If a business in this industry halves its investment index, which of the following is closest to the percent change in the business’s efficiency index required to keep the production index the same?

Answer Choices

Correct answer marked below

100% increase

50% increase

30% increase

30% decrease

Correct

50% decrease

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Explanation

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Official Explanation

Official

We are told that production index x is directly proportional to the square of efficiency index y, and indirectly (inversely) proportional to investment index z.

Thus, we can write:

x = k \frac{y^2}{z}

where k is a constant.

Let initial values be

x_1, y_1, z_1

and new values be

x_2, y_2, z_2

.

We are given that

z_2 = \frac{1}{2} z_1

and we want

x_2 = x_1

.

From the relation:

x_1 = k \frac{y_1^2}{z_1}

and

x_2 = k \frac{y_2^2}{z_2}

.

Since

x_1 = x_2

k \frac{y_1^2}{z_1} = k \frac{y_2^2}{z_2}

…

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What this question tests

What it tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Common trap

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.