Before the regime change, the National Museum… | GMAT Sprint

Free Practice Question

PS · Problem Solving

705-805

Fractions/Ratios/Decimals

Before the regime change, the National Museum regularly displayed only one third of the artifacts in its collection; the other two thirds were kept in storage. The National Museum’s curator estimates that one seventh to one fifth of the artifacts in the museum’s collection disappeared during the regime change. If the National Museum now wishes to display the same number of artifacts as it did before the regime change, and if none of the missing artifacts are recovered, then the museum will keep in storage:

Correct answer marked below

4/5

6/7

of artifacts in collection

9/14

13/20

3/5

5/7

7/12

11/18

Correct

7/18

5/12

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Explanation

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Official Explanation

Official

Let total artifacts before regime change = T.

Before regime change:

Displayed =

\frac{1}{3}T

Stored =

\frac{2}{3}T

During regime change,

\frac{1}{7}

\frac{1}{5}

of T disappeared.

Remaining artifacts =

T - \frac{1}{7}T = \frac{6}{7}T

(minimum) to

T - \frac{1}{5}T = \frac{4}{5}T

(maximum).

Now museum wants to display same number as before:

\frac{1}{3}T

artifacts.

Fraction of remaining collection that will be displayed =

\frac{\frac{1}{3}T}{\text{remaining}}

.

Minimum remaining case: remaining =

\frac{6}{7}T

…

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What this question tests

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

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