Solutions

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Question

A certain cake has two layers with pieces of fruit on top of each layer. Of all the pieces of fruit on the cake, 25 percent are strawberries. How many pieces of fruit are on the first layer of the cake?

I. Of the pieces of fruit on the first layer, 6 are strawberries.

II. 20 percent of the 20 pieces of fruit on the second layer are strawberries.


 

Option A:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Option B:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Option C:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Option D:

EACH statement ALONE is sufficient to answer the question asked.

Option E:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Difficulty Level

Medium

Solution

Option C is the correct answer.


Option Analysis

Say there are x pieces of fruit on the cake, thus we are given that there are 0.25x pieces of strawberries.

Statement I is insufficient: Of the pieces of fruit on the first layer, 6 are strawberries. No info about the second layer. Not sufficient.

Statement II is insufficient: 20 percent of the 20 pieces of fruit on the second layer are strawberries –> there are 0.2*20=4 pieces of strawberries on the second layer. No info about the first layer. Not sufficient.

Together I and II, From above we have that there are a total of 6+4=10 pieces of strawberries, thus there are a total of 40 pieces of fruit on the cake (from 0.25x=10). Since from (2) we have that there are 20 pieces of fruit on the second layer, then there are 40- 20=20 pieces of fruit on the first layer. Sufficient.