Solutions

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Question

If set B is a subset of Set A, how many elements are in set A?

I. Set B has 14 elements

II. Exactly 80% of the elements in set A are not in Set B


 

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

Easy

Solution

Option C is the correct answer.


Option Analysis

Set A contains Set B. Question is number of elements is Set A?

Statement I is insufficient: Set B is 14 elements. So Set A has to be greater than or equal to 14. So still we don’t know how many elements. So not sufficient,

Statement II is insufficient: We don’t know how many elements in set B. We only know that 20% of elements in Set A are in Set B.

Together I and II sufficient, 14 elements in set B is 20% of elements in set A. So set A has 70 elements. So sufficient.