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INSTRUCTIONS

This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts, you must indicate whether:

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

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

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

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

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$X$ denotes a data set with $8$ elements and $Y$ is a data set with $10$ elements. How many elements are in both sets?

(1) An equal number of elements exist only in set $X$ or only in set $Y$.

(2) There are $4$ more elements that exist only in set $X$ than elements that exist only in set $Y$.

A

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

B

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

C

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

D

EITHER statement ALONE is sufficient to answer the question.

E

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked - more relevant data is required.

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