Directions: Each Data Sufficiency problem con...
Directions: Each Data Sufficiency problem consists of a question and two statements labeled (1) and (2), that provide data. Based on the data given plus your knowledge of mathematics and everyday facts, you must decide whether the data are sufficient for answering the question. The five answer choices are the same for every data sufficiency question.
Esther is giving Christmas presents to her family members. Each family member gets the same number of presents and no presents were leftover. If each family member gets at least one present, did each family member receive more than one present?
(1) Esther has forty Christmas presents to give out.
(2) If the number of family members were doubled, it would not be possible for each family member to get at least one present.
• a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked;
• b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked;
• c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked,but NEITHER statement ALONE is sufficient;
• d)
• e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Directions: Each Data Sufficiency problem consists of a question and t...
The correct response is (B).
We know from the question that each family member got at least 1 present, that they all got the same number of presents, and that no presents were left over. Based on this information, we can write the following inequality:

(1) The first statement would be useful if we needed to know the number of family members, but it doesn't help to answer this yes/no question.
(2) Based on the information in statement (2), we can write the following inequality:

Combining the information in statement (2) and the information in the question stem, we find that:

Since each family member got at least one present, and the number of presents per family member is less than 2, we can conclude that each family member received only one present.
The answer to the original question is NO. However, if we can answer YES/NO to a data sufficiency question based on the information in a statement, then that statement is sufficient. Statement (2) is sufficient.
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