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What is the standard deviation of set S? (1) Set S contains five consecutive integers (2) The median of set S is 10

GMAT · 2021 · Quantitative
Question:
What is the standard deviation of set S? (1) Set S contains five consecutive integers (2) The median of set S is 10

Options

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
(D) EACH statement ALONE is sufficient
(E) Statements (1) and (2) TOGETHER are NOT sufficient
Answer: (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

Explanation:
Statement (1): Five consecutive integers have constant standard deviation regardless of starting value. For integers n, n+1, n+2, n+3, n+4, SD = √2. Sufficient. Statement (2): Median = 10 does not specify the spread. Insufficient.

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