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GMAT Diagnostic Test Question 16 Field: statistics Difficulty: 600-650

If set T contains more than one element, is the median of set T greater than its mean?

(1) Set T has positive range. (2) The elements of the set are not consecutive integers

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
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Statement 1: In general, range can be 0 or positive. If set T has positive range, then all elements of the set are not equal. Not suff. Statement 2: If the elements of the set are not consecutive integers, then all elements of the set could or could not have equal values. NSF.

S1 and S2 taken together tell us that elements of the set are not all equal. These elements are not consecutive integers. This information does not is not sufficient to answer whether the median is greater than mean because the set could be {1, 1, 1, 1, 1, 2} or {2, 2, 2, 2, 2, 1}. Set {1, 1, 1, 1, 1, 2} has mean > median and set {1, 2, 2, 2, 2, 2} has median > mean. NSF.
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