Question: What is the SD of a given set of numbers whose average is 5?

(1) None of the numbers are greater than this Average
(2) The Standard deviation is 0 when value of each of the given number is increased by 7

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.

Correct Answer: D
Solution and Explanation:
Approach Solution 1:

In order to answer this, we must be aware of a few crucial properties:
Each term in a set will change in value by the same constant if we add or subtract a constant from it.
SD won't modify it.

The mean will change by the same percentage whether we increase or decrease each term in a set by the same percentage (multiply all terms by the constant).
SD will change either way by the same percentage.
A list will contain only identical elements if the range or standard deviation of the elements is 0. Conversely, if a list has just identical members, its range and standard deviation are both 0. If there is only one element in the list, the range and SD are both 0.

This is so that SD = 0 since there is no deviation from the mean when a list comprises only identical members.

(1) None of the values exceed this Average — if no number exceeds the mean, then no number below the mean must also be present, indicating that all of the entries in this list are identical (or that there is only one element that is identical), therefore SD is equal to zero.
(2) The Standard deviation is 0 when the value of each of the given numbers is increased by 7 — hence, the SD remains constant whether we add or subtract a constant from each term in a set. Sufficient.

D is the correct choice

Approach Solution 2:

from:1
All items in the set are identical because the mean is 5 and none of the elements are bigger than the mean, hence the SD is 0 and all items in the set are 5.

from: 2
The SD won't change even if all the objects have a constant added to them. Consequently, the original set's SD is equal to 5

By the way, since both assertions provide SD, the correct response is D.

Approach Solution 3:
(1) None of the numbers are greater than this Average --> if no number is more than the mean then no number is less than mean, which implies that this list contains all identical elements (or which is the same just one element), so SD=0. Sufficient.
(2) The Standard deviation is 0 when the value of each of the given numbers is increased by 7 --> if we add or subtract a constant to each term in a set SD will not change, so SD=0. Sufficient.

“What is the SD of a given set of numbers whose average is 5?”- is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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