Each Term of Set T is Multiple of 5. Is Standard Deviation of T Positive? GMAT Data Sufficiency

Question: Each term of set T is multiple of 5. Is standard deviation of T positive?

1. Each term of set T is positive.
2. T consists of one term

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“Each term of set T is multiple of 5. Is standard deviation of T positive?” – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken f0rom the book "GMAT Quantitative Review". 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.

Answer

Approach Solution 1

There is only one approach solution to this problem

The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values. So, basically we can say that it in a sense measures the distance and the distance cannot be negative, which means that the standard deviation of any set is greater than or equal to zero: SD 0.

Next, the standard deviation of a set is zero if and only the set consists of identical numbers (or which is same if the set consists of only one number.

(1) Each term of set T is positive. If T = {5} then SD = 0 but if

Set T = {5,10} then SD > 0

Hence this statement is insufficient.

(2) Set T consists of one term. Any set with only one term has the standard deviation equal to zero.

Hence this statement is sufficient.

Correct option: B

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