If m, s are the average and standard deviation of integers a, b, c, and d, is s andgt; 0?I. m andgt; aII. a + b + c + d = 0a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect answer is option 'A'. Can you explain this answer?

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If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?

I. m > a
II. a + b + c + d = 0

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 is option 'A'. Can you explain this answer?

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If m, s are the average and standard deviation of integers a, b, c, an...

Step 1: Understand the Question Stem

What kind of an answer will the question fetch?
The question is an "Is" question. Answer to an "is" questions is either YES or NO.

When is the data sufficient?
The data is sufficient if we are able to get a DEFINITE Yes or No.
If the statements do not have adequate data to determine whether the standard deviation is greater than 0, the data is NOT sufficient.

When will the standard deviation be 0?
The standard deviation, s, will be 0 in two instances.

when all the elements in the set are the same.
the set contains only one element, which in this case is not possible.

Step 2: Evaluating Statement (1) ALONE: m > a

If a = b = c = d, the average m will be the same as a.
Since m > a, all the elements in the set cannot be the same, and therefore, s > 0.

Statement 1 ALONE is sufficient.
Eliminate choices B, C and E. Choices narrow down to A or D.

Step 3: Evaluating Statement (2) ALONE: a + b + c + d = 0

Approach: Look for a counter example

Example: When a = b = c = d = 0, s = 0
Counter Example: When a = -4, b = 0, c = 0, and d = 4, s > 0

Statement 2 ALONE is NOT sufficient.
Eliminate choice D.

Statement 1 ALONE is sufficient. Choice A is the answer.

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If m, s are the average and standard deviation of integers a, b, c, and d, is s > 0?I. m > aII. a + b + c + d = 0a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficientb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficientc)Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficiente)Statements (1) and (2) TOGETHER are NOT sufficientCorrect answer is option 'A'. Can you explain this answer?

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