What is the Sum of Five Numbers? GMAT Data Sufficiency

Question: What is the sum of five numbers?

(1) The average of the numbers is zero
(2) Only one of the numbers is positive.

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.

Correct Answer: A

Solution and Explanation:
Approach Solution 1:
Let the five numbers be n1 , n2 , n3 , n4 and n5

(1) The average of the numbers is zero
Average of 5 numbers = Sum/5 = (n1+n2+n3+n4+n5)/5
=>Sum = Average *5 = 0
=> n1+n2+n3+n4+n5 = 0
Sufficient

(2) Only one of the numbers is positive.
Not sufficient

Approach Solution 2:
Statement 1: Sum of 5= 0 => Sum= 5*0= 0.
Sufficient.

Statement 2: Only one number is positive. The other numbers are not known to us.
Insufficient.

Approach Solution 3:
When we modify the original condition and the question, they become AN=S(A:mean, N:number, S:sum), which makes sum related to mean and number.

For 1), if mean= 0, S=0 is derived from 0*N= S.
Sufficient.

“What is the sum of five numbers?”- 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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