Data Sufficiency

BTGmoderatorDC wrote: ↑

Sat Feb 15, 2020 6:36 pm

The average of 6 numbers in a set is equal to 0. What is the number of positive numbers in the set minus the number of negative numbers in the set?

(1) Each of the positive numbers in the set equals 10.
(2) Each of the negative numbers in the set equals –5.

OA E

Source: Manhattan Prep

Given: The average of 6 numbers in a set is equal to 0.
This tells us that the SUM of the six numbers is 0

Target question: What is the number of positive numbers in the set minus the number of negative numbers in the set?
When I SCAN the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the target question. So, I’m going to head straight to……

Statements 1 and 2 combined
Notice that we aren't told that each of the 6 numbers are either positive or negative. So it could be the case that some of the numbers are zero, which is neither positive nor negative.

Given this, there are at least two different cases that satisfy BOTH statements:
Case a: The set is {10, 10, -5, -5, -5, -5}. In this case, we have 2 positive numbers and 4 negative numbers. So, the answer to the target question is # of positives - # of negatives = 2 - 4 = -2
Case b: The set is {10, 0, 0, 0, -5, -5}. In this case, we have 1 positive number and 2 negative numbers. So, the answer to the target question is # of positives - # of negatives = 1 - 3 = -2
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent