The average of 6 numbers in a set is equal to 0. What is the

Question

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.

Bunuel · Accepted Answer

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?

Since the average of 6 numbers in the set is equal to 0, then the sum of 6 numbers is also 0. Which means that the sum of the negative numbers must compensate the sum of the positive numbers.

(1) Each of the positive numbers in the set equals 10. Not sufficient.
(2) Each of the negative numbers in the set equals –5. Not sufficient.

(1)+(2) The number of negative numbers (-5) must be twice the number of positive numbers (10). Possible cases are {-5, -5, -5, -5, 10, 10} and {-5, -5, 0, 0, 0, 10}. Thus the number of positive numbers minus the number of negative numbers could be either -2 or -1. Not sufficient.

Answer: E.

knightofdelta · Answer

If "Each of the positive numbers in the  set equals 10 " and "Each of the negative numbers in the  set equals -5 ", don't you think we have gotten our answer?

Bunuel · Answer

I don't understand your question.

Solution gives two possible sets which give two different answers to the question. Therefore the answer is E.

knightofdelta · Answer

It seems like combining (1) and (2) will only provide the first set in your solution i.e. {-5, -5, -5, -5, 10, 10}. Where did you get the zeros in {-5, -5, 0, 0, 0, 10} when each of the negative number is -5 and each of the positive number is 10?

Bunuel · Answer

Zero is neither negative nor positive number.

Now consider {-5, -5, 0, 0, 0, 10}: each of the positive numbers in the set equals 10 and each of the negative numbers in the set equals –5.

Hope it's clear.

josegf1987 · Answer

Hi Bunnuel,

I got C. Here is my explanation

(Sum of + numbers)+(Sum of - numbers) = 6

0 =   
0 = (Sum of + numbers)+(Sum of - numbers)

From 1. (Sum of + numbers) = 10*(Quantity of + numbers)

From 2. (Sum of - numbers) = 10*(Quantity of - numbers)

Can you explain where i made my mistake? Thanks.

Bunuel · Answer

Not sure that I completely understand your approach but I think that you missed that there could be some number of zeros in the set. Check the highlighted part for possible sets, proving E.

anairamitch1804 · Answer

Since the average of the 6 numbers in a set is 0, the sum of the 6 numbers is 0. We also know there could be positive numbers and negative numbers in the set. Zero is not mentioned, but this does not rule it out. In order for the sum of the numbers in the set to be 0, either all the terms are 0, or there are some positives and some negatives.

(1) INSUFFICIENT: Statement 1 tells us that the set has at least one positive number, and that each positive term is 10. We should try to prove insufficiency. For instance, the set could be {–2, –2, –2, –2, –2, 10}, and the number of positive terms minus the number of negative terms would be 1 – 5 = –4. Alternatively, the set could be {–20, –20, 10, 10, 10, 10}, and the answer would be 4 – 2 = 2.

(2) INSUFFICIENT: Statement 2 tells us that the set has at least one negative number, and that each negative term is –5. Again, we should try to prove insufficiency. The set could be {–5, 1, 1, 1, 1, 1}, and the number of positive terms minus the number of negative terms would be 5 – 1 = 4. The set could be {–5, –5, –5, 2, 5, 8}, and the answer would be 3 – 3 = 0.

(1) & (2) INSUFFICIENT: The statements together suggest that the set has twice as many –5 terms as 10 terms, in order to maintain a sum of 0. If every term is negative or positive, then the set would have to be {–5, –5, –5, –5, 10, 10} and the definitive answer would be 2 – 4 = –2. However, zero terms are possible, so the set could be {–5, –5, 0, 0, 0, 10} and an alternative answer would be 1 – 2 = –1.

Hence E.

BrentGMATPrepNow · Answer

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

HarshG7 · Answer

such an easy question but highly tricky at the same time. just a slight overlook and it gets you wrong

The average of 6 numbers in a set is equal to 0. What is the

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