Problem Solving

Vincen wrote:The average of 25 values is equal to product of these values. If only one of the numbers is 0, at most how many numbers can be greater than zero?

A) 0
B) 12
C) 13
D) 23
E) 24

If one of the 25 values is zero, then the PRODUCT of the 25 values will be 0
So, the AVERAGE of the 25 values is also 0
If the average is 0, then the SUM of all 25 values must be 0

At most how many numbers can be greater than zero?
We already know that one value is 0.
Can the other 24 values be greater than 0?
No. The sum of 0 and 24 positive values will always be positive.
So, we can ELIMINATE answer choice E

Can 23 values be greater than 0?
Yes. How about: {-23, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 }
Here, the average = 0, and we have 23 positive values in the set.
Answer: D

Cheers,
Brent

Hi Vincen,

This is a great 'concept' question - meaning that if you understand the concepts involved, then you don't have to do much math to get to the correct answer.

We're told that there are 25 numbers and that the AVERAGE of the numbers = PRODUCT of the numbers. THAT type of relationship can clearly only happen under certain circumstances. We're also told that JUST ONE of the numbers is 0. We're asked for the maximum number of those 25 values could be GREATER than 0.

Since we have a 0 in the group, we know that the product will be 0 (since anything multiplied by 0 will equal 0). To get an AVERAGE of 0, the SUM of all 25 terms must 'cancel out' and leave us with a 0. There are no limit on what the values could be, so as long as we had one NEGATIVE value to 'offset' the sum of all of the positive values, then we could hit a total sum of 0. Thus, we could have....
1 negative
1 zero
23 positives

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Vincen wrote:The average of 25 values is equal to product of these values. If only one of the numbers is 0, at most how many numbers can be greater than zero?

A) 0
B) 12
C) 13
D) 23
E) 24

Since the average is equal to the product and one value is zero, the product is zero. Thus, in order to have an average of zero, we need the sum to be zero also. We can have 23 numbers that are positive, one that is zero, and one that is negative with its absolute value as the sum of the 23 positive numbers.

Answer: D