The average (arithmetic mean) of a list of positive numbers is what

Question

The average (arithmetic mean) of a list of positive numbers is what percent of the sum of the numbers?

(1) The sum of the numbers in the list is 150. 
(2) There are 25 numbers in the list.

M36-04

Bunuel · Accepted Answer

Official Solution:

The average (arithmetic mean) of a list of positive numbers is what percent of the sum of the numbers? 
 
The average of a list =  \frac{(the \ sum \ of \ the \ numbers)}{(the \ number \ of \ terms)}=\frac{S}{N} 
 
The average as a percent of the sum of the numbers =  \frac{(the \ average)}{(the \ sum \ of \ the \ numbers)}*100=\frac{(\frac{S}{N})}{S}*100=\frac{1}{N}*100 
 
So, to answer the question all we need to find is the number of terms in the list (N).
 
(1) The sum of the numbers in the list is 150. Not sufficient
 
(2) There are 25 numbers in the list. Sufficient.

Answer: B

Abhishiek · Answer

Mean = \frac{sum of numbers}{count of numbers}

So % asked = (mean/sum of numbers ) * 100
 = 100/ count of numbers

1. Not helpful. We don't know the count.
2. We just need count.

B.

amanvermagmat · Answer

For given n numbers, their average = (their sum)/n OR average/Sum = 1/n
So if we are asked that average is what % of sum, we have to find 
Average/Sum * 100 = 1/n * 100

So if we can get n, we can get the answer. Statement 2 gives us the value of n, but statement 1 does not.

Hence  B answer

GMATinsight · Answer

Average as a percentage of the sum of the numbers =  Average of Number  *100 / Sum of the numbers

Average as a percentage of the sum of the numbers =  (Sum of Number/Count of Numbers)  *100 / Sum of the numbers

Average as a percentage of the sum of the numbers = 100/Count of Numbers)

Statement 1: NOT SUFFICIENT

Statement 2: SUFFICIENT

Answer: option B

Bunuel · Answer

Par of  GMAT CLUB'S New Year's Quantitative Challenge Set

NinetyFour · Answer

Tricky question. I was definitely fooled, but indeed the correct answer is B. The sum cancels out so it doesn't matter what the value is.

Avg * # of terms = sum

Avg =  \frac{Sum}{terms}

\frac{sum}{25} =  x% * sum

x = 4%

Kinshook · Answer

Asked: The average (arithmetic mean) of a list of positive numbers is what percent of the sum of the numbers?

Average = Sum of numbers / Count of numbers 
Average/Sum of numbers = 1/Count of numbers = (100/Count of numbers) %

(1) The sum of the numbers in the list is 150. 
Since average is unknown
NOT SUFFICIENT

(2) There are 25 numbers in the list.
Count of numbers = 25
Average/Sum of numbers = 1/Count of numbers = (100/Count of numbers) % = 4%
SUFFICIENT

IMO B

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The average (arithmetic mean) of a list of positive numbers is what

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