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

Question

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

(1) There are 8 numbers in the list.

(2) The sum of the numbers in the list is 100.

BrentGMATPrepNow · Answer

Beautiful question, Bunuel!!

Target question :    The average (arithmetic mean) of a list of numbers is what percent of the sum of the numbers?  
This is a good candidate for  rephrasing the target question . 
 Aside: the video below has tips on rephrasing the target question

Let n = the number of numbers in the list. 
The average =  (sum of all n numbers)/n

We can create the equation: ( (sum of all n numbers)/n )/(sum of all n numbers) = p percent  (the  target question  is essentially asking us to find the value of p)

Rewrite as: ( (sum of all n numbers)/n )/(sum of all n numbers) = p/100
Simplify the left side to get: 1/n = p/100 
Rewrite to get: p = 100/n
  REPHRASED target question :    What is the value of 100/n ?

Statement 1 : There are 8 numbers in the list.  
In other words n = 8
If n = 8, then the answer to the REPHRASED target question is  100/n = 100/8 = 12.5 (%) 
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : The sum of the numbers in the list is 100 
Since we have no information about n (the number of numbers in the list), we can’t answer the  REPHRASED target question  with certainty
Statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

QuantMadeEasy · Answer

Step 1: Understanding the question 
Let average of the numbers be x% of the sum of the numbers
Average = x% * (Sum of the numbers)

\frac{(Sum of the numbers) }{ (Number of readings)}  =  \frac{x}{100}  * (Sum of the numbers)

\frac{1}{ (Number of readings)}  =  \frac{x}{100}

\frac{100}{ (Number of readings)}  = x

Hence to find x, total number of readings are required

Step 2: Understanding statement 2 alone 
(1) There are 8 numbers in the list.
Total number of readings = 8
Hence, x = 100/8 = 12.5
Sufficient

Step 3: Understanding statement 2 alone 
(2) The sum of the numbers in the list is 100.
As the total number of readings cannot be calculated, the statement is not sufficient
Insufficient

IMO A

Akp880 · Answer

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

Explanation:  mean (M)=Sum of numbers(S)/count of numbers(N)

i.e  M=S/N 
question asks what is (M/S)*100??

(S1 ) There are 8 numbers in the list.
given N=8
then  (M/S)*100=(1/N)*100 
=100/8
= 12.5%

Hence S1 is sufficient. 
 
(S2)  The sum of the numbers in the list is 100.
Given S=100
then then  (M/S)*100=(1/N)*100 
Clearly not enough data to tell exact value
 Hence S2 is insufficient.

Thus A is the correct answer.

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

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