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# If the arithmetic mean of five different numbers is 50, how many of th

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Re: If the arithmetic mean of five different numbers is 50, how many of th [#permalink]
Bunuel wrote:
If the arithmetic mean of five different numbers is 50, how many of the numbers are greater than 50?

(1) None of the five numbers is greater than 100.

(2) Three of the five numbers are 24, 25 and 26, respectively.

Average of the five numbers = 50

So, Sum = 250

St 1 : None of the five numbers is greater than 100

Case 1 : The numbers are 50,50,50,50,50 Ans : Zero numbers are greater than 50

Case 2 : The numbers are 51,50,50,50,49 Ans : One

Since We are getting two different values for the answer

Not Sufficient

St 2 : Three of the numbers are 24,25,26

The sum of the remaining two = 250 - (24 + 25 +26) = 175

Case 1 : The other two numbers are 100,75 Ans : Two

Case 2 : The other two numbers are 125,50 Ans : One

Not Sufficient

St 1 and St 2 :

The cases where one of the other two numbers takes a value 50 or less is ruled out as then the fifth number will exceed 100

So, the other two values have to be each more than 50 Ex : 90,85

Unique Answer : Two numbers have value greater than 50

Sufficient

Choice C
Re: If the arithmetic mean of five different numbers is 50, how many of th [#permalink]
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