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Math Expert V
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If the arithmetic mean of five different numbers is 50, how many of th  [#permalink]

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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.

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

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Total = 250, as average of 5 numbers is 50.

From statement 1:
Clearly insufficient.

From statement 2:
3 of the numbers are 24,25,26, then the sum of remaining 2 is 250-75 = 175.
Still insufficient.

Combining both, we can say that 2 numbers are more than 50.

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

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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.

#1
in sufficient as either all of no could be 50 or some no >50 & few <50
#2
75+a+b=250
a+b=175
a & b can be 87,88 or else any no where a+b= 175
in sufficient

from 1& 2
sufficient to say that a& b are two no >50
IMO C
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GMAT Tutor B
Joined: 07 Nov 2016
Posts: 56
GMAT 1: 760 Q51 V42 Re: If the arithmetic mean of five different numbers is 50, how many of th  [#permalink]

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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] 31 Jan 2019, 04:06
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