If the average of four differnt number is 30, how many of : GMAT Data Sufficiency (DS)
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# If the average of four differnt number is 30, how many of

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Intern
Joined: 16 Apr 2010
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If the average of four differnt number is 30, how many of [#permalink]

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23 Jul 2010, 19:11
If the average of four differnt number is 30, how many of the numbers are greater than 30?
A. None of the four number is greater than 60
B. Two of the four numbers are 9 and 10 respectively
Manager
Joined: 16 Apr 2010
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23 Jul 2010, 21:58
Hi,

A is not sufficient.
Consider 20, 20, 40, 40 the average is 30 and non is greater than 60 (2 #s are greater than 30)
Consider 0, 40, 40, 40 the average is 30 and non is greater than 60 (3 #s are greater than 30)
Thus B alone is not sufficient.

B. Two of the four numbers are 9 and 10 then the sum of the other two numbers are 4*30 - (9+10) = 101
if one number is zero the other is 101 (1 # is greater than 30)
if one number is 60 the other other is 51 (2 #s are greater than 30)
Thus B alone is not sufficient.

Taking A and B, the answer will be sufficient and we will have two numbers greater than 30.

Regards,
Jack
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10 Oct 2010, 15:39
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C

1) set can be {30 30 30 30} or {10 10 50 50}.... multiple options

2) set can be {9 10 10 91} or {9 10 50 51}..... multiple options

together: { 9 10 x y}

x+y should be 101 and both need to be less than 60. if x is 59 then y will be 101-59 = 42.

if x is 31 then y is 80 - not good. increase x which in turn will reduce y but, both will be greater than 30 for sure.
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Re: DS   [#permalink] 10 Oct 2010, 15:39
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