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If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75 ?

Given: sum of six numbers = 6*75

(1) None of the six numbers is less than 75 --> all 6 numbers must be 75, because if even one of them is more than 75 then the sum will be more than 6*75. Sufficient.

(2) None of the six numbers is greater than 75 --> the same here: all 6 numbers must be 75, because if even one of them is less than 75 then the sum will be less then than 6*75. Sufficient.

104) If the average of six numbers is 75, how many of the numbers are equal to 75?

a) None of the six numbers is less than 75 b) None of the six numbers is greater than 75

a)none is less than 75 so all numbers are 75 as averagege is 75 b) Noe is greater than 75 so all numbers are 75 as average is 75. If any number become less than 75 then average will not 75 it will less than 75.
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Re: If the average (arithmetic mean) of six numbers is 75, how [#permalink]

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17 Aug 2017, 05:10

sum of all numbers is 6*75 = 450

a1+a2+a3+a4+a5+a6 = 450

1) none is less than 75 , if any one will go more than 75 then other have to go less than 75 which is not possible, hence all must be 75, so A or D 2) none is more than 75, again if anyone is less than 75 then other have to more than 75 which is again not possible. so again all are 75 so D Note this is because 75*6=450 D is the answer _________________

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Re: If the average (arithmetic mean) of six numbers is 75, how [#permalink]

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18 Aug 2017, 14:48

If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75?

\(Sum = 75 * 6\)

(1) None of the six numbers is less than 75.

If none of the six numbers is less than 75, then we can have only one possibility that all the 6 numbers are 75

Hence, (1) ===== is SUFFICIENT

(2) None of the six numbers is greater than 75.

If none of the six numbers is greater than 75, then we can have only one possibility that all the 6 numbers are 75

Hence, (2) ===== is SUFFICIENT

Hence, Answer is D _________________

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Re: If the average (arithmetic mean) of six numbers is 75, how [#permalink]

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10 Sep 2017, 21:51

GMATD11 wrote:

If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75 ?

(1) None of the six numbers is less than 75. (2) None of the six numbers is greater than 75.

I actually found this to be a bit harder than a 500 level question but anyways 1 must be true on the same basis as 2 and vice versa. Logically, one of the numbers must be greater than 75 if any of the numbers are less than 75. If none of the six numbers are greater than 75 then all six numbers must be 75. The same holds true if none of the numbers are less than 75.

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