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## OG 13 146

This topic has 1 expert reply and 0 member replies
oquiella Master | Next Rank: 500 Posts
Joined
12 May 2015
Posted:
164 messages
3

#### OG 13 146

Thu Dec 24, 2015 11:07 am
If the average 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

Explain in lamest terms.

### GMAT/MBA Expert

GMATGuruNY GMAT Instructor
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Thu Dec 24, 2015 5:13 pm
oquiella wrote:
If the average 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
Sum of the six numbers = (number)(average) = 6*75 = 450.

Statement 1:
Since none of six numbers may be less than 75, the least possible case is as follows:
{75, 75, 75, 75, 75, 75}
Here, the sum of the six numbers = 6*75 = 450.
If any of the six numbers above increases to a value ABOVE 75, the resulting sum will EXCEED 450.
Implication:
To satisfy the constraint that the sum of the six numbers = 450, all six numbers must be EQUAL to 75.
SUFFICIENT.

Statement 2:
Since none of six numbers may be greater than 75, the greatest possible case is as follows:
{75, 75, 75, 75, 75, 75}
Here, the sum of the six numbers = 6*75 = 450.
If any of the six numbers above decreases to a value BELOW 75, the resulting sum will be LESS THAN 450.
Implication:
To satisfy the constraint that the sum of the six numbers = 450, all six numbers must be EQUAL to 75.
SUFFICIENT.

The correct answer is D.

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