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by oquiella » Thu Dec 24, 2015 11:07 am

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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

Answer: D

Explain in lamest terms.

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by GMATGuruNY » Thu Dec 24, 2015 5:13 pm

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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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by [email protected] » Tue Mar 27, 2018 8:05 pm

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Hi All,

We're told that the AVERAGE of six numbers is 75. We're asked how many of the numbers are EQUAL to 75? This is a great 'concept question', meaning that you don't actually have to do any math to solve it (as long as you understand the concept involved). Here, we're dealing with Averages. When dealing with a group of numbers that has an average, one of two options exist:

Option #1: All of the numbers are the SAME, so the average is that number.
Option #2: The numbers vary (although there might be some duplicates), with some of the numbers being ABOVE the average and some of the numbers being BELOW the average.

We're told that the average of 6 numbers is 75, so one of the above two options has to describe the 6 values...

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

Since the AVERAGE = 75 and NONE of the numbers is less than 75, then we have to be dealing with Option #1 (above). Thus, all 6 numbers are 75 and the answer to the question is 6.
Fact 1 is SUFFICIENT

2. None of the six numbers is greater than 75

Since the AVERAGE = 75 and NONE of the numbers is greater than 75, then we have to be dealing with Option #1 (above). Thus, all 6 numbers are 75 and the answer to the question is 6.
Fact 2 is SUFFICIENT

Final Answer: D

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