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If the average (arithmetic mean) of 5 numbers is 20, what is

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by Max@Math Revolution » Wed Oct 24, 2018 11:55 pm

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A

B

C

D

E

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Difficulty—

[Math Revolution GMAT math practice question]

If the average (arithmetic mean) of 5 numbers is 20, what is their standard deviation?

1) Their minimum is 20.
2) Their maximum is 20.
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Source: — Data Sufficiency |
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by Max@Math Revolution » Sun Oct 28, 2018 6:09 pm
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Note that if the average and the maximum of a data set are the same, then all of the data values are the same and the standard deviation is 0. Similarly, if the average and the minimum of a data set are the same, all of the data values are the same and the standard deviation is 0.

Thus, each of conditions is sufficient on its own since the minimum and the maximum are the same as the average.

Therefore, D is the answer.
Answer: D
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by Jay@ManhattanReview » Mon Oct 29, 2018 2:37 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If the average (arithmetic mean) of 5 numbers is 20, what is their standard deviation?

1) Their minimum is 20.
2) Their maximum is 20.
Note that the average (arithmetic mean) of a set of numbers can neither be greater than the maximum number of the set nor be less than the minimum number of the set.

Per Statement 1, we know that the minimum number among 5 is 20 and the average is also 20, it implies that all the five numbers must be 20.

So, the set is: (20, 20, 20, 20, 20}.

We see that there is no deviation among the numbers, thus, Standard deviation = 0. Sufficient.

The same goes with Statement 2.

The correct answer: D

Hope this helps!

-Jay
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