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If the median of 5 positive integers is 10, is their average

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by Max@Math Revolution » Tue Feb 19, 2019 12:36 am

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[GMAT math practice question]

If the median of 5 positive integers is 10, is their average (arithmetic mean) greater than 10?

1) The largest number is 40
2) The smallest number is 1
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Source: — Data Sufficiency |
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by Max@Math Revolution » Wed Feb 20, 2019 11:53 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.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Suppose the numbers satisfy a ≤ b ≤ 10 ≤ c ≤ d. The question asks if ( a + b + 10 + c + d ) / 5 > 10 or a + b + c + d + 10 > 50.
This is equivalent to the inequality, a + b + c + d > 40.
If a question includes the words "greater than", then it asks us to look for a minimum.
Since a, b c, and d are positive, and d = 40 by condition 1), we must have a + b + c + d > 40.
Condition 1) is sufficient.

Condition 2)
If a = 1, b = 2, c = 11, and d = 40, then a + b + c + d > 40, and the answer is 'yes'.
If a = 1, b = 2, c = 11, and d = 12, then a + b + c + d < 40, and the answer is 'no'.
Thus, condition 2) is not sufficient since it does not yield a unique solution.

Therefore, A is the answer.
Answer: A
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