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Bunuel GMATBusters Why is it not B (St 2 only)?

Could you help us here?

Thank you in advance!
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phil2804

find the value of x?

1) The Standard deviation of the set A= {1, 2, 3, 4, 5} remains the same after the inclusion of a new value x in the set
2) The Mean of set {1, 2, 3, 4, 5} remains the same after the inclusion of a new value x in the set


Bunuel GMATBusters Why is it not B (St 2 only)?

Could you help us here?

Thank you in advance!

The question is flawed.

From (1), x can be \(\frac{15 + 2\sqrt{15}}{5}\) or \(\frac{15 + 2\sqrt{15}}{5}\), so we cannot determine a single value of x. Not sufficient.

Adding x = 3 to A = {1, 2, 3, 4, 5}, which has a standard deviation of \(\sqrt{2}\), produces {1, 2, 3, 3, 4, 5}, which has a standard deviation of \(\sqrt{\frac{5}{3}}≈1.2910\). Adding an element equal to the mean reduces the standard deviation (as long as the set has more than one non-identical element).

From (2), x = 3, and (2) is sufficient.

So (1) and (2) contradict each other, which never occurs in a proper GMAT DS question.

Ignore this question.

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