patternpandora wrote:

Bunuel wrote:

MaithiliGokarn wrote:

For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score for the exam?

A. 74

B. 76

C. 78

D. 80

E. 82

Welcome to GMAT Club. Below is a solution to your question.

A score of 58 was 2 standard deviations below the mean --> 58 = Mean - 2d

A score of 98 was 3 standard deviations above the mean --> 98 = Mean + 3d

Solving above for Mean = 74.

Answer: A.

Can someone please elaborate as how is this solved?

you can either solve as Bunuel did or exploit number properties and plug in from the answer choices:

58 = Mean - 2d -----> 2d = Mean - 58

98 = Mean + 3d -----> 3d = 98 - Mean

Thus your d must be both a multiple of 2 (2n) or a multiple of 3 (2n+1). Giving a fast glance at the answer choices, since E-E = E, the first equation is satisfied in every answer choice. The second equation, however, is satisfied in two answers only, respectively A and D.

Now, since d is a unique value for both equations, calculating d must yield the same result. It does but for one choice only and that choice is A.

\(d=\frac{74-58}{2}=\frac{98-74}{3}\)

This is intended to be a back-up method, for sure not as fast as that one Bunuel came up with but when you're under pressure everything that pops up in your mind is useful.

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