swerve wrote: ↑

Sat Jan 18, 2020 2:26 pm

The students in two classes of "Underachiever" high school took a test. x, a, and c are, respectively, the standard deviation, median, and the mean of the test scores of the students in class X. y, b, and d are, respectively, the standard deviation, median, and the mean of the scores of the students in class Y. Is x > y?

1) a < b
2) c < d

The OA is E

Source: Economist GMAT

Let's take each statement one by one.

1) a < b

Say there are three students in each class.

Case 1:

Class X: Say the scores of the three students are 10, 11, and 12. Thus, mean = a = 11. Let's not compute SD = x, now. In the GMAT, computation of the SD is out of scope; however, its interpretation is within the scope. Let's hold even interpretation until we discuss Class Y scores.

Class Y: Say the scores of the three students are 11, 12, and 13. Thus, mean = b = 12 > (a = 11).

Since the extreme scores for both the classes are ±1 away from their respective means, x = y. The answer is no.

Case 2:

Class X: Say the scores of the three students are 10, 11, and 12. Thus, mean = a = 11.

Class Y: Say the scores of the three students are 11.5, 12, and 12.5. Thus, mean = b = 12 > (a = 11).

Since the extreme scores for Class X are ±1 away from its mean, while that for Class Y is ±0.5 away from its mean, x > y. The answer is yes.

No unique answer. Insufficient.

2) c < d

For both cases discussed in Statement 1, if we swap mean with median, we have the same answer. Insufficient.

Thus, even after combining both statements, we cannot conclude whether x > y. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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