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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