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The students in two classes of "Underachiever" hig

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The students in two classes of "Underachiever" hig

by BTGmoderatorLU » Thu Jan 02, 2020 4:44 am
Source: Economist GMAT

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 mean of the test scores of the students in class Y. Is \(x > y\)?

1) \(a < b\)
2) \(c < d\)

The OA is E
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Source: — Data Sufficiency |
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by deloitte247 » Sat Jan 04, 2020 11:08 pm
There are 2 classes; class X and class Y.
In class X, x = standard deviation, a = median and c = mean
In class Y, y = standard deviation, b = median and d = mean
Question => is x>y?
Statement 1: a < b
Let score in class X = 10, 20, 30
Let score in class Y = 20, 30, 40
a=20, b=30, x=10 and y=10
a<b but x is not greater than 'y'.
Let stores in class X = 10, 20, 30
Let stores in class Y = 24, 25, 26
a=20, b=25, x=10 and y=1
a<b and x>y
The information available is not enough to arrive at a definite answer. Statement 1 is, therefore, NOT SUFFICIENT.

Statement 2: c<d
Let score in class X = 10, 20, 30
Let score in class Y = 20, 30, 40
c=20, d=30, x=10 and y=10
c<d but x is not greater than 'y'.
Let stores in class X = 10, 20, 30
Let stores in class Y = 24, 25, 26
c=20, d=25, x=10 and y=1
So, c<d and x>y. The information available is not enough to arrive at a definite answer. Statement 2 is, therefore, NOT SUFFICIENT.

Combining both statements together:
Let scores in X=10,20,30, and Y = 20, 30, 40
a=20, b=30, c=20, d=30, x=10, y=10
x=y
Let scores in X=10,20,30, and Y = 24, 25, 26
a=20, b=25, c=20, d=26, x=10, y=1
x>y
Both statements combined together are NOT SUFFICIENT. Therefore, option E is the correct answer
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