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4 friends A, B, C, and D appeared in a certain examination.

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4 friends A, B, C, and D appeared in a certain examination.

by AAPL » Mon Oct 21, 2019 1:05 am
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4 friends A, B, C, and D appeared in a certain examination. The marks obtained by B is 33.33% less than A and 50% less than C. If the marks obtained by D is at least 2.5 times of the marks of B, then what is the maximum percentage by which the combined score of A and C is more than the score of D?

A. 30%
B. 35%
C. 40%
D. 45%
E. 60%

OA C
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by Jay@ManhattanReview » Mon Oct 21, 2019 4:16 am
AAPL wrote:e-GMAT

4 friends A, B, C, and D appeared in a certain examination. The marks obtained by B is 33.33% less than A and 50% less than C. If the marks obtained by D is at least 2.5 times of the marks of B, then what is the maximum percentage by which the combined score of A and C is more than the score of D?

A. 30%
B. 35%
C. 40%
D. 45%
E. 60%

OA C
Say A got A% marks; thus, B scored A - 33.33% of A = 66.66% of A = 2A/3

Thus, B = 2A/3 ---(1)

Similarly, B = C - 50% of C = C/2

Thus, B = C/2 ---(2)

From (1) and (2), we get C = 4A/3 ---(3)

D's score ≥ 2.5*B ≥ 5B/2 ≥ 5A/3 ---(4)

The combined score of A and C = A + 4A/3 = 7A/3

Since we have to find out the maximum percentage by which the combined score of A and C is more than the score of D, let's assume that D scored minimum; thus D's marks = 5A/3

Thus, the required percent = [(7A/3 - 5A/3) / (5A/3)]*100% = 40%

The correct answer: C

Hope this helps!

-Jay
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