Data Sufficiency

BTGmoderatorLU wrote:Source: GMAT Prep

Of the N books on a table, some are English and the rest are Bangla. What is the value of N?

1) If 1 English book was removed from the N books, 1/5 of the remaining books would be English.
2) If 2 Bangla books were removed from the N books, 1/4 of the remaining books would be English.

The OA is C.

Say the there are x numbers of English books; thus, there are N - x numbers of Bangla books.

We have to get the value of N.

Let's take each statement one by one.

1) If 1 English book was removed from the N books, 1/5 of the remaining books would be English.

=> Numbers of English books = x - 1; the remaining books on the table = N - 1.

=> (x - 1)/(N - 1) = 1/5

Can't get the unique value of N. Insufficient.

2) If 2 Bangla books were removed from the N books, 1/4 of the remaining books would be English.

=> Numbers of Bangla books = N - x - 2; the remaining books on the table = N - 2.

=> (x)/(N - 2) = 1/4

Can't get the unique value of N. Insufficient.

(1) and (2) together

From (x)/(N - 2) = 1/4, we have x = (N - 2)/4 ---(1)
From (x - 1)/(N - 1) = 1/5, we have x = (N - 1)/5 + 1 ---(2)

from eqn (1) and (2), we have

(N - 2)/4 = (N - 1)/5 + 1

N = 26. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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