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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