BTGmoderatorDC wrote:At a certain school of 200 students, the students can study French, Spanish, both or neither. Just as many study both as study neither. One quarter of those who study Spanish also study French. The total number who study French is 10 fewer than those who study Spanish only. How many students study French only?
A. 30
B. 50
C. 70
D. 90
E. 120
OA B
Source: Magoosh
Say,
the number of students who study only French = f;
the number of students who study only Spanish = s;
the number of students who study both French & Spanish = b;
Thus,
the number of students who study French = f + b;
the number of students who study Spanish = s + b;
the number of students who study neither French nor Spanish = n = b (given)
=> f + s + b + n = 200 => f + s + 2b = 200 ---(1)
Given 'One-quarter of those who study Spanish also study French,' we have (s + b)/4 = b => s = 3b ---(2)
Given 'The total number who study French is 10 fewer than those who study Spanish only,' we have f + b = s - 10 => s = f + b + 10 ---(3)
From (2) and (3), we have f + b + 10 = 3b => f = 2b - 10 ---(4)
From (1) and (4), we have
f + s + 2b = 200
=> 2b - 10 + 3b + 2b = 200
b = 30
Thus, f = 2b - 10 = 2*30 - 10 = 50
The correct answer:
B
Hope this helps!
-Jay
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