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In Jefferson School, 300 students study French or Spanish or

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In Jefferson School, 300 students study French or Spanish or

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In Jefferson School, 300 students study French or Spanish or both. If 100 of these students do not study French, how many of these students study both French and Spanish?

(1) Of the 300 students, 60 do not study Spanish.
(2) A total of 240 of the students study Spanish.

OA D

Source: Official Guide

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BTGmoderatorDC wrote:
In Jefferson School, 300 students study French or Spanish or both. If 100 of these students do not study French, how many of these students study both French and Spanish?

(1) Of the 300 students, 60 do not study Spanish.
(2) A total of 240 of the students study Spanish.

OA D

Source: Official Guide
Say

# of students who study only French = F;
# of students who study only Spanish = S;
# of students who study both French and Spanish = B

Thus, we have

300 = F + B + S

Given that 100 of these students do not study French, we have S = 100.

Thus, from 300 = F + B + S, we have F + B = 200.

We have to get the value of B.

Let's take each statement one by one.

(1) Of the 300 students, 60 do not study Spanish.

=> F = 60.

Thus, from F + B = 200, we have B = 200 - 60 = 140. Sufficient.

(2) A total of 240 of the students study Spanish.

=> S + B = 240

Thus, 100 + B = 240 => B = 140. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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Given that 300 students study French , spanish or both and there is none who study neither french nor Spanish
300=French + Spanish -(Both french and spanish)
If 100 of the students do not study french, that means (Spanish)-(Both) =100 hence
300=(French) + 100
French = 300-100=200
Question= How many of these students study both Spanish and French?

Statement 1
Of the 300 students, 60 do not study Spanish.
(French)- (Both)= 60 From the question, we know that (French)= 200
200-(Both)= 60
Both=200-60=140 students
Statement 1 alone is INSUFFICIENT

Statement 2
A total of 240 students study Spanish.
(Spanish)=240
(Spanish)-Both=100
Both= (Spanish)-100
Both=240-100=140 students
Statement 2 alone is also sufficient

Both statement alone are SUFFICIENT
$$answer\ is\ Option\ D$$

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