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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

by AAPL » Tue Sep 11, 2018 6:53 pm

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In Jefferson School, 300 students study French and 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 French.
(2) A total of 240 of the students study Spanish.

OA D.
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Wed Sep 12, 2018 3:34 am

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AAPL wrote:Official Guide

The question is posted correctly. In Statement 1, Spanish should be there for French.

In Jefferson School, 300 students study French and 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.
Say,

S = Students who study Spanish
F = Students who study French
B = Students who study both

Thus,

300 = S + F - B

We are given that S - B = 100

Thus, from 300 = S + F - B, we have F = 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 - B = 60

From F = 200 and F - B = 60, we have B = 140. Sufficient.

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

=> S = 240

From 300 = S + F - B, F = 200, and S = 240, we have B = 140. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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by fskilnik@GMATH » Wed Sep 12, 2018 1:16 pm

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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.
\[? = {\text{French}} \cap {\text{Spanish}} = x\,\,\,\,\left( {{\text{see}}\,\,{\text{image}}\,\,{\text{attached}}} \right)\]

\[\left( 1 \right)\,\,\,300 = 60 + x + 100\,\,\,\,\, \Rightarrow \,\,\,\,x\,\,\,{\text{unique}}\]
\[\left( 2 \right)\,\,\,240 = x + 100\,\,\,\,\, \Rightarrow \,\,\,\,x\,\,\,{\text{unique}}\]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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