In a class of 200 students, 120 study Spanish and 100 study

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

In a class of 200 students, 120 study Spanish and 100 study

by AAPL » Mon May 07, 2018 4:51 am

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In a class of 200 students, 120 study Spanish and 100 study French. If a student must study at least one of these two languages, what percent of the students study French but NOT Spanish?

A. 80%
B. 40%
C. 30%
D. 20%
E. 10%

The OA is B.

Number of students study french = 200 - Numbre of students study spanish = 200 - 120 = 80

% of the students study french but not spanish = (80/200)*100 % = 40 %.

Has anyone another strategic approach to solve this PS question? Regards!

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Source: Beat The GMAT — Problem Solving | Mon May 07, 2018 4:51 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Mon May 07, 2018 10:48 am

Hi AAPL,

We're told that in a class of 200 students, 120 study Spanish and 100 study French and each student must study AT LEAST one of these two languages. We're asked for the percent of the students that study French but NOT Spanish. This question is a variation on a standard Overlapping Sets question, so we can use the Overlapping Sets Formula:

Total = (1st group) + (2nd group) - (Both) + (Neither)

200 = 120 + 100 - (Both) + (0)
200 = 220 - (Both)
Both = 20

Thus, those that study JUST French is 100 - 20 = 80 and the answer to the question is 80/200 = 8/20 = 4/10 = 40%

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Tue May 08, 2018 3:20 pm

AAPL wrote:In a class of 200 students, 120 study Spanish and 100 study French. If a student must study at least one of these two languages, what percent of the students study French but NOT Spanish?

A. 80%
B. 40%
C. 30%
D. 20%
E. 10%

We can create the equation:

Total = Spanish + French - both + neither

200 = 120 + 100 - both + 0

both = 20

So the number who study French but not Spanish is 100 - 20 = 80.

So 80/200 = 40/100 = 40% of the students study French but not Spanish.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]