In a class of 40 students, 12 enrolled for both English...

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Sun Jan 21, 2018 7:23 am

In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?

A. 30
B. 10
C. 18
D. 28
E. 32

The OA is C.

Please, can any expert explain this PS question for me? I can't get the correct answer. I need your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Sun Jan 21, 2018 7:23 am

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by [email protected] » Sun Jan 21, 2018 11:07 am

Hi swerve,

We're told that in a class of 40 students, 12 enrolled for both English AND German. 22 enrolled for German and the students of the class enrolled for AT LEAST one of the two subjects. We're asked for the number of students who enrolled for ONLY English and not German.

This question is essentially an Overlapping Sets question without the "neither" group, so you can approach the work in several different ways. Since we know that 22 of the students took German - and 12 of those 22 ALSO took English - we've accounted for 22 of the 40 students. This means that 40 - 22 =18 students remain... and those students are the ones who took ONLY English.

Final Answer: C

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

Contact Rich at [email protected]

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue Jan 23, 2018 9:14 am

swerve wrote:In a class of 40 students, 12 enrolled for both English and German. 22 enrolled for German. If the students of the class enrolled for at least one of the two subjects, then how many students enrolled for only English and not German?

A. 30
B. 10
C. 18
D. 28
E. 32

We can use the equation:

Total = Only German + Only English + Both + Neither

Since 22 enrolled in German and 12 enrolled in both, "Only German" is 22 - 12 = 10. Since all the students are enrolled for at least one of the two subjects, "Neither" is 0. So we have:

40 = 10 + E + 12 + 0

18 = E

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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