Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58435

In a class of 78 students 41 are taking French, 22 are taking German.
[#permalink]
Show Tags
Updated on: 15 Mar 2019, 04:23
Question Stats:
91% (01:09) correct 9% (01:07) wrong based on 153 sessions
HideShow timer Statistics
In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course? A. 6 B. 15 C. 24 D. 33 E. 54
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Originally posted by Bunuel on 03 Apr 2015, 05:12.
Last edited by Bunuel on 15 Mar 2019, 04:23, edited 1 time in total.
Updated.



Retired Moderator
Joined: 06 Jul 2014
Posts: 1220
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40

Re: In a class of 78 students 41 are taking French, 22 are taking German.
[#permalink]
Show Tags
Updated on: 03 Apr 2015, 06:00
Bunuel wrote: In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
A. 6 B. 15 C. 24 D. 33 E. 54
Kudos for a correct solution. Formula for calculating two overlapping sets: A + B  both + NOT(A or B) = Total so in our task we have equation: 41 (french) + 22 (german)  9 (both) + NOT = 78 54 + NOT = 78 NOT = 78  54 = 24 So answer is C
_________________
Originally posted by Harley1980 on 03 Apr 2015, 05:16.
Last edited by Harley1980 on 03 Apr 2015, 06:00, edited 1 time in total.



Manager
Joined: 18 Dec 2014
Posts: 99

Re: In a class of 78 students 41 are taking French, 22 are taking German.
[#permalink]
Show Tags
03 Apr 2015, 05:20
Total: 78 French total: 41 French and German: 9 419 = 32
German total: 22 French and German: 9 22  9 = 13
78  9  13  32 = 24.
C.



Retired Moderator
Status: On a mountain of skulls, in the castle of pain, I sit on a throne of blood.
Joined: 30 Jul 2013
Posts: 300

Re: In a class of 78 students 41 are taking French, 22 are taking German.
[#permalink]
Show Tags
03 Apr 2015, 09:24
Bunuel wrote: In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
A. 6 B. 15 C. 24 D. 33 E. 54
Kudos for a correct solution. Total=French+GermanBoth+Neither 78=41+229+Neither Neither=7854 Neither=24 Answer: C



Manager
Joined: 26 Dec 2012
Posts: 144
Location: United States
Concentration: Technology, Social Entrepreneurship
WE: Information Technology (Computer Software)

Re: In a class of 78 students 41 are taking French, 22 are taking German.
[#permalink]
Show Tags
05 Apr 2015, 01:14
Total = F+G+neitherboth 78=41+229+neither; therefore neither=24
Hence answer is C
Thanks,



Current Student
Joined: 25 Nov 2014
Posts: 96
Concentration: Entrepreneurship, Technology
GPA: 4

Re: In a class of 78 students 41 are taking French, 22 are taking German.
[#permalink]
Show Tags
05 Apr 2015, 21:29
Using the set formula : A'U'B  ~(A'U'B) = A + B  AB need to find ~(A'U'B) = x, say. 78  x = 41 + 22  9 => x = 24.
_________________



Math Expert
Joined: 02 Sep 2009
Posts: 58435

Re: In a class of 78 students 41 are taking French, 22 are taking German.
[#permalink]
Show Tags
06 Apr 2015, 06:44
Bunuel wrote: In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
A. 6 B. 15 C. 24 D. 33 E. 54
Kudos for a correct solution. OFFICIAL SOLUTION:You could solve this by drawing a Venn diagram. A simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking French to find the number taking only French. Likewise find those taking only German. Then we have:Total = only French + only German + both + neither 78 = (419) + (229) + 9 + neither. Not enrolled students = 24. Answer: C.
_________________



Manager
Joined: 06 Dec 2016
Posts: 231

Re: In a class of 78 students 41 are taking French, 22 are taking German.
[#permalink]
Show Tags
18 Mar 2017, 08:43
You could even do this way as well P(F) = 41/78 P(G) = 22/78 P(FNG) = 9/78
1  P(FUG) = 41/78 + 22/78  9/78 1 P(FUG) = 54/78 P(FUG) = 1  54/78 P(FUG) = 24/78
Therefore, answer is C



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2815

Re: In a class of 78 students 41 are taking French, 22 are taking German.
[#permalink]
Show Tags
10 Apr 2018, 11:16
Bunuel wrote: In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
A. 6 B. 15 C. 24 D. 33 E. 54 [Note: Here we are assuming that every student learns either Physics or Chemistry or both.] Let’s let b = the number of students learning both Physics and Chemistry. Let’s also assume that there are 100 students. Since 70% of the students learn Physics and 65% of the students learn Chemistry, we could say that: 100 = 65 + 70  b 100 = 135  b b = 35 Answer: C
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews
If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Intern
Joined: 31 May 2018
Posts: 9

Re: In a class of 78 students 41 are taking French, 22 are taking German.
[#permalink]
Show Tags
31 May 2019, 00:32
I got to the answer in 21 seconds with quick mental math.
41 French + 22 German = 63 63 F&G  9 in both = 54 in foreign language classes. 7854 ends in a 4 and narrows my answer choices to 24 or 54. I know easily that 54+54 is too big so I’m left with only 24, C, as my option
Posted from my mobile device




Re: In a class of 78 students 41 are taking French, 22 are taking German.
[#permalink]
31 May 2019, 00:32






