In a class of 78 students 41 are taking French, 22 are taking German.

Question

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

Harley1980 · Answer

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

SavageBrother · Answer

Total: 78
French total: 41
French and German: 9
41-9 = 32

German total: 22
French and German: 9
22 - 9 = 13

78 - 9 - 13 - 32 = 24.

C.

AmoyV · Answer

Total=French+German-Both+Neither
78=41+22-9+Neither
Neither=78-54
Neither=24

Answer: C

lipsi18 · Answer

Total = F+G+neither-both
78=41+22-9+neither; therefore neither=24

Hence answer is C

Thanks,

SherLocked2018 · Answer

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.

Bunuel · Answer

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 = (41-9) + (22-9) + 9 + neither.

Not enrolled students = 24.

Answer: C.

matthewsmith_89 · Answer

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

JeffTargetTestPrep · Answer

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

sdilley · Answer

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. 
78-54 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

CrackverbalGMAT · Answer

Since 9 are taking both courses,

Only French = 41 - 9 =32

Only German = 22 - 9 =13

Total = Only French + Only German + Both + Neither

=> 78 = 32 + 13 + 9 + Neither

=> Neither = 78 - 54 = 24

Alternately,

Total=French + German -Both +Neither

=>78=41+22-9+Neither

=>Neither=78-54 = 24

(option c)

D.S
GMAT SME

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

In a class of 78 students 41 are taking French, 22 are taking German.

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In a class of 78 students 41 are taking French, 22 are taking German.

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards