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Permutation and Combination using Sets

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Permutation and Combination using Sets

by s91arvindh » Sun May 04, 2014 7:41 pm

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In a class of 25 students, every student takes either Spanish, Latin or French or two of the three but not all three. 9 take Spanish, 7 take Latin and 5 take exactly two languages.Number of students who take French ?

[spoiler]
Answer 14[/spoiler]

Note: The above question is from a handout which is intended for understanding the concepts
Last edited by s91arvindh on Sun May 04, 2014 8:00 pm, edited 1 time in total.
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by [email protected] » Sun May 04, 2014 7:53 pm
Hi s91arvindh,

This looks like the set-up to a question, but there doesn't appear to be an actual question attached.

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by s91arvindh » Sun May 04, 2014 8:01 pm
Hi Rich,

Sorry Missed to attach the question and I have edited the question
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by Tushar14 » Sun May 04, 2014 8:27 pm
Simple way to solve,
Lets assume F number takes French, S takes Spanish = 9 and L takes Latin = 7.

Now, total number of students is 25.
So, F + S + L - 5(coz this number would be attached to any language group) = 25
or, F + 9 + 7 - 5 = 25
F = 25 - 16 + 5 = 14, is the number of students who take up French...

I am not sure if this is correct approach, but wanted to give a try and get feedback from experts.
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Re: Permutation and Combination using Sets

by Stuebs » Fri Jun 19, 2020 3:57 pm
I understand how the answer was found, but am confused why it has to be 14. Couldn’t the 5 students be taking Spanish and Latin, making it 9 who study French? Or couldn’t they be taking any combination of two out of the three languages, making those who study French anywhere between 9 and 14? I’m confused, please help! 😅
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Re: Permutation and Combination using Sets

by Brent@GMATPrepNow » Thu Aug 20, 2020 10:54 am
s91arvindh wrote: ↑
Sun May 04, 2014 7:41 pm
 In a class of 25 students, every student takes either Spanish, Latin or French or two of the three but not all three. 9 take Spanish, 7 take Latin and 5 take exactly two languages.Number of students who take French ?

[spoiler]
Answer 14[/spoiler]

Note: The above question is from a handout which is intended for understanding the concepts
I'm not a big fan of memorizing formulas, so here's a way to solve the question using diagrams.
We're going to start from the center and work our way out.

Each student studies either Spanish, Latin, or French, or two of the three, but no students study all three languages.
First we can place 0 in the intersection of all three circles.
Image



5 study exactly two language
Since we aren't told that the distribution of those five students who study exactly two languages, we can distribute them anyway we want.
Here's one option:
Image



9 study Spanish, 7 study Latin
We'll add 5 and 4 in order to meet the conditions above
Image


There are 25 students in the class
So far, we've accounted for 14 of the 25 students.
So the remaining 11 students must study only French
Image

So the TOTAL number of students studying French = 2 + 0 + 1 + 11 = 14

Answer: C

Cheers,
Brent
Last edited by Brent@GMATPrepNow on Mon Aug 24, 2020 5:33 pm, edited 1 time in total.
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Re: Permutation and Combination using Sets

by gentvenus » Thu Aug 20, 2020 12:39 pm
Quantity A: 14
Quantity B: 14

Answer: C
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Re: Permutation and Combination using Sets

by Scott@TargetTestPrep » Mon Aug 24, 2020 2:15 pm
s91arvindh wrote: ↑
Sun May 04, 2014 7:41 pm
 In a class of 25 students, every student takes either Spanish, Latin or French or two of the three but not all three. 9 take Spanish, 7 take Latin and 5 take exactly two languages.Number of students who take French ?

[spoiler]
Answer 14[/spoiler]

Note: The above question is from a handout which is intended for understanding the concepts
Solution:

We can use the formula:

Total = Spanish + Latin + French - Exactly Two Sets - 3 * All Three Sets + None

Since All Three Sets and None are both 0, we have:

25 = 9 + 7 + F - 5

25 = 11 + F

14 = F

Answer: 14

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Re: Permutation and Combination using Sets

by Brent@GMATPrepNow » Mon Aug 24, 2020 5:36 pm
gentvenus wrote: ↑
Thu Aug 20, 2020 12:39 pm
 Quantity A: 14
Quantity B: 14

Answer: C
Ha!
ME: Why is that guy writing Quantity A? It's like he's confusing this with a GRE question.

Took me longer than I care to admit to figure out what you were doing :-)
This question is also on a GRE prep forum (https://greprepclub.com/forum/in-a-clas ... 10288.html) and after answering it there, I thought I'd paste it hear as well. Looks like I forgot to delete the GRE stuff :-)
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