Permutation and Combination using Sets

Hi s91arvindh,

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

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

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.




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:




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



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


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

Answer: C

Cheers,
Brent

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

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