Of the students at a certain school, 40 took French, 30 took Latin, an

Question

Of the students at a certain school, 40 took French, 30 took Latin, and 20 took Spanish. How many students at the school took only two of the three languages?

(1) 5 students at the school took all three of the languages.

(2) 52 students at the school took at least one of the languages.

Kinshook · Accepted Answer

jawnjon 
Given: Of the students at a certain school, 40 took French, 30 took Latin, and 20 took Spanish.
Asked: How many students at the school took only two of the three languages?

All = 40 + 30 + 20 - Exactly 2 - 2*All 3 + none

(1) 5 students at the school took all three of the languages.
All = 40 + 30 + 20 - Exactly 2 - 2*5 + none
At least one = 40 + 30 + 20 - Exactly 2 - 2*5 
Since number of all students opting for all languages and number of students opting for none of the languages are unknown
NOT SUFFICIENT

(2) 52 students at the school took at least one of the languages.At least one = 40 + 30 + 20 - Exactly 2 - 2*all 3 = 52
Since number of all students opting for all languages is unknown
NOT SUFFICIENT

(1) 5 students at the school took all three of the languages.
(2) 52 students at the school took at least one of the languages.
At least one = 40 + 30 + 20 - Exactly 2 - 2*5 = 52
Number of student opting for Exactly 2 languages = 40 + 30 + 20 - 52 - 10 = 28
SUFFICIENT

IMO C

sayan640 · Answer

Total - neither language = total of set 1 + total of set2 + total of set 3 - only 2 - 2* all 3
At least one of the three = 40 + 30 + 20 - only 2 - 2*All3

Statement 1 gives the info about all 3 i.e 5
Statement 2 gives the info about at least one of the three i.e 52 ( total no of students in the school minus students learning no language )

C is the answer.

nnusantoro · Answer

why do you do 2*All three?

Posted from my mobile device

AnkurGMAT20 · Answer

nnusantoro  when asked about or exact 2 is mentioned, we will subtract all three twice.

babyulikeit · Answer

Bunuel

Can you please explain?
Thank you.

Bunuel · Answer

This should help to solve:  ADVANCED OVERLAPPING SETS PROBLEMS

phoenixvr106 · Answer

Can someone explain why E is not the answer? Does this particular question stem really imply that the amount of students who took *none* of the three languages is = 0? I thought that was a stretch to imply. Straight forward question if that nuance is clear, which in my opinion it isn't.

Bunuel · Answer

It's not assumed that the number of students who took none of the languages is 0.

From (2), we know that the total of those who took one, two, or all three languages is 52. So, this is the total without "none":

52 = 40 + 30 + 20 - (those who took only two of the three languages) - 2(those who took all three languages).

From (1), we know that (those who took all three languages) = 5, so:

52 = 40 + 30 + 20 - (those who took only two of the three languages) - 2(5).

(Those who took only two of the three languages) = 28.

Hope it's clear.

NEYR0N · Answer

at least 1 translates to ALL minus none.

Of the students at a certain school, 40 took French, 30 took Latin, an

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