Of 200 members of a certain association each member who speaks German also speaks English and 70 of the members speak only Spanish. If no members speak all 3 languages; how many members speak 2 of 3 languages.

A. 60 of the members speak only English
B. 20 of the members do not speak any of the three languages.


DS question.

Answer is C.

I got this question in my first attempt.

But, the key to the question is that those who speak German also speak English, hence German only speakers = 0. We already know values for the rest of the variables from both statements combined, hence C is the solution and not E.

more specifically:

there are eight subsets:
none
E only
G only
S only
ES
EG
GS
EGS

let's fill in the list with the information that we already have from the problem:

none = 20 (from statement 2)
E only = 60 (from statement 1)
G only = 0 (because they all speak english too)
S only = 70 (given)
ES = _______
EG = _______
GS = _______
EGS = 0 (given)

the only blanks combine to give the desired quantity. we can't find the values of the individual blanks, but we don't care; all that matters is their sum, which is easily found by subtracting 20, 60, and 70 (as well as the two 0's, if you want) from the total of 200. there's no need to perform this calculation, because it's data sufficiency and we know there's going to be a unique numerical answer.

ans = c