Of 200 members of a certain association

[divya]

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.

[manic]

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.

[RonPurewal]

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

[commit.gmat]

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

Ron,

Also from the given information, GS = 0. Isn't it?

Because, whoever speaks G also speaks E and no one speaks all three languages. Therefore GS should be zero as well, although this doesn't influence the answer.

Is my observation correct?

[RonPurewal]

Ron,

Also from the given information, GS = 0. Isn't it?

Because, whoever speaks G also speaks E and no one speaks all three languages. Therefore GS should be zero as well, although this doesn't influence the answer.

Is my observation correct?

absolutely correct.

you would be a rock star on the lsat (specifically the "logic games" portion of the lsat). too bad you're taking the gmat, heh.

[rachelhong2012]

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

Ron,

With regard to "those who speak German also speak English", it doesn't mean the converse is true right? It doesn't imply that "all of those who speak English also speak German". Just wondering because I saw a similar statement in another GMAT prep problem and it took me some time to figure it out because of the logic.

Thanks!

[tim]

that is correct. in fact, one of the common traps on the GMAT (especially in CR) is that they give you a true statement and try to get you to infer the converse, which is not necessarily true..

[rachelhong2012]

that is correct. in fact, one of the common traps on the GMAT (especially in CR) is that they give you a true statement and try to get you to infer the converse, which is not necessarily true..

Thanks again Tim :)

[tim]

:)