If all 60 members of the junior class joined the Young Democrats, the

Question

If all 60 members of the junior class joined the Young Democrats, the Chess Club, or the Varsity Club, did more than half of the students join more than 1 club?

(1) 31 students did not join either the Chess Club or the Varsity Club.
(2) 28 students joined the Chess Club and 31 students joined the Young Democrats.

HKD1710 · Answer

Total members = YD + CC + VC = 60

stmt-1:

31 did not join the two clubs CC & VC

we are given that ALL 60 joined the club. ZERO left out. Then it means 29 were those who joined CC & VC.

It does not matter if there was an overlap or not because the question asked is "if there was an overlap of TWO GROUP or ALL THREE or both of such overlap then WAS THE COUNT > 30?"

So we clearly know if 31 went to ONLY one group then NOT MORE THAN 30 went to more than 1 group.

Sufficient - The answer is NO.

Stmt-2:

CC = 28
YD = 31

It is a possibility that VC = 28 (went to CC) or VC = 31 (went to YD) or no overlap i.e. VC = 1.

so we are not sure whether there was an overlap of 31 or 28 or none.

Insufficient.

IMO Answer is A.

matthewsmith_89 · Answer

1 is sufficient.
It would be easier to say 1 is sufficient if you know the probability formula
P(YUCUV) = P(Y) + P(C) + P(V) - P(YNC) - P(PNV) - P(CNV) + P(YNVNV)

P(YNC), P(PNV), P(CNV) & P(YNCNV) - more than half of students did not join more than 1 club.

2 is insufficient. We need more information to answer if more than half of the students join more than 1 club.

Answer: A

mohshu · Answer

matthewsmith_89  plz explain how is the formula helpful in answering the question
thanks

KarishmaB · Answer

The wording of statement 1 is a bit clumsy and I doubt one would see this on actual GMAT.

"Not either A or B" is accepted to be "Not A and Not B" though a much better way of writing would be "Neither A nor B".

Total members who joined at least 1 club = 60

(1) 31 students did not join either the Chess Club or the Varsity Club.
31 students, i.e. more than half, did not join 2 of these clubs. So these 31 joined the third club only i.e. the Young Democrats. So actually, less than half of the students joined 2 or more clubs. We can answer the question asked with a definite 'No'.
Sufficient.

(2) 28 students joined the Chess Club and 31 students joined the Young Democrats.
We don't know the overlap here. 
It is possible that 28 joined only Chess club, 31 joined only Young Democrats and the leftover 1 student joined only Varsity club so all 60 joined only 1 club.
It is also possible that 28 joined Chess club and the rest of the 32 joined the Varsity club (making up for the 60 students). Then of these 60, 31 join the Young Democrats so 31 (more than half) students join 2 clubs.
Hence we cannot answer the question.
Not sufficient.

Answer (A)

If all 60 members of the junior class joined the Young Democrats, the

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