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In a party, 70% of the people like at least one of two type of drinks: 26 Dec 2015, 03:48
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In a party, 70% of the people like at least one of two type of drinks: hard drink and soft drink. Is the number of people who like both the drinks more than those who don't like either of the two drinks?

(1) The number of people who like soft is 2/5th of those who like only hard drinks.

(2) The number of people who like exactly one drink is 2/3 times of those who like neither.

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In a party, 70% of the people like at least one of two type of drinks: 26 Dec 2015, 04:07
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jyotibrata
In a party, 70% of the people like at least one of two type of drinks: hard drink and soft drink. Is the number of people who like both the drinks more than those who don't like either of the two drinks?

(1) The number of people who like soft is 2/5th of those who like only hard drinks.

(2) The number of people who like exactly one drink is 2/3 times of those who like neither.
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hi,
the Q can be best solved with the Venn diag taking a circle eac for soft and hard with overlap..
i'll try to explain in words..
let only soft drinkers=S..
let only hard drinkers=H..
both drinks =B...
neither=N..
the Q gives us that S + H +B=70%=7/10..
so N=3/10..
we are asked whether B>N..

lets see the statements..
(1) The number of people who like soft is 2/5th of those who like only hard drinks.
it means.. S+B=H*2/5..
add H to both sides.. S+B+H=H*2/5 +H=7H/5=7/10..
so H=1/2... S+B=2/5*H=(2/5)*(1/2)=1/5..
therefore even if we maximize B by making S as 0.. B<N..
so answer to "whether B>N.." is NO... suff

(2) The number of people who like exactly one drink is 2/3 times of those who like neither.
S+H=2/3 *N.. but N=3/10...
so S+H=2/3 * 3/10=1/5
But S + H +B=70%=7/10..
so B=7/10-1/5=5/10=1/2..
so B>N suff.
ans D..

Note:- here each statements gives oposite answer. Normally in GMAT, the two statement give th esame answer
S+H=7/10
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In a party, 70% of the people like at least one of two type of drinks: 31 Dec 2015, 02:47
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jyotibrata
In a party, 70% of the people like at least one of two type of drinks: hard drink and soft drink. Is the number of people who like both the drinks more than those who don't like either of the two drinks?

(1) The number of people who like soft is 2/5th of those who like only hard drinks.

(2) The number of people who like exactly one drink is 2/3 times of those who like neither.
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This question is not gmat-like. both FS are giving opposite answers, which isn't the case in GMAT.
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In a party, 70% of the people like at least one of two type of drinks: 05 Jun 2016, 02:44
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In a party, 70% of the people like at least one of two type of drinks: hard drink and soft drink. Is the number of people who like both the drinks more than those who don't like either of the two drinks?

(1) The number of people who like soft is 2/5th of those who like only hard drinks.

(2) The number of people who like exactly one drink is 2/3 times of those who like neither.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements (1) and (2) TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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In a party, 70% of the people like at least one of two type of drinks: 05 Jun 2016, 02:52
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We know that 70% of the people like at least one of the two drinks that means rest 30% like none. The question is to know whether the number of people who like both more than those who like none i.e. 30%. The question becomes: is the number of people who like both > 30%?

We want to know if b > 30%

Statement (1). The number of people who like soft drink is 2/5th of those who like only hard drink i.e. a + b = 2/5c it implies a + b + c = 2/5 c + c = 7/5c which should be 70%. Hence, c = 50% i.e. the number of people who like only hard drink is 50% and as the number of people who like at least one drink is 70%, the number of people who like both i.e. b can be maximum 20%.

Thus, b cannot be greater than 30% i.e. number of people who like both is less than those who like none. Thus Statement (1) is sufficient alone.

Statement (2). The number of people who like exactly one drink is 2/3 times of those who like none which means a + c = 2/3 of 30% it implies a + c = 20% and as we know a + b + c = 70% we get b = 50% which is more than 30%.

Thus the number of people who like both the drinks is more than those who like none of the drinks. So Statement (2) is sufficient alone.

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In a party, 70% of the people like at least one of two type of drinks: 05 Jun 2016, 03:18
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mukulgupta5
We know that 70% of the people like at least one of the two drinks that means rest 30% like none. The question is to know whether the number of people who like both more than those who like none i.e. 30%. The question becomes: is the number of people who like both > 30%?

We want to know if b > 30%

Statement (1). The number of people who like soft drink is 2/5th of those who like only hard drink i.e. a + b = 2/5c it implies a + b + c = 2/5 c + c = 7/5c which should be 70%. Hence, c = 50% i.e. the number of people who like only hard drink is 50% and as the number of people who like at least one drink is 70%, the number of people who like both i.e. b can be maximum 20%.

Thus, b cannot be greater than 30% i.e. number of people who like both is less than those who like none. Thus Statement (1) is sufficient alone.

Statement (2). The number of people who like exactly one drink is 2/3 times of those who like none which means a + c = 2/3 of 30% it implies a + c = 20% and as we know a + b + c = 70% we get b = 50% which is more than 30%.

Thus the number of people who like both the drinks is more than those who like none of the drinks. So Statement (2) is sufficient alone.

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