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# Of all the attendees at a dinner party, 40% were women. If

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SVP
Joined: 24 Aug 2006
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Of all the attendees at a dinner party, 40% were women. If [#permalink]  14 Nov 2006, 13:03
Of all the attendees at a dinner party, 40% were women. If each attendee arrived at the party either alone or with another attendee of the opposite sex, what percentage of the total number of attendees arrived at the party alone?

(1) 50% of the male attendees arrived with a woman.

(2) 25% of the attendees arriving alone were women.

I get D
Manager
Joined: 29 Aug 2006
Posts: 157
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Lets assume 100 attended the party.
Since, 40% are women, women=40 and men=60.

S1 says that 50% of the male arrived with a women.
Which means 30 men arrived with a women and 30 didnt.

Since total number of women attending are 40 and 30 of them came with men, only 10 came alone.

So 10 women and 30 men , which is 40% arrived alone.

S2 says 25% of the lone attendees were women.
Let that nbr be x
so nbr of women who've come with men is 40-x.
From among 60 men, 40-x have come with a woman and 60-(40-x) have come alone.

x=0.25(x+20+x)
x=10

hence suff

Hence D.

Nice one!...I assumed A intially..have to be careful of such trciky ones in the exam.
Senior Manager
Joined: 08 Jun 2006
Posts: 341
Location: Washington DC
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D
This is a good one..The key point in S2 is
Number of men came together = number of women came together
GMAT Instructor
Joined: 04 Jul 2006
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Re: Dinner Party [#permalink]  14 Nov 2006, 15:04
kidderek wrote:
Of all the attendees at a dinner party, 40% were women. If each attendee arrived at the party either alone or with another attendee of the opposite sex, what percentage of the total number of attendees arrived at the party alone?

(1) 50% of the male attendees arrived with a woman.

(2) 25% of the attendees arriving alone were women.

60% of the attendees were men, so if the number of attendees was n, the number of men was 0.6n.

(1) Half of the 0.6n male attendees arrived with a women, so the number of women was 0.3n+ the number of women who arrived alone. Thus the number of women who arrived alone was n-0.3n-0.6n=0.1n, and the number of people who arrived alone was 0.1n (women)+0.3n (men), i.e 40% of the total.

(1) is sufficient

(2) If k is the number of women who arrived alone, 3k men arrived alone. The rest of the people arrived with a member of the opposite sex, so the number of men-the number of women=2k=0.2n, where n is the number of attendees. Thus 4k (the number of people who arrived alone) is 0.4n, 40% of the total

(2) is sufficient

D
Re: Dinner Party   [#permalink] 14 Nov 2006, 15:04
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