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

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

20 Dec 2006, 14:03

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20 Dec 2006, 14:51

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.

40%T Women so 60%T Men

1) => 30%T men came with 30%T women => 10%T women and 30%T men came alone = 40%

2) 25% of attendeed who arrived alone were women => 75% of them were men. So i X arrived alone
0.25X Women
0.75X Men

We need to find X/T, but this info is not sufficient.

IMO A
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20 Dec 2006, 15:06

I get D.

A - same as above.

B:

Let X be the total number of people

0.4X --> number of women

0.25* 0.4X = 0.1 X -> number of women alone

=> 0.3X --> number of women with partner.

To find total who came with partner, it is essentially double 0.3X, so 0.6X or 60%. Thus people who came alone = 40%.

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20 Dec 2006, 15:12

Going for D

consider total = 100 people
From 2)
x is the number of alone people
alone women = x/4
alone men = 3x/4

From the question we get 40 women and 60 men.

Number of men together = number of women together
=> 40 - x/4 = 60 -3x/4
=> x = 40

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20 Dec 2006, 16:47

I remember the kaplan equation for groups
T = G1 + G2 - B
T: total
G1: group 1
G2: group 2
B: both (overlap between G1 and G2)

Now, given in the question
G1 (men) , G2 ( women)
G1 + B = 60 [ eq. 1]
G2 + B = 40 [ eq. 2]
T = 100 ( assume )

Statement 1: B = 0.5 G1
-----------------------------
you already have two equations with three unknowns: G1,G2 and B
with this third equation you can solve for all variables
The question asks for (G1+G2)/T

Statement 2: G2/(G1+G2) = 0.25
---------------------------------------
Also a third equation that lets you solve for G1,G2 and B

So, my answre is D

Although i didn't solve for the variables or get to the solution, but the quick analysis let me answer the question really fast
P.S. this is a data sufficiency question

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21 Dec 2006, 09:11

i am still with A

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

This says 25% of attendees arriveing alone and NOT 25% of total attendees.

Hence the assumption above that alone women = 0.25* Total attendees is incorrect
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21 Dec 2006, 09:26

gmat_enthus wrote:

Yes, you are right, read the question again.
I read the question to be 25% of the women attending were alone.

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23 Dec 2006, 02:00

IMHO, B is also sufficient.

See attached image.

My pick is D.

Attachments

B.jpeg [ 18.5 KiB | Viewed 524 times ]

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23 Dec 2006, 06:49

Me for D ..

This is How :

As per the question, this is what is given :
_________________________________
________Alone_____With_____Total___
Men________________________60
Women ____________________ 40
Total _____________________ 100

Statement -1: 50% i.e 1/2 of the males arrived with a woman i.e 30 men with 30 women. Which implies 10 women were alone and 30 men were alone.

_________________________________
________Alone_____With_____Total___
Men _____ 30______ 30______ 60
Women -----10______30______ 40
Total --------40______60______ 100

Hence statement 1 is suffiecient to answer the Question.

Statement 2 : 1/4th of the alone were women. Let the alone be x. Hence alone women .25x.

_________________________________
________Alone_____With___________Total___
Men .75x ______ 60-0.75x ______ 60
Women .25x ______ 40-0.25x ______ 40
Total x__ ______ _______ ______ 100

At 1st glance it looks impossible to solve this. But here to go .

Since men and women together come in pairs hence no of men coming together will be equal ti women coming together.

hence : 60 - 0.75x = 40-0.25x
20 = 0.50x
x = 40
And we can find fill the remaining table..

Hence St2 is also suff..

Hence D .

[#permalink] 23 Dec 2006, 06:49

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

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

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