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

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Manager
Joined: 04 Nov 2006
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Location: California
Of all the attendees at a dinner party, 40% were women. If  [#permalink]

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20 Dec 2006, 14:03
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Difficulty:

95% (hard)

Question Stats:

30% (02:30) correct 70% (02:28) wrong based on 909 sessions

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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.
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Re: DS - Solo + Pair  [#permalink]

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04 Nov 2011, 00:13
4
2
enigma123 wrote:
Of all the attendees at a dinner party, 40% were women. If each attendee arrived at a party either alone of 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 attendes arriving alone were women.

This is how I am trying to solve this. Can someone please explain where I am getting it wrong ?

Considering statement 1
Solo Pairs Total
Men 30 30 60
Women 10 30 40
Total 40 60 100

If 30 men come in pairs then they have to be paired with 30 women. And therefore total people arrived solo are 40 and therefore this statement is sufficient.

Considering Statement 2 --> I am really struggling to solve this.

You got statement 1 so I will ignore that.
Statement 2: 25% of the attendes arriving alone were women.
To make calculations easier, lets assume that total number of people is 100. Then total number of women = 40 and total number of men = 60

Say, the number of alone women = x
Since this is 25% of total alone people, 3x is the number of alone men.

Now, total number of women with men = 40 - x
Then total number of men with women = 40 - x

(40-x)*2 + x + 3x = 100
x = 10
Women arriving alone = 10. men arriving alone = 30
% of people arriving alone = 40%
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Karishma
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Joined: 09 Aug 2006
Posts: 485

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23 Dec 2006, 06:49
11
3
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 .
##### General Discussion
Intern
Joined: 17 Dec 2006
Posts: 22

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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
Director
Joined: 28 Dec 2005
Posts: 876

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20 Dec 2006, 15:06
2
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%.
Senior Manager
Joined: 08 Jun 2006
Posts: 308
Location: Washington DC

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20 Dec 2006, 15:12
8
1
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
Director
Joined: 30 Nov 2006
Posts: 548
Location: Kuwait

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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

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
Intern
Joined: 17 Dec 2006
Posts: 22

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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
Director
Joined: 28 Dec 2005
Posts: 876

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21 Dec 2006, 09:26
gmat_enthus wrote:
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

Yes, you are right, read the question again.
I read the question to be 25% of the women attending were alone.
SVP
Joined: 08 Nov 2006
Posts: 1511
Location: Ann Arbor
Schools: Ross '10

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23 Dec 2006, 02:00
6
2
IMHO, B is also sufficient.

See attached image.

My pick is D.
Attachments

B.jpeg [ 18.5 KiB | Viewed 15098 times ]

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

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03 Nov 2011, 15:19
Of all the attendees at a dinner party, 40% were women. If each attendee arrived at a party either alone of 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 attendes arriving alone were women.

This is how I am trying to solve this. Can someone please explain where I am getting it wrong ?

Considering statement 1
Solo Pairs Total
Men 30 30 60
Women 10 30 40
Total 40 60 100

If 30 men come in pairs then they have to be paired with 30 women. And therefore total people arrived solo are 40 and therefore this statement is sufficient.

Considering Statement 2 --> I am really struggling to solve this.
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Manager
Joined: 19 Oct 2011
Posts: 64
Re: DS - Solo + Pair  [#permalink]

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03 Nov 2011, 18:24
enigma123 wrote:
Of all the attendees at a dinner party, 40% were women. If each attendee arrived at a party either alone of 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 attendes arriving alone were women.

This is how I am trying to solve this. Can someone please explain where I am getting it wrong ?

Considering statement 1
Solo Pairs Total
Men 30 30 60
Women 10 30 40
Total 40 60 100

If 30 men come in pairs then they have to be paired with 30 women. And therefore total people arrived solo are 40 and therefore this statement is sufficient.

Considering Statement 2 --> I am really struggling to solve this.

suppose there are x people in total and y people arrived alone. according to (2), women alone are 0.25y, then women with men are 0.4x-0.25y. men alone are 0.75y, men with women are 0.6x-o.75y. The two should be equal, so we can solve the equation and derive that y=0.4x, so (2) is sufficient.
Senior Manager
Joined: 18 Sep 2009
Posts: 256
Re: DS - Solo + Pair  [#permalink]

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04 Nov 2011, 11:30
1
stmnt (2) tells same thing as stmnt (1)

according to the questiom we know that attendes come alone or with opposite sex.

according to the stmnat (2) 25% came alone.
let assume that
women =40, men=60.
40*1/4=10 (came alone).
Remaining women 40-10= 30 should come with opposite sex i.e men.
so number of men come with pairs are 30.
number of men came alone 60-30=30.
% of atenddes came alone are men (30)+ women (10)=40.
Senior Manager
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Re: DS - Solo + Pair  [#permalink]

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04 Nov 2011, 11:54
Sorry Karishma - But I am struggling to understand how did you get

Since this is 25% of total alone people, 3x is the number of alone men.

Do you mind letting me know please?
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E.

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Manager
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Re: DS - Solo + Pair  [#permalink]

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04 Nov 2011, 11:56
Missed B . Thanks for the explanations.
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Re: DS - Solo + Pair  [#permalink]

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04 Nov 2011, 12:12
Ok - I have tried it another way. Please let me know if my approach is corrrect.

Women Man Total

Solo 6 18 24

Pair y Y

Total 0.4X 0.6X
X

Let say total solo people = 24 & total people = x

25% of solo people are women i.e. 6 women and 18 men are single.

Let the women in pair be y so man will be y as well.

Two equations are

6+y=0.4x
18+y = 0.6x

x = 60
Single people = 24/60*100= 40%
_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
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Joined: 16 Oct 2010
Posts: 9433
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Re: DS - Solo + Pair  [#permalink]

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05 Nov 2011, 03:31
1
enigma123 wrote:
Sorry Karishma - But I am struggling to understand how did you get

Since this is 25% of total alone people, 3x is the number of alone men.

Do you mind letting me know please?

We are given that 25% of people who came alone were women. So 75% of people who came alone were men. So number of men who came alone is three times the number of women who came alone (75% is 3 times 25%).
Since we are assuming that number of women who came alone = x
number of men who came alone will be = 3x
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Re: Of all the attendees at a dinner party, 40% were women. If  [#permalink]

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04 Jun 2013, 20:42
what if party had children as well ?
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Re: Of all the attendees at a dinner party, 40% were women. If  [#permalink]

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20 Mar 2015, 14:28
1
Here is a way to think about (2). The number of women arriving alone and the number of men arriving alone must be equal since anyone arriving with a partner must be someone of the opposite sex.

Assume there is 100 people. Therefore, there are 40 women and 60 men. Which number could I subtract from both women and men to leave a ratio of 1 woman to 3 men (because alone women represents 25% of alone people)? If I subtract 10 from each, I get 30 women and 50 men. If I subtract 20 from each, I get 20 women and 40 men. If I subtract 30 from each, I get 10 women and 30 men -- bingo.
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Re: Of all the attendees at a dinner party, 40% were women. If  [#permalink]

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28 Jul 2015, 20:49
This is how I did it. Please Correct me if I am wrong.

Let say, total number of people are p. And, total alone people be A.

So we need to find A/p

Women 40p/100 Men=60p/100

1. 1/2 of 60p/100 arrived with a women,so 30p/100 arrived with women, that means (40p/100-30p/100) are alone women and 30p/100 are alone men.

Alone= 10p/100 + 30p/100

2. A/4= women and 3/4A=Men

So 40p/100-A/4=60P/100-3A/4 , that is they should come in pairs.
2A/4=20P/100

So, in both cases we get the ratio of A/P

Hence, D

Please let me know in case I am wrong.
Re: Of all the attendees at a dinner party, 40% were women. If   [#permalink] 28 Jul 2015, 20:49

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