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

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Director
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Of all the attendees at a dinner party, 40% were women. If [#permalink]  03 Nov 2011, 14:19
00:00

Difficulty:

5% (low)

Question Stats:

24% (01:01) correct 76% (01:03) wrong based on 21 sessions
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.
[Reveal] Spoiler: OA

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610

Manager
Joined: 19 Oct 2011
Posts: 87
Followers: 0

Kudos [?]: 17 [0], given: 1

Re: DS - Solo + Pair [#permalink]  03 Nov 2011, 17:24
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.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
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Location: Pune, India
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Kudos [?]: 4781 [1] , given: 163

Re: DS - Solo + Pair [#permalink]  03 Nov 2011, 23:13
1
KUDOS
Expert's post
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%
_________________

Karishma
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Senior Manager
Joined: 18 Sep 2009
Posts: 373
Followers: 3

Kudos [?]: 56 [0], given: 2

Re: DS - Solo + Pair [#permalink]  04 Nov 2011, 10:30
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.
Director
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 563
Location: United Kingdom
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 13

Kudos [?]: 361 [0], given: 217

Re: DS - Solo + Pair [#permalink]  04 Nov 2011, 10:54
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?
_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610

Manager
Joined: 28 Jul 2011
Posts: 114
Followers: 0

Kudos [?]: 1 [0], given: 6

Re: DS - Solo + Pair [#permalink]  04 Nov 2011, 10:56
Missed B . Thanks for the explanations.
Director
Status: Preparing for the 4th time -:(
Joined: 25 Jun 2011
Posts: 563
Location: United Kingdom
GMAT Date: 06-22-2012
GPA: 2.9
WE: Information Technology (Consulting)
Followers: 13

Kudos [?]: 361 [0], given: 217

Re: DS - Solo + Pair [#permalink]  04 Nov 2011, 11:12
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

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 4668
Location: Pune, India
Followers: 1073

Kudos [?]: 4781 [1] , given: 163

Re: DS - Solo + Pair [#permalink]  05 Nov 2011, 02:31
1
KUDOS
Expert's post
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
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

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Re: DS - Solo + Pair   [#permalink] 05 Nov 2011, 02:31
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