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

Question

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.

(1) 50% of the male attendees arrived with a woman.
(2) 25% of the attendees arriving alone were women.

Amit05 · Accepted Answer

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 .

KarishmaB · Answer

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%

mbagal1 · Answer

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%.

anindyat · Answer

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

Mishari · Answer

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  
G2 + B = 40  
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

ncp · Answer

IMHO, B is also sufficient.

See attached image.

My pick is D.

enigma123 · Answer

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.

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.

enigma123 · Answer

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?

KarishmaB · Answer

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

ScottTargetTestPrep · Answer

Solution:

We can let the number of attendees be 100. Thus, there were 40 women and 60 men.

Statement One Alone: 
50% of the male attendees arrived with a woman.

We see that there are 30 men arriving with their 30 female companions. That gives us 60 - 30 = 30 men and 40 - 30 = 10 women arriving alone. Thus, the percentage of people who arrived at the party alone is (30 + 10)/100 = 40/100 = 40%.

Statement one alone is sufficient.

Statement Two Alone: 
25% of the attendees arriving alone were women.

Let the total number of people who arrived alone be n. Since 25% of the guests who arrived alone were women, n/4 women arrived alone, and 3n/4 men arrived alone. Since the number of women who arrived with a man must equal the number of men who arrived with a woman, we must have:

40 - n/4 = 60 - 3n/4

160 - n = 240 - 3n

2n = 80

n = 40

Thus, the percentage of people who arrived alone is 40/100 = 40%.

Statement two alone is sufficient.

Answer: D

Kinshook · Answer

Given: Of all the attendees at a dinner party, 40% were women. Asked: 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. Screenshot 2020-06-25 at 9.23.37 PM.png Since Men with Opp Sex = Women with Opp Sex = 30% SUFFICIENT (2) 25% of the attendees arriving alone were women. Screenshot 2020-06-25 at 9.38.51 PM.png Since Men with Opp Sex = Women with Opp Sex .25x + y = 40% .75x + y = 60% x + 2y = 100% .5x = 20% x = 40% y = 30% SUFFICIENT IMO D

sidship21 · Answer

Hi experts  Bunuel   VeritasKarishma   chetan2u

Just wanted to confirm that this would be a very different question had we been told that a female/male member can arrive either alone, or with a guest of the opposite sex (rather than just that an attendee can arrive either alone or with an attendee of the opposite sex. Both are attendees in case of thhe given question, whereas in my version, there are two groups: members and guests).

The table below illustrates my scenario. Please note that numbers are absolute, not percentages.

_________________________________
________Alone_____With Guests_____Total___
Men _____ 30______ 30______ 60
Women -----5/15______35/25______ 40
Total --------35/45______65/55______ 100

Thank you

KarishmaB · Answer

From what I understand, you are differentiating between two kinds of attendees on the basis of whether they are members or guests (say of a Golf Club which requires membership or you can play as a guest of a member). That would be a different questions. Here. the question talks only about attendees. Everyone who arrives is an attendee.

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

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