AAPL 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 GMAT, 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.

The OA is 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.

Hence, the correct answer is D.

Has anyone another strategic approach to solve this DS question? Regards!

Say the percentage of men attending alone = m, the percentage of women attending alone = w, and the percentage of partners attending together = b.

Thus, 100 = m + w + b; note that among partners, b/2 would be men and b/2 would be women.

Given: w + b/2 = 40;

=> m + b/2 = 100 - 40 = 60

From w + b/2 = 40 and m + b/2 = 60, we get m - w = 20

We have to get the value of (m + w).

Let's take each statement one by one.

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

50% of (m + b/2) = b/2

=> b = 2m

From b = 2m, and m + b/2 = 60, we have m = 30. From m = 30 and m - w = 20, we have w = 10.

Thus, m + w = 30 + 10 = 40. Sufficient.

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

25% of (m + w) = w

=> m = 3w

From m = 3w and m - w = 20, we have m = 30 and w = 10.

Thus, m + w = 30 + 10 = 40. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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AAPL wrote: ↑

Thu Jun 14, 2018 7:00 am

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 GMAT, 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.

The OA is D.

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.

So we have 30 men arriving with women. That gives us 60 - 30 = 30 men and 40 - 30 = 10 women arriving alone. So 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 4n. Since 25% of the guests who arrived alone were women, 4n*(0.25) = n women arrived alone and 4n - n = 3n 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 = 60 - 3n

3n - n = 60 - 40

2n = 20

n = 10

Thus, 4n = 4(10) = 40 people arrived alone, and the percentage of people who arrived alone is 40/100 = 40%.
Statement two alone is sufficient.

Answer: D