Everyone at a party is either a man or a woman. After 8 women leave, there are four times as many men as women. After 35 men leave (and the 8 women do not return), there are twice as many women as men.

Quantity A

The number of women originally at the party

Quantity B

15

(A) Quantity A is greater.

(B) Quantity B is greater.

(C) The two quantities are equal.

(D) The relationship cannot be determined from the information given.

Go to it! My answer will appear in the comments.

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## 4 comments:

I'm tired and not thinking totally straight tonight, but here's my attempt at an answer.

Let m = original # of men.

Let w = original # of women.

1st phase: we have m and w.

[All men & women are present.]

2nd phase: we have m and (w - 8).

[Eight women have left.]

3rd phase: we have (m - 35) and (w - 8).

[Thirty-five men have left.]

Given (per what we know of the second phase, and what the word problem tells us):

m = 4(w - 8)

And for the third phase:

(w - 8) = 2(m - 35)

At this point, it's a matter of systems of equations.

m = 4w - 32 (2nd phase)

2m = w + 62 (3rd phase)

Multiply the first equation by 2:

2m = 8w - 64

Match it up with the other equation and solve:

2m = 8w - 64

-(2m = w + 62)

=

0 = 7w - 126

7w = 126

w = 18

The original number of women was 18, so Quantity A is greater.

I'm going with (A).

Yeah, I got A, too, although my process was not nearly as detailed. I just took 15 as a possible number of women at the party, subtracted 8, and multiplied by 4 to get 28 men originally at the party. Since the question then says that 35 men left the party, I knew that the original number of women had to be greater than 15, so the answer was A.

It took me about five times as long to write the above paragraph as it did to work out the answer. I never did figure out how many women were originally at the party.

Yep-- your method's much faster. In this case, plug-and-chug is the way to go.

Indeed you are powerful, as the Emperor has foreseen.

I suck at the maths, but I'm awesome at plugging and chugging.

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