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Problem

by ivonneqf » Thu Feb 07, 2013 3:45 am
Hi guys,

help me with this one:

Q: How many more men than women are in the room?
(1) There is a total of 20 women and men in the room.
(2) The number of men in the room equals the square of the number of women in the room.

not sure about the answer...

Thanks
I
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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Feb 07, 2013 4:34 am
ivonneqf wrote:Hi guys,

help me with this one:

Q: How many more men than women are in the room?
(1) There is a total of 20 women and men in the room.
(2) The number of men in the room equals the square of the number of women in the room.
Statement 1: M+W = 20.
No way to determine the value of M-W.

Statement 2: M = W².
No way to determine the value of M-W.

Statements combined:
Substituting M=W² into M+W=20, we get:
W² + W = 20.
Make a list of possible values for W and W² and look for a combination with a sum of 20:
W=1, W²=1
W=2, W²=4
W=3, W²=9
W=4, W²=16.
Since 4+16 = 20, W=4, implying that M=W²=4²=16.
Thus, M-W = 16-4 = 12.
SUFFICIENT.

The correct answer is C.

When the statements are combined, we could also use algebra:
W² + W = 20
W² + W - 20 = 0
(W+5)(W-4) = 0
W=-5 or W=4.
Since the number of women must be positive, W=4.
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by Ian Stewart » Thu Feb 07, 2013 5:10 am
ivonneqf wrote:Hi guys,

help me with this one:

Q: How many more men than women are in the room?
(1) There is a total of 20 women and men in the room.
(2) The number of men in the room equals the square of the number of women in the room.

not sure about the answer...

Thanks
I
Neither statement is sufficient alone. Together, if there are w women, there are w^2 men, and from Statement 1 we know that w^2 + w = 20. Clearly as w gets bigger, so does w^2 + w, so there can only be one positive integer solution to this equation and the answer is C. It's a DS question, so there's no need to bother finding the solution.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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