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by nakul17 » Wed Oct 16, 2013 2:25 am
If there are x men and y women in a choir, and there are z more men than there are women in that choir, what is z?

(1) x2 - 2xy + y2 - 9 = 0

(2) x2 + 2xy + y2 - 225 = 0


Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.
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Source: — Data Sufficiency |
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by theCodeToGMAT » Wed Oct 16, 2013 2:36 am
z = x - y

Statement 1:
(x-y)^2 = 9
x - y = 3
So, z = 3
SUFFICIENT

Statement 2:
(x+y)^2 = 225
x + y = 15
we can have many combinations to reach sum 15
INSUFFICIENT

Answer [spoiler]{A}[/spoiler]
R A H U L
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by mevicks » Wed Oct 16, 2013 6:05 am
nakul17 wrote:If there are x men and y women in a choir, and there are z more men than there are women in that choir, what is z?
(1) x2 - 2xy + y2 - 9 = 0
(2) x2 + 2xy + y2 - 225 = 0
Given:
y + z = x
z = x - y

z more men than there are women --> (x > y)
(x - y) > 0
z > 0

Q: z = ?

St1: x² - 2xy + y² - 9 = 0
(x - y)² = 3² ... Factorize
z² = 3²
z = ±3
z = 3 ... z > 0
SUFFICIENT

St2: x² + 2xy + y² - 225 = 0
(x + y)² = 15² ... Factorize
x + y = ±15
x + y = 15 ... sum of people cant be negative
we know that x > y but we can test different numbers to add up to 15
x = 8, y = 7; x = 10, y = 5 ...
INSUFFICIENT

Answer A

Regards,
Vivek
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by Brent@GMATPrepNow » Wed Oct 16, 2013 8:17 am
I love this question, because it requires test-takers to fully appreciate what the target question is asking.
So, rather than ask "What is the value of z?", we must first recognize that this is the same as asking "What is the value of x - y?"
SOME students will look at this rephrased target question and conclude that, in order to answer it, they must find the individual values of x and y, but this is incorrect. We need not find the individual values of x and y. We need only find the value of x-y.

So, when we get to statement 1 and conclude that x - y = 3, we must recognize that we now have enough information to answer the target question (even though we cannot determine the individual values of x and y)

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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