BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Equations

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 8
Joined: Fri Aug 02, 2013 6:54 am

Equations

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.
Top
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

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
Top
Master | Next Rank: 500 Posts
Posts: 269
Joined: Thu Sep 19, 2013 12:46 am
Thanked: 94 times
Followed by:7 members

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
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

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
Image
Top
Post new topic Post Reply
• Page 1 of 1