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

Redeem

Absolute values...

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 103
Joined: Sat Jun 02, 2012 9:46 pm
Thanked: 1 times

Absolute values...

by topspin360 » Wed Feb 26, 2014 4:51 pm
Can someone please help solve..

If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x - 12y = 0

(2) |x| - |y| = 16

A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C) Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are NOT sufficient.

Thanks
Top
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 1248
Joined: Thu Mar 29, 2012 2:57 pm
Location: Everywhere
Thanked: 503 times
Followed by:192 members
GMAT Score:780

by Bill@VeritasPrep » Wed Feb 26, 2014 7:06 pm
I started with 2. Lots of different values will make that true. x=24 and y=8 , for instance, or x=24 and y=-8. Not sufficient to find the product of x and y.

We can manipulate 1 to give us 4x = -12y, or x = -3y. We can then plug into the equation from the stem:

|-3y| + |y| = 32

This will give us two values for each variable. You could have y=8 and x=-24, or you could have y=-8 and x=24. Each pair of values will give you the same product, so this is sufficient on its own.
Join Veritas Prep's 2010 Instructor of the Year, Matt Douglas for GMATT Mondays

Visit the Veritas Prep Blog

Try the FREE Veritas Prep Practice Test
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Wed Feb 26, 2014 9:06 pm
Hi topspin360,

Since this DS question is built around Absolute Values, we'll have to keep track of positive AND negative possibilities.

We're told that X and Y are non-0 integers and |X| + |Y| = 32. We're asked for the value of XY.

Again, since X and Y could be positive OR negative, then XY might be a positive OR negative answer.

Fact 1: -4X - 12Y = 0

As a general rule, it's a good idea to simplify your "math" any time there's a possibility to do so.

-X - 3Y = 0

-X = 3Y

This tells us that ONE of the variables is positive and ONE is negative. If we ignore the "signs" for a moment, it also tells us that one number is 3 TIMES the other. Combined with the information from the prompt, we have...

(Number) + (3)(Number) = 32

8 and 24 are the only options. HOWEVER, we have to account for the fact that one of those numbers is POSITIVE and one is NEGATIVE.

This gives us....
8 and -24 and the answer to the question is -192
OR
-8 and 24 and the answer to the question is -192

Fact 1 is SUFFICIENT

Fact 2: |X| - |Y| = 16

Using some of the deductions from Fact 1, we know that 24 and 8 work perfectly here, but we don't know if we're really dealing with + or - 24 NOR + or - 8

The answer to the question could be -192 OR +192
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Feb 27, 2014 3:07 am
If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x - 12y = 0

(2) |x| - |y| = 16
Statement 1: -4x - 12y = 0.
-4x = 12y
x = -3y.

Substituting x= -3y into |x| + |y| = 32, we get:
|-3y| + |y| = 32
3|y| + |y| = 32
4|y| = 32
|y| = 8
y = 8 or y = -8.

If y=8, then x = -3*8 = -24, and xy = (-24)(8) = -192.
If y= -8, then x = -3*(-8) = 24, and xy = -8*24 = -192.
Since xy = -192 in each case, SUFFICIENT.

Statement 2: |x| - |y| = 16.
Adding this equation to |x| + |y| = 32, we get:
2|x| = 48.
|x| = 24
x=24 or x = -24.

This means:
24 + |y| = 32
|y| = 8.
y = 8 or y = -8.

If x=24 and y=8, then xy = 192.
If x= -24 and y=8, then xy = -192.
Since xy can be different values, INSUFFICIENT.

The correct answer is A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Post new topic Post Reply
• Page 1 of 1