Absolute values...

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topspin360: Master | Next Rank: 500 Posts; Posts: 103; Joined: Sat Jun 02, 2012 9:46 pm; Thanked: 1 times

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

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Source: Beat The GMAT — Data Sufficiency | Wed Feb 26, 2014 4:51 pm

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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.

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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

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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.

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