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equation with absolutes

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by Brent@GMATPrepNow » Sat Jan 10, 2009 3:30 pm
If x + |x| + y = 7 and x + |y| – y = 6, then x+y=?
a. 1
b. 2
c. 3
d. 4
e. 5
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by cramya » Sat Jan 10, 2009 3:37 pm
C) 3

2x+y = 7
x-2y=6

y=-1 x=4
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Re: equation with absolutes

by logitech » Sat Jan 10, 2009 3:44 pm
Brent Hanneson wrote:If x + |x| + y = 7 and x + |y| – y = 6, then x+y=?
a. 1
b. 2
c. 3
d. 4
e. 5
X:Y pair can be (+,+), (-,-), (+,-) or (-,+)

if you add two equations we have

2x+|x|+|y| = 13

if you subtract two equations we have

2y + |x|-|y| = 1

so this two equations give:

x+y=1

and x=6 and y =-5

Do I miss something here ?
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by Brent@GMATPrepNow » Sat Jan 10, 2009 5:06 pm
X:Y pair can be (+,+), (-,-), (+,-) or (-,+)
This part is correct.
From here we need to try each case and see which one avoids contradictory results.

Example, case 1 (+,+):
If y is positive then x + |y| – y = 6 simplifies to be x=6 (since |y|-y = 0 for all positive values of y.
When we plug x=6 into the equation x + |x| + y = 7, we get y=-5
But this can't be since this case assumes that y is positive.
Contradictory result.

Each case except "x is positive and y is negative" will yield a contradictory result (or solution that does not work for both equations).

The answer is C
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by logitech » Sat Jan 10, 2009 5:10 pm
Got it! Thanks!
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