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by GMATGuruNY » Sun Sep 21, 2014 7:25 am
What is the value of y?

(1) 3|x2 - 4| = y - 2

(2) |3 - y| = 11
Statement 1: 3|x² - 4| = y - 2.
If x=0, then y=14.
If x=2, then y=2.
Since both y=14 and y=2 are possible, insufficient.

Statement 2: |3 - y| = 11.
Solving 3-y = 11 and 3-y = -11, we get:
y = -8 or y=14.
Since both y = -8 and y=14 are possible, insufficient.

Statements 1 and 2 combined:
Statement 2 requires that y = -8 or y=14.
Plugging y = -8 into 3|x² - 4| = y - 2, we get:
3|x² - 4| = -8-2
3|x² - 4| = -10
Not possible, since the left side cannot yield a negative result.
Thus, y=14.
Sufficient.

The correct answer is C.
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by j_shreyans » Fri May 29, 2015 8:02 am
Hi ,

Whats wrong with the below method.

Statement 1: 3|x^2-4|=y-2

if i solve this

3x^2-12=y-2
3x^2-y=10 ..............(1)

3|x^2-4|=y-2

so 3x^2-12=-y+2

3x^2+y=14 .............(2)

from 1 and 2

x=2 & -2

if we put x in 3|x^2-4|=y-2

so we will get y = 2

Please advise and correct me.

Thanks,
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by [email protected] » Fri May 29, 2015 9:27 am
Hi j_shreyans,

The equation that we're given in Fact 1 has an INFINITE number of solutions, so part of the problem is that you're focusing on just X=2 and X=-2.

As it stands, BOTH of those values of X lead to Y equaling 2, which does NOT fit the equation given in Fact 2. This is a wordy way of saying that you're discussing numbers that are NOT solutions to the system of equations that we're given.

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