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DS Absolute value equation: What is the value of y?

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goenkavivek
 Post subject: DS Absolute value equation: What is the value of y?
 Post Posted: Sun Jul 17, 2011 2:54 pm 
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Students


Posts: 2
What is the value of y?

(1) 3|x^2 – 4| = y – 2

(2) |3 – y| = 11

May I please request for your help with this. Thanks a million!

This is what I tried to do:

(1) INSUF because has another variable X

(2) Within the absolute value bracket, the sign can be changed, thus the eqn becomes
|y - 3| = 11

Case 1: Y-3>0

Y-3=11
Y=14

Case 2:
Y-3<0
Y-3=-14
Y= -11

Insuff

So, I chose (E)

How wrong is wrong?
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RonPurewal
 Post subject: Re: DS Absolute value equation: What is the value of y?
 Post Posted: Wed Jul 20, 2011 5:30 am 
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ManhattanGMAT Staff


Posts: 7146
first, you made a calculation mistake -- i've fixed it in blue:

goenkavivek wrote:
What is the value of y?

(1) 3|x^2 – 4| = y – 2

(2) |3 – y| = 11

May I please request for your help with this. Thanks a million!

This is what I tried to do:

(1) INSUF because has another variable X

(2) Within the absolute value bracket, the sign can be changed, thus the eqn becomes
|y - 3| = 11

Case 1: Y-3>0

Y-3=11
Y=14

Case 2:
Y-3<0
Y-3=-11
Y= -8

Insuff

So, I chose (E)

How wrong is wrong?


you didn't think about combining the two statements -- apparently, you went straight to (e) from figuring out that the two individual statements weren't sufficient.
BUT
from statement (1), notice that y = 3(absolute value) + 2. this means that y is AT LEAST 0 + 2 = 2, because absolute values can't be negative.
in combination with statement (2), this rules out the case y = -8, and so you only have y = 14 left.

therefore (c)
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aps_asks
 Post subject: Re: DS Absolute value equation: What is the value of y?
 Post Posted: Sun Mar 25, 2012 1:12 pm 
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Forum Guests


Posts: 134
Hi Ron ,

How to solve Statement 1) in an algebraic way and not consider
that |x2 – 4| is positive.

Please let me know your comments.
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RonPurewal
 Post subject: Re: DS Absolute value equation: What is the value of y?
 Post Posted: Mon Mar 26, 2012 7:41 am 
Offline
ManhattanGMAT Staff


Posts: 7146
aps_asks wrote:
Hi Ron ,

How to solve Statement 1) in an algebraic way and not consider
that |x2 – 4| is positive.

Please let me know your comments.


you can't!

basically, what you are asking me amounts to the following: “how can i use this absolute value, while ignoring the most salient property of absolute value?”
you have to consider the fact that absolute values are positive; that is the primary defining characteristic of absolute values, so you're not going to get around it with any neat little tricks.

it's possible to use algebra to split this equation up into two or more sub-equations, but to do so would be ultimately pointless -- it would be substantially more work, and you would still need to realize that the absolute-value expression is positive in order to do it.
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aps_asks
 Post subject: Re: DS Absolute value equation: What is the value of y?
 Post Posted: Mon Apr 02, 2012 11:48 pm 
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Forum Guests


Posts: 134
Thanks Ron !
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RonPurewal
 Post subject: Re: DS Absolute value equation: What is the value of y?
 Post Posted: Wed Apr 04, 2012 3:15 pm 
Offline
ManhattanGMAT Staff


Posts: 7146
aps_asks wrote:
Thanks Ron !


sure.
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