What is the value of y?

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What is the value of y?

by bharathh » Mon Aug 31, 2009 8:23 am
What is the value of y?

(1) 3|x^2 – 4| = y – 2

(2) |3 – y| = 11

Can someone please take a look at what I did and let me know if what my answer is correct?

[spoiler]
For statement 1

3 | (x-2) (x+2) | + 2 = y

x = 0, y = 14
x = 1, y = 11
x = 2, y = 2
x = 3, y = 17
x = 4, y = 38


Can't narrow down value of y from this statement... so insufficient

For Statement 2

Only if y = 14 or y = -8 can this statement be true. However there are 2 possible values for y .. so insufficient.


Combining 1 and 2 we can see that y = 14.. So C?
[/spoiler]
Source: — Data Sufficiency |

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by grockit_jake » Mon Aug 31, 2009 9:10 am
I think it's best to start with (2) here, since it's clear that (1) is insufficient and (2) will give you an exact set of values for y.

From (2), y = -8 or 14.

When we plug these back into

(1) 3|x^2 – 4| = y – 2

we can see that y = -8 is not an option since that will leave the right side negative. This is impossible for an absolute value, so we can only use y = 14.

No need to solve for x, but together y must = 14. So yes, you are correct.
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by imhimanshu » Sat Dec 17, 2011 11:23 pm
Hi
Can someone help me in explaining that as in equation 2 we are taking two cases, one when y>=0 and another when y<0
then, Why are we not opening the modulus of equation 1
i.e Two Cases when x^2-4>= 0 and when x^2-4<0
Why we are taking that |x^2-4| will be positive.

Please explain
Thanks