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# What is the value of y?

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What is the value of y? [#permalink]

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22 Feb 2012, 19:51
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What is the value of y?

(1) 3|x^2 – 4| = y – 2
(2) |3 – y| = 11
[Reveal] Spoiler: OA

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Re: What is the value of y? [#permalink]

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22 Feb 2012, 21:50
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What is the value of y?

(1) $$3|x^2-4|=y-2$$. Now, since we are asked to find the value of y, from this statement we can conclude only that $$y\geq{2}$$, as LHS is absolute value which is never negative, hence RHS als cannot be negative. Not sufficient.

(2) $$|3 - y| = 11$$:

$$y<3$$ --> $$3-y=11$$ --> $$y=-8$$;
$$y\geq{3}$$ --> $$-3+y=11$$ --> $$y=14$$.

Two values for $$y$$. Not sufficient.

(1)+(2) Since from (1) $$y\geq{2}$$, then from (2) $$y=14$$. Sufficient.

Hope it's clear.
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Re: What is the value of y? (1) 3|x2 – 4| = y – 2 (2) |3–y|=11 [#permalink]

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23 Apr 2012, 22:33
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C for sure is the answer ,
Bunuel your explanations are simply awsome.
Thanks
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Re: What is the value of y? (1) 3|x2 – 4| = y – 2 (2) |3–y|=11 [#permalink]

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28 Apr 2012, 11:01
Answer C, Bunuel's explaination has definitely helped me better understand absolute value questions.

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Re: What is the value of y? [#permalink]

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05 Jul 2012, 11:52
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Bunuel wrote:
What is the value of y?

(1) $$3|x^2-4|=y-2$$. Now, since we are asked to find the value of y, from this statement we can conclude only that $$y\geq{2}$$, as LHS is absolute value which is never negative, hence RHS als can not be negative. Not sufficient.

(2) $$|3 - y| = 11$$:

$$y<3$$ --> $$3-y=11$$ --> $$y=-8$$;
$$y\geq{3}$$ --> $$-3+y=11$$ --> $$y=14$$.

Two values for $$y$$. Not sufficient.

(1)+(2) Since from (1) $$y\geq{2}$$, then from (2) $$y=14$$. Sufficient.

Hope it's clear.

Sorry I can't to figure out why y >= 2........

1) 3x^2 - 4 = y-2 and -3x^2 + 4 = y-2 and then ??'

thanks
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Re: What is the value of y? [#permalink]

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05 Jul 2012, 11:57
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carcass wrote:
Bunuel wrote:
What is the value of y?

(1) $$3|x^2-4|=y-2$$. Now, since we are asked to find the value of y, from this statement we can conclude only that $$y\geq{2}$$, as LHS is absolute value which is never negative, hence RHS als can not be negative. Not sufficient.

(2) $$|3 - y| = 11$$:

$$y<3$$ --> $$3-y=11$$ --> $$y=-8$$;
$$y\geq{3}$$ --> $$-3+y=11$$ --> $$y=14$$.

Two values for $$y$$. Not sufficient.

(1)+(2) Since from (1) $$y\geq{2}$$, then from (2) $$y=14$$. Sufficient.

Hope it's clear.

Sorry I can't to figure out why y >= 2........

1) 3x^2 - 4 = y-2 and -3x^2 + 4 = y-2 and then ??'

thanks

We are given that $$3|x^2-4|=y-2$$. Now, the left hand side in this expression ($$3|x^2-4|$$) is an absolute value, so it cannot be negative, so the right hand side of the expression ($$y-2$$) must also be non-negative: $$y-2\geq{0}$$ --> $$y\geq{2}$$.

Hope it's clear.
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Re: What is the value of y? [#permalink]

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03 Oct 2012, 20:05
pls point out if i am wrong
1.
3(x^2- 4) = y- 2
and 3(x^2-4)= - (y-2)
y=-4
y=-16

from 2
y = 8
y= 14

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Re: What is the value of y? [#permalink]

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04 Oct 2012, 01:29
Archit143 wrote:
pls point out if i am wrong
1.
3(x^2- 4) = y- 2
and 3(x^2-4)= - (y-2)
y=-4
y=-16

from 2
y = 8
y= 14

from 2
y = 8 - should be y = -8; |3-8| = |-5| = 5 and not 11; |3-(-8)| = |3+8| = 11
y= 14

3(x^2- 4) = y-2 it should be $$3|x^2-4|=y-2$$ if $$y-2\geq0$$.
and 3(x^2-4)= -(y-2) it should be $$3|x^2-4|=-(y-2)$$ if $$y-2<0$$
but we don't have any information about $$y$$.
y=-4
y=-16
No justification for these values, we don't know what is the value of $$x.$$
Statement (1) is not sufficient.

Statement (2) provides two possible values for $$y$$, not sufficient.

Taken together (1) and (2): since $$y-2$$ equals an absolute value, it should be non-negative. Only $$y = 14$$ is acceptable.
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Re: What is the value of y? [#permalink]

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20 Oct 2012, 13:01
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nitzz wrote:
What is the value of y?

(1) 3|$$x2$$ – 4| = y – 2

(2) |3 – y| = 11

1) x can be any number and hence we can substitute any number of x and get various values for y. Insufficient

2) y can either be 14 or -8. Insufficient

1 & 2 together. |$$x2$$ – 4| should be positive since modulus cannot take negative values. So $$\frac{y-2}{3}$$ should be positive. So y is 14.

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Re: What is the value of y? [#permalink]

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06 Apr 2013, 11:35
Bunuel,
I understand from statement 1 we get $$y>=2$$ , but when we combine both statements together we get $$y>=2$$ and $$y=14$$. Now how can we just assume y to be 14, because y can also take the value of 2 right .
I chose E on this basis .

Thanks
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Re: What is the value of y? [#permalink]

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06 Apr 2013, 15:11
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thinktank wrote:
Bunuel,
I understand from statement 1 we get $$y>=2$$ , but when we combine both statements together we get $$y>=2$$ and $$y=14$$. Now how can we just assume y to be 14, because y can also take the value of 2 right .
I chose E on this basis .

Thanks
TT

That's not correct. Y cannot be 2, otherwise the second equation would not be true.
$$|3-2|=11$$, $$1=11$$ As you can see if we pick 2, the second equation is not verified. If take a look at the explanations above, you'll find out that statement 2 defines two possible vaules for y (-8,14)[ not enough to say the value of y]; and that statement 1 is true only for $$y>=2$$, because
$$3|x^2-4|=y-2$$, the left part is always $$>=0$$ (thanks to the abs value), and so the right part must be $$>=0$$ too.
If we merge those conditions:$$y=-8$$ or $$y=14$$ with $$y>=2$$, the only value that y can have is 14

Hope it's clear now
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Re: What is the value of y? [#permalink]

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28 Apr 2013, 15:17
I know this is not needed for this problem but can someone show me how to solve 3|x^2 - 4| = y-2 from statement 1? Like what are the equations you could form if you tried to isolate y in this example?

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Re: What is the value of y? [#permalink]

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29 Apr 2013, 02:08
jmuduke08 wrote:
I know this is not needed for this problem but can someone show me how to solve 3|x^2 - 4| = y-2 from statement 1? Like what are the equations you could form if you tried to isolate y in this example?

We have y = $$2+3|x^2-4|$$

Case I: x>2 -->

We can remove the modulus sign as it is and y = $$2+3(x^2-4) = 3x^2-10$$

Case II : -2<x<2 -->

$$y = 2+3(4-x^2) = 14-3x^2$$

Case III : x<-2

Just as in Case I;$$y = 3x^2-10$$

For x=2 or x=-2,

y = 2.
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Re: What is the value of y? [#permalink]

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26 Jun 2013, 10:28
What is the value of y?

(1) 3|x^2 – 4| = y – 2
(2) |3 – y| = 11

(1) 3|x^2 – 4| = y – 2
It would take a long time to solve out for the positive and negative cases for x and even if we did I don't believe it would help us get an exact value for y because we would still have two variables to solve for (x, y) with no additional given information.

What we do know is that (y-2) must be ≥0 as it equals an absolute value, so y≥2
INSUFFICIENT

(2) |3 – y| = 11

Two cases:

Positive: y≤3: 3-y=11 ===> -y=8 ===> y=-8
Valid, as -8 falls within the range of ≤3
Negative: y>3: -3+y=11 ===> y=14
Valid, as 14 falls within the range of y>3
INSUFFICIENT - there are two valid solutions for y.

1+2)

What we know
y≥2
y=-8
OR
y=14

The only solution for y that also satisfies y≥2 is y=14
SUFFICIENT.

(C)

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Re: What is the value of y? [#permalink]

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26 Jun 2013, 11:51
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Again solving intuitively, and reaching the answer faster.

Picking the statement 2 first as it is the simpler of the two.
(2) |3 – y| = 11

we get two values of Y; one +ve(14) and one -ve(-8). Not sufficient.

(1) 3|x^2 – 4| = y – 2
or, y= 3|x^2-4|+2 (RHS expression can never be -ve under any circumstance, since it involves a mod expression and '+2').
Therefore the value of Y is always +ve. But the statement in itself is not sufficient since we don't know the value of x.

Hence combining the two statements we can select the +ve value of Y from statement 2.

Thanks.
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Re: What is the value of y? [#permalink]

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24 Jul 2013, 16:55
What is the value of y?

(1) 3|x^2 – 4| = y – 2

No way to determine exact values for x or y.
INSUFFICIENT

(2) |3 – y| = 11
y<3
3 - y = 11
y = -8 Valid as -8 falls within the range of y<3
OR
y>3
-(3 - y) = 11
-3 + y = 11
y = 14 Valid as y falls within the range or y > 3
Two valid solutions for y
INSUFFICIENT

1+2) 3|x^2 – 4| = y – 2 and |3 – y| = 11
We could plug in values of y for the positive and negative cases of 3|x^2 - 4| or we could look at#1 and realize that because y-2 = an absolute value, it must be positive. Between the two solutions for y (-8 and 14) the only one that makes y - 2 positive is y = 14.
SUFFICIENT

(C)

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Re: What is the value of y? [#permalink]

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06 Sep 2013, 23:04
thanks Bunuel... it was really helpful in understanding the concept of absolute values even more clerared now.. thank you

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Re: What is the value of y? [#permalink]

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24 Sep 2013, 20:00
Bunuel wrote:
What is the value of y?

(1) $$3|x^2-4|=y-2$$. Now, since we are asked to find the value of y, from this statement we can conclude only that $$y\geq{2}$$, as LHS is absolute value which is never negative, hence RHS als cannot be negative. Not sufficient.

(2) $$|3 - y| = 11$$:

$$y<3$$ --> $$3-y=11$$ --> $$y=-8$$;
$$y\geq{3}$$ --> $$-3+y=11$$ --> $$y=14$$.

Two values for $$y$$. Not sufficient.

(1)+(2) Since from (1) $$y\geq{2}$$, then from (2) $$y=14$$. Sufficient.

Hope it's clear.

Hi,

Can I solve statement 1 like this:

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

Now since this is an absolute value

I would 1st solve for x

x^2-4=0
x2=4
and x=+/-2
now if I substituent the value of x in the above expression
If x= +2
3|x^2-4|=y-2
3|(2)^2-4|=y-2
3|0|=y-2
therefore y=2

now if x=-2
3|x^2-4|=y-2
3|(-2)^2-4|=y-2
3|0|=y-2
and therefore y=2

In both the cases I will get the same value for Y.

Can someone please explain what is wrong with this approach.

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Re: What is the value of y? [#permalink]

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25 Sep 2013, 00:52
davidfrank wrote:
Bunuel wrote:
What is the value of y?

(1) $$3|x^2-4|=y-2$$. Now, since we are asked to find the value of y, from this statement we can conclude only that $$y\geq{2}$$, as LHS is absolute value which is never negative, hence RHS als cannot be negative. Not sufficient.

(2) $$|3 - y| = 11$$:

$$y<3$$ --> $$3-y=11$$ --> $$y=-8$$;
$$y\geq{3}$$ --> $$-3+y=11$$ --> $$y=14$$.

Two values for $$y$$. Not sufficient.

(1)+(2) Since from (1) $$y\geq{2}$$, then from (2) $$y=14$$. Sufficient.

Hope it's clear.

Hi,

Can I solve statement 1 like this:

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

Now since this is an absolute value

I would 1st solve for x

x^2-4=0
x2=4
and x=+/-2
now if I substituent the value of x in the above expression
If x= +2
3|x^2-4|=y-2
3|(2)^2-4|=y-2
3|0|=y-2
therefore y=2

now if x=-2
3|x^2-4|=y-2
3|(-2)^2-4|=y-2
3|0|=y-2
and therefore y=2

In both the cases I will get the same value for Y.

Can someone please explain what is wrong with this approach.

We don't know whether x^2-4=0, thus all your further steps are based on that false assumption. If we knew that x^2-4=0, then x^2-4=0=y-2 --> y-2=0 --> y=2.

Also, you can notice that your approach is not correct from the fact that on the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other. From (2) we have that y is -8 or 14, and if from (1) you get that y is 2 it would mean that the statements clearly contradict.

Does this make sense?
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Re: What is the value of y? [#permalink]

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25 Sep 2013, 03:22
1) we don't the value of x so we cannot calculate Y so A is insufficient.

2)Modules always give positive value so B sufficient .

why C is the ans its not clear to me .

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Re: What is the value of y?   [#permalink] 25 Sep 2013, 03:22

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