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What is the value of y?

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

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New post 25 Sep 2013, 03:33
ricsharm wrote:
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 .

Please explain


We don't need the value of x to find the value of y.

From (1) y>=2
From (2) y=-8 or y=14

(1)+(2) y=14.

Check here: what-is-the-value-of-y-127976.html#p1048509

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

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New post 16 Oct 2013, 06:34
What is the value of y?

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


(1) 3|x^2 - 4| = y - 2

the LHS is an absolute value so RHS has to be positive or zero: y - 2 >=0. Multiple values for y so not sufficient.

(2) |3 – y| = 11

y can either be -8 or 14
|3 - (-8)| = |11| = 11
|3 - 14| = |-11| = 11
two possible values for y so not sufficient

(1) + (2)

from (1) we know that y >= 2
from (2) we know that y = -8 or y = 11
therefore y = 11

Answer: C

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

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New post 28 Oct 2013, 09:10
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.

Answer: C.

Hope it's clear.


Hi Bunuel,

in the second statement, you solved the inequality and got -8 and 14 which satisfy the inequality if you plug them.

but, what about if you get two answers, and one satisfies the inequality and one doesn't. for example |x+3| = 4x-3, how do you go about that?
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Re: What is the value of y? [#permalink]

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New post 04 Nov 2013, 15:25
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.

Answer: C.

Hope it's clear.


I have a general question...
I went ahead and solved the equation in st. 1 and got that x = sqrt(8)...
Now, if we were told that both x and y were integers, than does that mean that both statements were not sufficient?
Would have it affected our final result?
Because st.1 doesn't really just say that y>= 2 right?
It actually gives y a value.....?

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New post 05 Nov 2013, 07:20
ronr34 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.

Answer: C.

Hope it's clear.


I have a general question...
I went ahead and solved the equation in st. 1 and got that x = sqrt(8)...
Now, if we were told that both x and y were integers, than does that mean that both statements were not sufficient?
Would have it affected our final result?
Because st.1 doesn't really just say that y>= 2 right?
It actually gives y a value.....?


How did you get from (1) that \(x=\sqrt{8}\)? That's not correct. You cannot solve \(3|x^2-4|=y-2\).

Next, yes y is some number but whatever number it is from \(3|x^2-4|=y-2\) it follows that it's more than or equal to 2.
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Re: What is the value of y? [#permalink]

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New post 17 Apr 2014, 02:00
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 .

tnx dear
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New post 17 Apr 2014, 02:42
dvinoth86 wrote:
What is the value of y?

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


Statement I is insufficient

x will take multiple values and so will y.The only takeaway from this option is that y = 3(+ve) + 2 hence y is a positive number

Statement II is insufficient:

3 - y = 11

y = -8

3 - y = -11
y = 14

Combining is sufficient.

First statement says that y is a positive number and second statement says that y is either -11 or 14 hence y is equal to 14.
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New post 17 Apr 2014, 02:49
gmatonline 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 .

tnx dear


From (1): \(y\geq{2}\);
From (2): \(y=-8\) or \(y=14\).

To satisfy both statements y must be 14.

Does this make sense?
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New post 07 Sep 2014, 02:51
dvinoth86 wrote:
What is the value of y?

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



1. from one we could conclude either y is greater than or equal to 2 as |x^2 - 4| always greater than -ive values. but we cant determine the values hence Insuff.

2. y could be -8 or 14 , two values .. In sufff.

combining-- from one , y is greater than or equal to 2 & from two y= -8 or 14 .. y should be 14. Hence C

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New post 05 Nov 2014, 05:57
Quick couple of questions around Absolute value and inequalities

1.When 4\(|x + 1/2|\) = 18 can become + (x + 1/2) = 4.5 or –(x + 1/2) = 4.5, why can't 3|\(x^2\) – 4| = y – 2 become (\(x^2\) – 4)= (y – 2)/3 or -(\(x^2\) – 4) = (y – 2)/3 ?

2. What happens to the inequality when you take the square root on both the sides? For e.g. \(x^2\) \(<=\)1. Also, please let me know if there are any specific rules when squaring on both sides?

Thanks in advance :)

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New post 05 Nov 2014, 06:11
Blackbox wrote:
Quick couple of questions around Absolute value and inequalities

1.When 4\(|x + 1/2|\) = 18 can become + (x + 1/2) = 4.5 or –(x + 1/2) = 4.5, why can't 3|\(x^2\) – 4| = y – 2 become (\(x^2\) – 4)= (y – 2)/3 or -(\(x^2\) – 4) = (y – 2)/3 ?

2. What happens to the inequality when you take the square root on both the sides? For e.g. \(x^2\) \(<=\)1. Also, please let me know if there are any specific rules when squaring on both sides?

Thanks in advance :)


1. We could, but this is no help in finding the value of y.

2. Check here: inequalities-tips-and-hints-175001.html

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

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New post 05 Nov 2014, 07:47
Bunuel wrote:
1. We could, but this is no help in finding the value of y.



Thank you. For a few hours I was searching all over fanatically to verify if my fundamental understanding of modulus theory is flawed. Now, I know what else I could do when a modulus operator is present. And thanks also for the linky, I will check it out now.

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New post 21 Nov 2014, 09:38
Hello Bunuel

Thanks for your posts!

Btw, Why couldn't 'y' take both the values ( -8 & 14) as per statement 2?!

Iam unable to paste links;I could find sites like 'sosmath' where both the values
are shown as solutions :!:

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New post 21 Nov 2014, 09:52
musejoy wrote:
Hello Bunuel

Thanks for your posts!

Btw, Why couldn't 'y' take both the values ( -8 & 14) as per statement 2?!

Iam unable to paste links;I could find sites like 'sosmath' where both the values
are shown as solutions :!:


y could be either -8 or 14. What is confusing there?
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Re: What is the value of y? [#permalink]

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New post 21 Nov 2014, 20:23
Bunuel wrote:
musejoy wrote:
Hello Bunuel

Thanks for your posts!

Btw, Why couldn't 'y' take both the values ( -8 & 14) as per statement 2?!

Iam unable to paste links;I could find sites like 'sosmath' where both the values
are shown as solutions :!:


y could be either -8 or 14. What is confusing there?


So,if 'y' can take both values, that would mean statement 2 is right kno?
Linear absolute value equations can have 2 values as solutions, am i right please?

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New post 22 Nov 2014, 04:05
1) 3|x^2 – 4| = y – 2 :
Above equation indicates that y is positive.
No definite value of y so INSUFFICIENT.

2) |3 – y| = 11
Square both sides and solving this equation for y
9+y^2-6|y|=121
so y=14 or -4
No definite values of y .INSUFFICIENT.

Combining both statements, once can say y=14 is definite answer.

Answer is C

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musejoy wrote:
Bunuel wrote:
musejoy wrote:
Hello Bunuel

Thanks for your posts!

Btw, Why couldn't 'y' take both the values ( -8 & 14) as per statement 2?!

Iam unable to paste links;I could find sites like 'sosmath' where both the values
are shown as solutions :!:


y could be either -8 or 14. What is confusing there?


So,if 'y' can take both values, that would mean statement 2 is right kno?
Linear absolute value equations can have 2 values as solutions, am i right please?


No. When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable. So, the second statement is NOT sufficient because we can two possible values of y, not one.

Hope it's clear.
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New post 22 Nov 2014, 11:29
yes bunuel ..Thanks :)

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

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New post 01 Sep 2015, 01:59
Bunuel wrote:
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.

Answer: C.

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?


Why cannot we solve the 1st as :

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

x^2-4 = (y-2)/3

x^2= (y+10)/3 -----(1)

and considering the negative sign i.e

x^2-4=-(y-2)/3

x^2= (-y+14)/3 -----(2)

and then equating 1 and 2

we will get y = 2

What is wrong with this approach??

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New post 01 Sep 2015, 04:41
believer700 wrote:
Bunuel wrote:
davidfrank wrote:
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?


Why cannot we solve the 1st as :

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

x^2-4 = (y-2)/3

x^2= (y+10)/3 -----(1)

and considering the negative sign i.e

x^2-4=-(y-2)/3

x^2= (-y+14)/3 -----(2)

and then equating 1 and 2

we will get y = 2

What is wrong with this approach??


Those are 2 separate cases: |x^2 - 4| = x^2 - 4, when x^2 - 4 > 0 and |x^2 - 4| = -(x^2 - 4), when x^2 - 4 < 0.
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Re: What is the value of y?   [#permalink] 01 Sep 2015, 04:41

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