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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 06 May 2016, 20:47
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.


Why is Y>=0? Can't we write 'Y>0'? If LHS is positive and RHS must also be positive then, RHS has to be greater than 0. As 0 is neither positive nor negative, how can we write Y>=0?

|some value|= some value. Since LHS is an absolute value, RHS has to be positive as well. Why is RHS>=0 and not RHS>0?

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

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New post 06 May 2016, 21:12
shekhar4847 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.


what if y is between 2 and 3?
In that case we will have two values of y.
Could you please clarify?


Hi shekhar4847,

I gives you \(y\geq{2}\)...
II gives you two cases..
a) \(y<3\) --> \(3-y=11\) --> \(y=-8\);
this means if y<3, it can have ONLY -8 as the value,
so when we combine this with \(y\geq{2}\),which does not fit between 2 and 3.. hence WRONG

b)\(y\geq{3}\) --> \(-3+y=11\) --> \(y=14\)
this means if \(y\geq{3}\), it can have ONLY 14 as the value,
so when we combine this with \(y\geq{2}\), 14 fits in both the ranges.. hence CORRECT
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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

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New post 06 May 2016, 21:15
bimalr9 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.


Why is Y>=0? Can't we write 'Y>0'? If LHS is positive and RHS must also be positive then, RHS has to be greater than 0. As 0 is neither positive nor negative, how can we write Y>=0?

|some value|= some value. Since LHS is an absolute value, RHS has to be positive as well. Why is RHS>=0 and not RHS>0?


Hi,
an ABSOLUTE value is NOT necessarily positive, it is NON-NEGATIVE, so it can include both 0 and +ive value..
if in statement I x is 2 or -2, LHS will be 0 and hence y=2..
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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

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New post 07 May 2016, 00:49
dvinoth86 wrote:
What is the value of y?


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

Y = ?

stmt:1 - it has two variables X AND Y. we need value of Y. insuff.

stmt:2 - Y=-8 or Y=11 insuff.

combined: -

frm stmt-1 3|x^2 – 4| = y – 2

X^2 is positive. value of mod is positive. so left hand side is POSITIVE.

frm stmt-2 Y=-8 or Y=11

so we can only pick 11 as the value to keep right hand side POSITIVE.

Option C is right.
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What is the value of y? [#permalink]

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New post 14 Aug 2016, 00:44
Hi Bunuel,

Please correct me if i am wrong.

i). 3|x^2 - 4| =y-2

3x^2 = y+ 10 OR 3x^2 = -y +14
equating the 2 values of 3x^2 Cant we equate these 2 values?
y=10 = -y +14
y=2


ii). gives 2 values of y -8 & 14

therefore, answer is A

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

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New post 14 Aug 2016, 01:39
shrashtisinghal wrote:
Hi Bunuel,

Please correct me if i am wrong.

i). 3|x^2 - 4| =y-2

3x^2 = y+ 10 OR 3x^2 = -y +14
equating the 2 values of 3x^2 Cant we equate these 2 values?
y=10 = -y +14
y=2


ii). gives 2 values of y -8 & 14

therefore, answer is A


How do you know that we have

3x^2 - 12 =y-2

or

12 - 3x^2 =y-2

Since, we donot know which of the above equations is valid. We cannot deduce a single value.

As per Modulus property,

Mod(x) = x if x>0
= -x if x<0.

Hence A is not sufficient.

In B also, we are getting two values of y, so not sufficient.

But, when you combine the statements, you will see the equation is satisfied only for y =14. hence, C.
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Re: What is the value of y? [#permalink]

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New post 17 Oct 2016, 20:37
While at first glance, seeing two variables you might think you need two equations, statement 1 alone is actually sufficient. By factoring out common terms (2y on top, 3 on bottom), you're left with:
2y(2x+1)3(2x+1)=y−3
So the (2x+1) terms cancel, leaving just:
2y3=y−3, a linear equation that allows you to solve for the value of y. Statement 1 is sufficient

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

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New post 17 Oct 2016, 23:52
dvinoth86 wrote:
What is the value of y?

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


FROM 1
(y-2)/3 >= 0 , thus y>= 2 ... ... insuff

from 2

3-y = 11 or 3-y = -11 , thus Y could be either -8 or 14.. insuff

both together

since from 1 y>= 2 and from 2 y = -8 or 14 then y = 4 ( common domain) ...C

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

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New post 14 Aug 2017, 20:32
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.



Brilliant approach! I'd never thought it could be this easy.

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

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Re: What is the value of y?   [#permalink] 22 Sep 2017, 09:22

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