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If x is not equal to y and if √x = y, what is the value of y

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If x is not equal to y and if x =y , what is the value of  [#permalink]

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If x is not equal to y and if \(\sqrt{x}=y\), what is the value of \(y^3\) ?

(1) \(x = y^x\)

(2) \(x^3 = 8\)



can somebody explain how 1 is sufficient. i am getting confused...help

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Originally posted by kamalkicks on 02 May 2011, 22:16.
Last edited by kamalkicks on 03 May 2011, 06:50, edited 1 time in total.
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Re: If x is not equal to y and if , what is the value of y^3 ?  [#permalink]

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New post 04 May 2011, 04:39
3
2
(1)
x = y^x
=> y^2 = y^x

=> x = 2
=> y^3 = (2)^3/2

Sufficient

(2)

X^3 = 8

=> x = 2
=> Y = (2)^3/2
Sufficient
Answer - D
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Re: If x is not equal to y and if , what is the value of y^3 ?  [#permalink]

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New post 02 May 2011, 23:02
b can be straightaway eliminated.However, it gives a possible value for x=2.which can be used to evaluate a.

a. y = 2^(1/2)
x = [2^(1/2)]^x

x =2 is the only possible value apart from x=y=1.

hence a.
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Re: If x is not equal to y and if , what is the value of y^3 ?  [#permalink]

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New post 03 May 2011, 06:34
1
amit2k9 wrote:
b can be straightaway eliminated.However, it gives a possible value for x=2.which can be used to evaluate a.

a. y = 2^(1/2)
x = [2^(1/2)]^x

x =2 is the only possible value apart from x=y=1.

hence a.


What if:
\(y=\sqrt[3]{3}, \hspace{3} x=3\)
OR
\(y=\sqrt[4]{4}, \hspace{3} x=4\)

In fact it will hold good for at least all integers > 1;
\(y=\sqrt[n]{n}, \hspace{3} x=n\)

Answer should be "C" in my opinion.

Kamalkicks:
Question reads: If x is not equal to y and if "IS SOMETHING MISSING", what is the value of y^3 ?

Is there anything missing after second if?
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Re: If x is not equal to y and if , what is the value of y^3 ?  [#permalink]

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New post 03 May 2011, 06:50
fluke wrote:
amit2k9 wrote:
b can be straightaway eliminated.However, it gives a possible value for x=2.which can be used to evaluate a.

a. y = 2^(1/2)
x = [2^(1/2)]^x

x =2 is the only possible value apart from x=y=1.

hence a.


What if:
\(y=\sqrt[3]{3}, \hspace{3} x=3\)
OR
\(y=\sqrt[4]{4}, \hspace{3} x=4\)

In fact it will hold good for at least all integers > 1;
\(y=\sqrt[n]{n}, \hspace{3} x=n\)

Answer should be "C" in my opinion.

Kamalkicks:
Question reads: If x is not equal to y and if "IS SOMETHING MISSING", what is the value of y^3 ?

Is there anything missing after second if?


sorry... question corrected
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Re: If x is not equal to y and if , what is the value of y^3 ?  [#permalink]

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New post 04 May 2011, 06:55
My answer is D.

Given Sqrt(x) = y
=> y ^3= x* Sqrt(x) = sqrt(x^3)

1. x = y ^x
=> y ^3= sqrt(x^3)
=sqrt(y^(3x))
from this we can find x. Hence is sufficient to find y^3.

2.from this we can find x. Hence is sufficient to find y^3.

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Re: If x is not equal to y and if , what is the value of y^3 ?  [#permalink]

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New post 04 May 2011, 18:54
Hey subhashghosh

Here is my interpretation of y. x = y^2. so x is +ve but the sign of y is unknown.

Hence the value of y^3 is a black box now. Do you agree? S1 and S2 provide the same information. But the sign of y is unknown. So the answer should be E :o

subhashghosh wrote:
(1)
x = y^x
=> y^2 = y^x

=> x = 2
=> y^3 = (2)^3/2

Sufficient

(2)

X^3 = 8

=> x = 2
=> Y = (2)^3/2
Sufficient
Answer - D
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Re: If x is not equal to y and if , what is the value of y^3 ?  [#permalink]

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New post 05 May 2011, 04:28
@gmat1220 we don't need to worry about sign of y, consider one more thing, if y is negative (y)^3/2 takes us in the realm of complex numbers, which is beyond the scope of GMAT.
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Re: If x is not equal to y and if , what is the value of y^3 ?  [#permalink]

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New post 05 May 2011, 19:15
1
kamalkicks wrote:
If x is not equal to y and if \(\sqrt{x}=y\), what is the value of \(y^3\) ?

(1) \(x = y^x\)

(2) \(x^3 = 8\)

can somebody explain how 1 is sufficient. i am getting confused...help



Try to connect the data in the question stem to the data given in the statement.
Data in Question Stem: \(\sqrt{x}=y\)
or \(x = y^2\) (I think of doing this because the statement gives the relation of 'x' with 'y', not of 'square root x' with 'y')

(1) \(x = y^x\)
or from above, \(y^2 = y^x\)
Hence \(x = 2\) and \(y = \sqrt{2}\)
Therefore, \(y^3 = (\sqrt{2})^3\)

If logic confuses you, try and use simple algebra. Once you see it using algebra, reason it out to understand the concept well.
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Re: If x is not equal to y and if , what is the value of y^3 ?  [#permalink]

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New post 06 May 2011, 10:11
Karishma

y^3 can have two values i.e. 1.414^3 or -1.414^3, there has to be some constraint on y to get a single value of y^3. So is the answer D or E.
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If x is not equal to y and if √x = y, what is the value of y  [#permalink]

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New post Updated on: 01 Apr 2012, 23:54
3
If x is not equal to y and if √x = y, what is the value of y^3 ?

(1) x = y^x
(2) x^3=8

Originally posted by Smita04 on 01 Apr 2012, 23:35.
Last edited by Bunuel on 01 Apr 2012, 23:54, edited 1 time in total.
Edited the question and added the OA
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Re: Exponents  [#permalink]

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New post 01 Apr 2012, 23:54
2
2
Smita04 wrote:
if x is not equal to y and if √x = y, what is the value of y^3 ?

1) x = xy
2) x^3=8


Question should read:
If x is not equal to y and if √x = y, what is the value of y^3 ?

(1) x = y^x --> since from \(\sqrt{x}=y\) we have that \(x=y^2\) then \(y^2=y^x\) --> \(y=1\) or \(x=2\) (the first solutions is not valid since given that \(x\neq{y}\) and if \(y=1\) then \(x=y^2=1\) too). So, \(x=2\) --> \(y=\sqrt{x}=\sqrt{2}\). Sufficient.

(2) x^3=8 --> \(x=2\) --> \(y=\sqrt{x}=\sqrt{2}\). Sufficient.

Answer: D.
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Re: If x is not equal to y and if √x = y, what is the value of y  [#permalink]

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New post 16 Jun 2015, 03:18
1
Bunuel wrote:
Smita04 wrote:
if x is not equal to y and if √x = y, what is the value of y^3 ?

1) x = xy
2) x^3=8


Question should read:
If x is not equal to y and if √x = y, what is the value of y^3 ?

(1) x = y^x --> since from \(\sqrt{x}=y\) we have that \(x=y^2\) then \(y^2=y^x\) --> \(y=1\) or \(x=2\) (the first solutions is not valid since given that \(x\neq{y}\) and if \(y=1\) then \(x=y^2=1\) too). So, \(x=2\) --> \(y=\sqrt{x}=\sqrt{2}\). Sufficient.

(2) x^3=8 --> \(x=2\) --> \(y=\sqrt{x}=\sqrt{2}\). Sufficient.

Answer: D.


Where can I buy such mathematical look-through-glasses? I need them desperately!!!! :roll:
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Re: If x is not equal to y and if √x = y, what is the value of y  [#permalink]

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New post 17 Jun 2015, 12:49
Bunuel wrote:
Smita04 wrote:
if x is not equal to y and if √x = y, what is the value of y^3 ?

1) x = xy
2) x^3=8


Question should read:
If x is not equal to y and if √x = y, what is the value of y^3 ?

(1) x = y^x --> since from \(\sqrt{x}=y\) we have that \(x=y^2\) then \(y^2=y^x\) --> \(y=1\) or \(x=2\) (the first solutions is not valid since given that \(x\neq{y}\) and if \(y=1\) then \(x=y^2=1\) too). So, \(x=2\) --> \(y=\sqrt{x}=\sqrt{2}\). Sufficient.

(2) x^3=8 --> \(x=2\) --> \(y=\sqrt{x}=\sqrt{2}\). Sufficient.

Answer: D.


To proof statement 1, would it be allowed to process as follows?

What is the value of y^3?

Since \(x = y^x\), we know that \(y^3=x\) and therefore \(x = 3\). If \(x =3\) then \(y^3=3\), which is sufficient.

Any mistake in this?
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If x is not equal to y and if √x = y, what is the value of y  [#permalink]

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New post 17 Jun 2015, 12:56
reto wrote:

To proof statement 1, would it be allowed to process as follows?

What is the value of y^3?

Since \(x = y^x\), we know that \(y^3=x\) and therefore \(x = 3\). If \(x =3\) then \(y^3=3\), which is sufficient.

Any mistake in this?


Hello reto
From which part you infer that \(y^3=x\)?

From this statement \(x = y^x\) we can't say that \(y^3=x\) because y and x can have infinite number of values x and y:
x = 1 and y =1
x = 2 and y = \(\sqrt{2}\)
x = 3 and y =cube root (3) and so on

and only in first case (x =1 and y =1) your conclusion that \(y^3=x\) will be true
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Re: If x is not equal to y and if √x = y, what is the value of y  [#permalink]

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New post 17 Jun 2015, 13:05
Harley1980 wrote:
reto wrote:

To proof statement 1, would it be allowed to process as follows?

What is the value of y^3?

Since \(x = y^x\), we know that \(y^3=x\) and therefore \(x = 3\). If \(x =3\) then \(y^3=3\), which is sufficient.

Any mistake in this?


Hello reto
From which part you infer that \(y^3=x\)?


Because we have this equation here: x=y^x > if you plug y^3 on RHS you can infer that x = 3
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If x is not equal to y and if √x = y, what is the value of y  [#permalink]

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New post 17 Jun 2015, 13:09
reto wrote:
Harley1980 wrote:
reto wrote:

To proof statement 1, would it be allowed to process as follows?

What is the value of y^3?

Since \(x = y^x\), we know that \(y^3=x\) and therefore \(x = 3\). If \(x =3\) then \(y^3=3\), which is sufficient.

Any mistake in this?


Hello reto
From which part you infer that \(y^3=x\)?


Because we have this equation here: x=y^x > if you plug y^3 on RHS you can infer that x = 3


But if we will follow to such logic then we can plug y^4 or y^5 and infer that x=4 or x=5 right?

P.S. I am a little change my previous answer, please reread it.
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Re: If x is not equal to y and if √x = y, what is the value of y  [#permalink]

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New post 17 Jun 2015, 13:30
Harley1980 wrote:



But if we will follow to such logic then we can plug y^4 or y^5 and infer that x=4 or x=5 right?

P.S. I am a little change my previous answer, please reread it.


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If x is not equal to y and if √x = y, what is the value of y  [#permalink]

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New post 22 Jun 2016, 13:28
Question : y^3 = x^(3/2) = ? we need x to answer

(1) x=y^x, and from the question we know that x=y^2, so x=2, Sufficient

(2) x^3 = 8, x=2, Sufficient
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Re: If x is not equal to y and if √x = y, what is the value of y  [#permalink]

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New post 08 Sep 2017, 20:05
kamalkicks wrote:
If x is not equal to y and if \(\sqrt{x}=y\), what is the value of \(y^3\) ?

(1) \(x = y^x\)

(2) \(x^3 = 8\)



can somebody explain how 1 is sufficient. i am getting confused...help


Easy. Always try to simplify the stimulus- manipulate the equations in their given form in a granular more clear way.

\sqrt{x}=y - square both sides
x=y^2

St 1

Substitute. Y^2=y^x

suff

St 2

X must be 2- there is no ambiguity since y is to an odd power

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Re: If x is not equal to y and if √x = y, what is the value of y   [#permalink] 08 Sep 2017, 20:05
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