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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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02 May 2011, 22:16
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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
[Reveal] Spoiler: OA

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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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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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03 May 2011, 06:34
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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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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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04 May 2011, 04:39
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(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
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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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04 May 2011, 06:55

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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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

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

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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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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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05 May 2011, 19:15
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Expert's post
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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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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01 Apr 2012, 23:35
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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

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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01 Apr 2012, 23:54
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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

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.

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

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16 Jun 2015, 03:18
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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

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.

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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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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

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.

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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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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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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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?

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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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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?

Harley1980
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Re: If x is not equal to y and if x =y , what is the value of [#permalink]

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Re: If x is not equal to y and if x =y , what is the value of   [#permalink] 22 Jun 2016, 09:05

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