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

Question

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

Bunuel · Accepted Answer

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
eq{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.

subhashghosh · Answer

(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

amit2k9 · Answer

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 =  ^x

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

hence a.

fluke · Answer

What if:
 y=\sqrt {3}, \hspace{3} x=3 
OR
 y=\sqrt {4}, \hspace{3} x=4

In fact it will hold good for at least all integers > 1;
 y=\sqrt {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?

kamalkicks · Answer

sorry... question corrected

Spidy001 · Answer

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.

Posted from my mobile device

gmat1220 · Answer

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

(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

subhashghosh · Answer

@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.

KarishmaB · Answer

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.

gmat1220 · Answer

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.

Smita04 · Answer

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

reto · Answer

Where can I buy such mathematical look-through-glasses? I need them desperately!!!! :roll:

reto · Answer

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?

Harley1980 · Answer

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

reto · Answer

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

Harley1980 · Answer

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.

reto · Answer

Harley1980 :-D

Well of course you are right. I have nothing more to say without my lawyer. Thank you. Good night

Alex75PAris · Answer

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

Nunuboy1994 · Answer

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

D

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

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GMAT Data Sufficiency (DS) Questions

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

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