MGMATQuest Bank: Numb Props: Cubing Y from X Is Ans Wrong?

[gmatmonkey]

If x is not equal to y and if x^(1/2) = y, what is the value of y^3 ?

(1) x = y^x

(2) x^3 = 8


MGMAT Solution: We can rephrase the question as "What is y?" or since we know that x^(1/2) = y, "What is x?"

(1) SUFFICIENT: From the question we know that x^(1/2) = y, so x = y^2. According to the statement, we also know that x = y^x. If we set the two equations equal to one another,
y^2 = y^x. x then must be equal to 2. (There is another solution to this equation: Both x and y are equal to 1. However, the question stem states that x is not equal to y so we can eliminate this possibility.)

(2) SUFFICIENT: If we take the cube root of both sides of the equation x^3 = 8, we find that x = 2.

The correct answer is D.

I understand the MGMAT Solution but my question is that for statement 1, y can have the value -1.414 or +1.414 and still satisfy the condition for statement 1. So since there are two possible answers for y^3, wont the correct answer be B. I will really appreciate it if anyone can comment on the logic. :cry:

[GMATmonkey]

Sorry statement 1 is

x=y^x

[guest]

Seems like a valid argument because -1.4 square of root of 2 does satisfy both the conditions ie. Statement 1 and the Question. But I am having a hard beleiving that MGMAT is wrong. Anyone care to comment?

[GMATmonkey]

Sorry for the repeat post. I will appreciate it if someone can post their thoughts, This question is driving me nuts

[Saurav]

If x is not equal to y and if x^1/2 = y, what is the value of y^3 ?

y^3 = x^(3/2)

(1) x = y^x

y= x^(1/x)
y^3=x^(3/x)

value of X is not known, hence Not Sufficient

(2) x^3 = 8
gives x=2
hence Y^3 = 2^(3/2)

Sufficient.

hence B

[GmatMonkey]

Thanks Saurav but MGMAt says correct answer is D

[GMATMonkey]

Would greatly appreciate it if any MGMAT instructor can provide clarity on the above. Thank you

[esledge]

Sorry for the delay. For future reference, we always respond to questions in the order in which they are posted. When you post a follow-up request, that revises the last posting date, inadvertently bumping your question to the bottom of the list.

This was the original constraint: sqrt(x) = y
This constraint implies that x and y can't be negative. sqrt(neg) is not defined in GMAT-land, so x>=0. No matter what positive x we take the square root of, the result (y) must be positive. In other words, sqrt(2) does not equal -1.414.

Your confusion comes from 1st manipulating by squaring both sides:
sqrt(x) = y
x = y^2
Both a positive and negative solution exist: 2 = (+1.414)^2 and 2 = (-1.414)^2.
However, only one of these is a solution to the original constraint.

Take-away: Squaring an equation can introduce "extra" solutions. Always check these solutions by plugging back into the original.

[malikrulzz]

From A we get x = 0 or y = 1. With both of these we get x=y which can't be true as per question. Moreover in B we are get X as 2 which is no way near to value of X from A.

[esledge]

From A we get x = 0 or y = 1. With both of these we get x=y which can't be true as per question. Moreover in B we are get X as 2 which is no way near to value of X from A.

Hi Malik, I think you are looking at a typo in the original post, which I should have fixed when I responded earlier. I'll do so in the original post now...

Come to think of it, here's another way to combine (1) and the question stem constraint, without squaring any equations. It's similar to the official explanation, just slightly different substitution.

From question stem: sqrt(x) = x^(1/2) = y
From (1): x = y^x

Substituting x from (1) into question stem equation:
[y^x]^(1/2) = y
y^(x/2) = y
y^(x/2) = y^1

Same base, so set the exponents equal:
(x/2) = 1
x = 2

This method does not introduce any invalid negative solutions.