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x2 = y2 + 1 and y ≠ 0.

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 123

Kudos [?]: 1972 [0], given: 397

x2 = y2 + 1 and y ≠ 0. [#permalink]  06 Apr 2018, 15:36
Expert's post
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Question Stats:

35% (00:43) correct 64% (00:44) wrong based on 28 sessions
$$x^2 = y^2 + 1$$ and y ≠ 0.

 Quantity A Quantity B $$x^4$$ $$y^4+1$$

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 1
Question: 12
Page: 509
[Reveal] Spoiler: OA
Intern
Joined: 03 Apr 2018
Posts: 22
Followers: 0

Kudos [?]: 7 [0], given: 13

Re: x2 = y2 + 1 and y ≠ 0. [#permalink]  07 Apr 2018, 07:27
You can solve this by addding variables but I think it’s easier, tell me if I’m wrong, to look at y^4 + 1. By definition this will be always greater than x^4. Solution is A.
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 123

Kudos [?]: 1972 [0], given: 397

Re: x2 = y2 + 1 and y ≠ 0. [#permalink]  18 Apr 2018, 15:39
Expert's post
Explanation

Plugging in 2 for y gives you $$x^2 = 5$$ in the given equation and 17 for Quantity B.

Squaring this gives you $$x^4 = 25$$ for Quantity A, which is therefore larger.

Plugging in any other number gives the same result.

Alternatively, doing algebra by squaring both sides of the given equation reveals Quantity A: $$x4 = (y^2 + 1)(y^2 + 1) = y^4 + 2y^2 + 1$$.

The only difference between Quantities A and B is the $$2y^2$$ in Quantity A.

You are told that y ≠ 0, so $$2y^2$$ is always positive, and Quantity A will always therefore be larger. The answer is choice (A).
_________________

Sandy
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Intern
Joined: 15 May 2018
Posts: 38
Followers: 0

Kudos [?]: 5 [0], given: 1

Re: x2 = y2 + 1 and y ≠ 0. [#permalink]  09 Jul 2018, 18:43
sandy wrote:
$$x^2 = y^2 + 1$$ and y ≠ 0.

 Quantity A Quantity B $$x^4$$ $$y^4+1$$

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 1
Question: 12
Page: 509

Intern
Joined: 04 May 2017
Posts: 36
Followers: 0

Kudos [?]: 26 [0], given: 6

Re: x2 = y2 + 1 and y ≠ 0. [#permalink]  10 Jul 2018, 08:35
x^2=y^2+1 -> x^4=y^4+2y^2+1-> x^4=(y^4+1)+2y^2. Since y#0 -> y^2>0 -> x^4>(y^4+1) -> A.
_________________

Do not pray for an easy life, pray for the strength to endure a difficult one - Bruce Lee

Manager
Joined: 27 Feb 2017
Posts: 189
Followers: 1

Kudos [?]: 55 [0], given: 15

Re: x2 = y2 + 1 and y ≠ 0. [#permalink]  05 Aug 2018, 15:23
Plugging in values makes more sense. i tried solving the algebra way, I was stuck. Can someone explain to me how that method works really? I mean I expanded it and stuff and this is what I got:
A: x^4= y^4+2y^2+1
B: y^4+1=x^4-2y^2

I mean how do we know from here which one is bigger?
Re: x2 = y2 + 1 and y ≠ 0.   [#permalink] 05 Aug 2018, 15:23
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