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Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2918 , given: 394

x2 = y2 + 1 and y ≠ 0. [#permalink]
Expert's post 00:00

Question Stats: 41% (00:43) correct 58% (00:36) wrong based on 48 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 , given: 13

Re: x2 = y2 + 1 and y ≠ 0. [#permalink]
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. Retired Moderator Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 171

Kudos [?]: 2918  , given: 394

Re: x2 = y2 + 1 and y ≠ 0. [#permalink]
1
KUDOS
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).
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Sandy
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Intern Joined: 15 May 2018
Posts: 38
Followers: 0

Kudos [?]: 6 , given: 1

Re: x2 = y2 + 1 and y ≠ 0. [#permalink]
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 [?]: 29 , given: 6

Re: x2 = y2 + 1 and y ≠ 0. [#permalink]
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.
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Manager Joined: 27 Feb 2017
Posts: 188
Followers: 1

Kudos [?]: 77 , given: 15

Re: x2 = y2 + 1 and y ≠ 0. [#permalink]
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?
Senior Manager  Joined: 10 Feb 2020
Posts: 479
Followers: 1

Kudos [?]: 115 , given: 289

Re: x2 = y2 + 1 and y ≠ 0. [#permalink]
kruttikaaggarwal wrote:
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?

2y^2 is additional term in quantity A after expanding hence its bigger
_________________

Ever Tried? Ever Failed? No Matter. Try Again. Fail Again. Fail Better!! Re: x2 = y2 + 1 and y ≠ 0.   [#permalink] 18 Jun 2020, 17:29
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