 It is currently 21 Jul 2019, 07:47 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # x2 = y2 + 1 and y ≠ 0.  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4809
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 123

Kudos [?]: 1972 , given: 397

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

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

Kudos [?]: 1972 , given: 397

Re: x2 = y2 + 1 and y ≠ 0. [#permalink]
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
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

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

Kudos [?]: 5 , 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 [?]: 26 , 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.
_________________

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 , 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? Re: x2 = y2 + 1 and y ≠ 0.   [#permalink] 05 Aug 2018, 15:23
Display posts from previous: Sort by

# x2 = y2 + 1 and y ≠ 0.  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.