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x2 = y2 + 1 and y ≠ 0.

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GMAT Club Legend
GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4704
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1601 [0], given: 373

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x2 = y2 + 1 and y ≠ 0. [#permalink] New post 06 Apr 2018, 15:36
Expert's post
00:00

Question Stats:

29% (00:41) correct 70% (00:46) wrong based on 24 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
Intern
Joined: 03 Apr 2018
Posts: 22
Followers: 0

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

Re: x2 = y2 + 1 and y ≠ 0. [#permalink] New post 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.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4704
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 90

Kudos [?]: 1601 [0], given: 373

CAT Tests
Re: x2 = y2 + 1 and y ≠ 0. [#permalink] New post 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
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Kudos [?]: 5 [0], given: 1

Re: x2 = y2 + 1 and y ≠ 0. [#permalink] New post 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

My Answer is B
Intern
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Kudos [?]: 21 [0], given: 6

Re: x2 = y2 + 1 and y ≠ 0. [#permalink] New post 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.
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Re: x2 = y2 + 1 and y ≠ 0. [#permalink] New post 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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x2 = y2 + 1 and y ≠ 0.

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