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# GRE Math Challenge #112- In the xy-coordinate system

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GRE Prep Club Legend
Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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GRE Math Challenge #112- In the xy-coordinate system [#permalink]  09 May 2015, 11:30
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Question Stats:

100% (02:21) correct 0% (00:00) wrong based on 2 sessions
In the xy-coordinate system, the point (x, y) lies on the circle with equation $$x^2 + y^2 = 1$$

Quantity A: x + y
Quantity B: 1.01

• Quantity A is greater.
• Quantity B is greater.
• Both Quantities are Equal
• Cannot be determined
[Reveal] Spoiler: OA

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Sandy
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Intern
Joined: 22 Aug 2016
Posts: 31
Followers: 0

Kudos [?]: 9 [0], given: 5

Re: GRE Math Challenge #112- In the xy-coordinate system [#permalink]  21 Mar 2017, 13:43
How to solve this problem?

Thanks!
GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 117

Kudos [?]: 1889 [1] , given: 397

Re: GRE Math Challenge #112- In the xy-coordinate system [#permalink]  21 Mar 2017, 16:32
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Expert's post
Explanation

Lets start by writing the quantities A and B side by side

$$x + y ...??... 1.01$$
squaring both sides
$$(x + y)^2 ...??... 1.01^2$$

or $$x^2 + y^2 + 2xy ...??... 1.0201$$

Now we know from the question that $$x^2 + y^2 = 1$$. so putting that in our equation

$$1 + 2xy ...??... 1.0201$$ or $$2xy ...??... 0.0201$$

So if x = 0 and y= 1 then Quantity B is greater but if we take $$x = 1/\sqrt{2}$$ and $$y = 1/\sqrt{2}$$ then Quantity A is greater.

Hence option D is correct.
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Sandy
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Re: GRE Math Challenge #112- In the xy-coordinate system   [#permalink] 21 Mar 2017, 16:32
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