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

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GRE Math Challenge #112- In the xy-coordinate system [#permalink] New post 09 May 2015, 11:30
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Question Stats:

100% (02:14) correct 0% (00:00) wrong based on 1 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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Re: GRE Math Challenge #112- In the xy-coordinate system [#permalink] New post 21 Mar 2017, 13:43
How to solve this problem?

Thanks!
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Re: GRE Math Challenge #112- In the xy-coordinate system [#permalink] New post 21 Mar 2017, 16:32
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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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Re: GRE Math Challenge #112- In the xy-coordinate system   [#permalink] 21 Mar 2017, 16:32
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GRE Math Challenge #112- In the xy-coordinate system

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