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GRE Math Challenge #112- In the xy-coordinate system, the po
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Updated on: 20 Feb 2020, 13:43
Updated on: 20 Feb 2020, 13:43
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Question Stats:
37% (01:07) correct
62% (01:18) wrong based on 74 sessions
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In the xy-coordinate system, the point (x, y) lies on the circle with equation \(x^2 + y^2 = 1\)
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Quantity A |
Quantity B |
x+y |
1.01 |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Re: GRE Math Challenge #112- In the xy-coordinate system
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21 Mar 2017, 13:43
21 Mar 2017, 13:43
How to solve this problem?
Thanks!
Thanks!
Re: GRE Math Challenge #112- In the xy-coordinate system
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21 Mar 2017, 16:32
21 Mar 2017, 16:32
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Expert Reply
1
Bookmarks
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.
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.
