If x^2 + y^2 = 100 , all of the following could be true EXCEPT: A. |x| + |y| = 10 B. |x| \gt |y| C. |x| \gt |y| + 10 D. |x| = |y| E. |x| - |y| = 5

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AditiDeokar

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20 Dec 2025, 02:28

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Hi hr1212,
How did you figure out values such as sqrt 50 for option D, could you please explain further?

hr1212

I think this question is pretty relevant. The key is to select numbers that quickly eliminate incorrect options. All you need is one good example to rapidly narrow down your choices -

A. \(|x| + |y| = 10\) => x=10 & y=0
B. \(|x| \gt |y|\) => x=10 & y=0
C. \(|x| \gt |y| + 10\) => x & y can take max value of 10, because in that case other variable would be 0. And if we have, y=0.01, then x=10.01 as per this equation, which is not possible, hence this is incorrect.
D. \(|x| = |y|\) => x=sqrt(50) & y=sqrt(50)
E. \(|x| - |y| = 5\) => This could seem a bit tricky to eliminate directly but one way here could be to square this => x^2 + y^2 - 2|x||y| = 25 => 2|x||y| = 75. So there does exist some value of x & y satisfying this equation.

IMO: C

If you can't figure out direct ways, figure out smart ways to quickly walk through options.

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23 Dec 2025, 09:16

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Hi AditiDeokar,

Given x^2 + y^2 = 100,

if x = y, then x^2 + x^2 = 100
2*x^2 = 100
x^2 = 50
x = sqrt(50)
y = x = sqrt(50)

AditiDeokar

Hi hr1212,
How did you figure out values such as sqrt 50 for option D, could you please explain further?

ahaim

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03 Jan 2026, 05:30

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I did not quite understand the solution. Is this question relevant to the GMAT Focus?
AsI know, there is no Geometry..

Bunuel

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03 Jan 2026, 05:39

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ahaim

I did not quite understand the solution. Is this question relevant to the GMAT Focus?
AsI know, there is no Geometry..

This is not a geometry question. If you read the discussion, you will see that it can be solved without using any geometry concepts. Also, even though heavy geometry is no longer tested on the GMAT, coordinate geometry, functions, coordinate planes, and lines are still relevant and tested.

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