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GMAT Diagnostic Test Question 44

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Math Expert
Joined: 02 Sep 2009
Posts: 41884

Kudos [?]: 128932 [0], given: 12183

Re: Quantitative :: Problem solving :: Algebra :: D01-44 [#permalink]

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15 Dec 2013, 04:50
mniyer wrote:
$$x^2+y^2=100$$. All of the following could be true EXCEPT
(A) |x|+|y|=10
(B) |x|>|y|
(C) |x|>|y|+10
(D) |x|=|y|
(E) |x|−|y|=5

PS: Did my best to search for an existing post and couldn't find any.

[Reveal] Spoiler:
A. |x|+|y|=10 is possible if one is 0 and the other is 10.
B. |x|>|y| is possible if |x|>|52√| and |y|<|52√|
C. |x|>|y|+10 is never possible because if |x|>10, x2+y2 becomes greater than 100, which is wrong.
D. |x|=|y| is possible if each is equal to |52√|.
E. |x|−|y|=5 is possible if |x|=|9.11| and |y|=|4.11|.
Therefore all but C are possible. |x|>|y|+10 means x is greater than 10, which is not possible

Is there any alternate way to tackle this problem besides just plugging in numbers? It's very challenging to figure out 9.11 and 4.11 could be two possibilities to rule out E.

Here's what I did to solve this problem. Got stuck at this step and did not have a clue to proceed further...Any algebraic help will get kudos
$$x^2+y^2=100$$
$$(x+y)^2-2xy = 10^2$$
$$(x+y)^2 = \frac{10^2}{-2xy}$$
$$|x +y| = \frac{|10|}{\sqrt{-2xy}}$$ => Root of negative number will result in imaginary and therefore it's likely that this condition might be the answer. But I'm not even sure if this is the correct approach and could not relate |x+y| and |10|.

Merging similar topics. Please refer to the solutions on page 1 and ask if anything remains unclear.
_________________

Kudos [?]: 128932 [0], given: 12183

Manager
Joined: 04 Oct 2013
Posts: 162

Kudos [?]: 119 [0], given: 55

Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Re: Quantitative :: Problem solving :: Algebra :: D01-44 [#permalink]

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24 Dec 2013, 13:28
Bunuel wrote:
mniyer wrote:
$$x^2+y^2=100$$. All of the following could be true EXCEPT
(A) |x|+|y|=10
(B) |x|>|y|
(C) |x|>|y|+10
(D) |x|=|y|
(E) |x|−|y|=5

PS: Did my best to search for an existing post and couldn't find any.

[Reveal] Spoiler:
A. |x|+|y|=10 is possible if one is 0 and the other is 10.
B. |x|>|y| is possible if |x|>|52√| and |y|<|52√|
C. |x|>|y|+10 is never possible because if |x|>10, x2+y2 becomes greater than 100, which is wrong.
D. |x|=|y| is possible if each is equal to |52√|.
E. |x|−|y|=5 is possible if |x|=|9.11| and |y|=|4.11|.
Therefore all but C are possible. |x|>|y|+10 means x is greater than 10, which is not possible

Is there any alternate way to tackle this problem besides just plugging in numbers? It's very challenging to figure out 9.11 and 4.11 could be two possibilities to rule out E.

Here's what I did to solve this problem. Got stuck at this step and did not have a clue to proceed further...Any algebraic help will get kudos
$$x^2+y^2=100$$
$$(x+y)^2-2xy = 10^2$$
$$(x+y)^2 = \frac{10^2}{-2xy}$$
$$|x +y| = \frac{|10|}{\sqrt{-2xy}}$$ => Root of negative number will result in imaginary and therefore it's likely that this condition might be the answer. But I'm not even sure if this is the correct approach and could not relate |x+y| and |10|.

Merging similar topics. Please refer to the solutions on page 1 and ask if anything remains unclear.

There seems to be an error in the steps above.
The line above rewritten after correction as
$$(x+y)^2 = 10^2 + 2xy$$

Kudos [?]: 119 [0], given: 55

Intern
Joined: 13 Dec 2013
Posts: 39

Kudos [?]: 19 [0], given: 10

Schools: Fuqua (I), AGSM '16
GMAT 1: 620 Q42 V33
Re: GMAT Diagnostic Test Question 44 [#permalink]

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23 Feb 2014, 15:16
I clicked on C and got it wrong. It says it is D. Scanned through the answers, yet never found if the right answer was changed to D somewhere along the thread. Which one is it then?

Kudos [?]: 19 [0], given: 10

Math Expert
Joined: 02 Sep 2009
Posts: 41884

Kudos [?]: 128932 [0], given: 12183

Re: GMAT Diagnostic Test Question 44 [#permalink]

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23 Feb 2014, 15:29
Enael wrote:
I clicked on C and got it wrong. It says it is D. Scanned through the answers, yet never found if the right answer was changed to D somewhere along the thread. Which one is it then?

It's C. Edited the OA.
_________________

Kudos [?]: 128932 [0], given: 12183

Re: GMAT Diagnostic Test Question 44   [#permalink] 23 Feb 2014, 15:29

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GMAT Diagnostic Test Question 44

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