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# GMAT Diagnostic Test Question 44

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GMAT Diagnostic Test Question 44 [#permalink]

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07 Jun 2009, 01:12
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GMAT Diagnostic Test Question 44

Field: algebra
Difficulty: 700

$$x^2 + y^2 = 100$$. 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
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Last edited by Bunuel on 23 Feb 2014, 15:29, edited 6 times in total.
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Re: GMAT Diagnostic Test Question 44 [#permalink]

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14 Jun 2009, 09:26
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Explanation

A. |x| + |y| = 10 is possibl;e if one is 0 and the other is 10.
B. |x| > |y| is possible if |x| > |5sqrt2| and |y| < |5sqrt2|
C. |x| > |y| + 10 is never possible because if |x| > 10, (x^2+y2) becomes >100, which is wrong.
D. |x| = |y| is possible if each is equal to |5sqrt2|.
E. |x| - |y| = 5 is possible if 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.
So C is best.
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Last edited by bb on 29 Sep 2013, 22:06, edited 1 time in total.
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Re: GMAT Diagnostic Test Question 44 [#permalink]

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18 Jul 2009, 11:23
How could be possible answer D. |x| = |y| ?
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Re: GMAT Diagnostic Test Question 44 [#permalink]

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18 Jul 2009, 22:13
saruba wrote:
How could be possible answer D. |x| = |y| ?

If |x| = |y|= |5sqrt2|
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Re: GMAT Diagnostic Test Question 44 [#permalink]

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20 Jul 2009, 08:17
2
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probably better to rephrase the question as, all of the following could be true EXCEPT

that phrasing seems to be much more common on standardized tests
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Re: GMAT Diagnostic Test Question 44 [#permalink]

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29 Sep 2009, 04:41
GMAT TIGER wrote:
Explanation
 Rating:

A. |x| + |y| = 10 is possibl;e if one is 0 and the other is 10.
B. |x| > |y| is possible if |x| > |5sqrt2| and |y| < |5sqrt2|
C. |x| > |y| + 10 is never possible because if |x| > 10, (x^2+y2) becomes >100, which is wrong.
D. |x| = |y| is possible if each is equal to |5sqrt2|.
E. |x| - |y| = 5 is possible if 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.
So C is best.

Hi GMAT TIGER,

I don't quite understand some of the answers. The question stem states all of the following MUST be true, except 1.
And if x^2 + y^2 = 100 then x=6 and y=8 is one potential solution as is x=0 and y=10.

For statement a) |x| + |y| = 10 is only true if x=0 and y=10. But if x = 6 and y=8 then it wouldn't always be true?

Maybe I'm missing something?
Intern
Joined: 01 Sep 2009
Posts: 34
Re: GMAT Diagnostic Test Question 44 [#permalink]

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01 Oct 2009, 10:50
I agree.. dont think the wording of the sentence is correct. I dont think MUST should be in there.. maybe could

A does not have to be true
B does not have to be true
D does not have to be true
E does not have to be true
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Re: GMAT Diagnostic Test Question 44 [#permalink]

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18 Oct 2009, 14:35
yangsta8 wrote:
GMAT TIGER wrote:
Explanation
 Rating:

A. |x| + |y| = 10 is possibl;e if one is 0 and the other is 10.
B. |x| > |y| is possible if |x| > |5sqrt2| and |y| < |5sqrt2|
C. |x| > |y| + 10 is never possible because if |x| > 10, (x^2+y2) becomes >100, which is wrong.
D. |x| = |y| is possible if each is equal to |5sqrt2|.
E. |x| - |y| = 5 is possible if 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.
So C is best.

Hi GMAT TIGER,

I don't quite understand some of the answers. The question stem states all of the following MUST be true, except 1.
And if x^2 + y^2 = 100 then x=6 and y=8 is one potential solution as is x=0 and y=10.

For statement a) |x| + |y| = 10 is only true if x=0 and y=10. But if x = 6 and y=8 then it wouldn't always be true?

Maybe I'm missing something?

I agree here too - how come 5 ^ 2 + 5 ^ 2 = 100? Maybe I missed something - Unlike to see questions on GMAT with more than one answer
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Re: GMAT Diagnostic Test Question 44 [#permalink]

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19 Oct 2009, 01:45
I used Pythagoras principle here:

let x and y be the sides of a triangle and 10 be the hypotenuse.

Now, A and C both are not possible.
A: sum of two sides cannot be equal to 10, the sum of two sides should be > 10.
C: x should be less than sum of y and 10.
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Posts: 215
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Re: GMAT Diagnostic Test Question 44 [#permalink]

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21 Nov 2009, 09:12
GMAT TIGER wrote:
Explanation
 Rating:

A. |x| + |y| = 10 is possibl;e if one is 0 and the other is 10.
B. |x| > |y| is possible if |x| > |5sqrt2| and |y| < |5sqrt2|
C. |x| > |y| + 10 is never possible because if |x| > 10, (x^2+y2) becomes >100, which is wrong.
D. |x| = |y| is possible if each is equal to |5sqrt2|.
E. |x| - |y| = 5 is possible if 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.
So C is best.

I have a hard time finding a way to prove E. How did you came up with the number?
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Joined: 14 Dec 2009
Posts: 76
Re: GMAT Diagnostic Test Question 44 [#permalink]

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22 Dec 2009, 06:02
lonewolf wrote:
GMAT TIGER wrote:
Explanation
 Rating:

A. |x| + |y| = 10 is possibl;e if one is 0 and the other is 10.
B. |x| > |y| is possible if |x| > |5sqrt2| and |y| < |5sqrt2|
C. |x| > |y| + 10 is never possible because if |x| > 10, (x^2+y2) becomes >100, which is wrong.
D. |x| = |y| is possible if each is equal to |5sqrt2|.
E. |x| - |y| = 5 is possible if 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.
So C is best.

I have a hard time finding a way to prove E. How did you came up with the number?

Just solve the system of equations:
x^2+y^2=100
x - y = 5
and you'll get the numbers to prove E.
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Joined: 08 Dec 2009
Posts: 409
Re: GMAT Diagnostic Test Question 44 [#permalink]

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10 Feb 2010, 19:36
Igor010 wrote:
Just solve the system of equations:
x^2+y^2=100
x - y = 5
and you'll get the numbers to prove E.

I don't think that'll work buddy:

x - y = 5
x = y + 5, substitute into first eq yields:

(y+5)^2 + y^2 = 100

rearranging gives: 2y^2 + 10y - 75 = 0....
there's no solution for the above: (check: b^2 - 4ac term is negative, which implies imaginary roots).
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Re: GMAT Diagnostic Test Question 44 [#permalink]

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11 Feb 2010, 10:25
Igor010 wrote:
Just solve the system of equations:
x^2+y^2=100
x - y = 5
and you'll get the numbers to prove E.

I don't think that'll work buddy:

x - y = 5
x = y + 5, substitute into first eq yields:

(y+5)^2 + y^2 = 100

rearranging gives: 2y^2 + 10y - 75 = 0....
there's no solution for the above: (check: b^2 - 4ac term is negative, which implies imaginary roots).

I'm sorry adalfu, $$2y^2+10y-75=0$$ gives us $$100-(4*2*(-75))$$ which gives us +700. You can get square root and solve for Y. Even if you know approx. value of Y, you can find approx. value of X and then plug in to prove your results.
Seems like you forgot to change the sign...
Hope this helped.
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Posts: 409
Re: GMAT Diagnostic Test Question 44 [#permalink]

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11 Feb 2010, 10:55
doh! brilliant... thanks Igor010

i feel that all my quant errors are due to some sort of simple arithmetic mistakes (i'm a math/stats major but i've forgotten my basic algebra... sometimes i forget what 7x9 or 6x9 is -- i have to seriously think about it; it just doesn't come natural anymore).

thanks
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Re: GMAT Diagnostic Test Question 44 [#permalink]

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17 Sep 2011, 12:56
1
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Economist wrote:
I used Pythagoras principle here:

let x and y be the sides of a triangle and 10 be the hypotenuse.

Now, A and C both are not possible.
A: sum of two sides cannot be equal to 10, the sum of two sides should be > 10.
C: x should be less than sum of y and 10.

But the question didn't say X, Y, and 10 are the vertices of a triangle, so X or Y can be zero (and they don't need to follow the Pythagoras principle).
So, just C is the right answer.
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Joined: 07 Nov 2012
Posts: 13
Re: GMAT Diagnostic Test Question 44 [#permalink]

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15 Nov 2012, 11:20
I don't get the solution at all....

I can't see beyond the fact that for x^2 + y^2 = 100, x and y must be one of these combinations:

10, 0
-10, 0
6, 8
-6, 8
6, -8
-6, -8

In which case:

A) |x| + |y| = 10..... could be if 10, 0

B) |x| > |y| ..... could be if 10, 0

C) |x| > |y| +10 ........ not for any of the above combinations

D) |x| = |y| ....... not for any of the above combinations

E) |x| - |y| = 5 ....... not for any of the above combinations

Potential answer C, D or E.
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Re: GMAT Diagnostic Test Question 44 [#permalink]

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21 Nov 2013, 04:37
Its more than 3 years since the last post. But can anyone answer my question

How is 5^2 + 5^2 = 100 ?

According to the reasoning provided by GMAT TIGER for D as a possibility

Quote:
D. |x| = |y| is possible if each is equal to |5sqrt2|.

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Re: GMAT Diagnostic Test Question 44 [#permalink]

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21 Nov 2013, 04:40
Anshulmodi wrote:
Its more than 3 years since the last post. But can anyone answer my question

How is 5^2 + 5^2 = 100 ?

According to the reasoning provided by GMAT TIGER for D as a possibility

Quote:
D. |x| = |y| is possible if each is equal to |5sqrt2|.

It's $$5\sqrt{2}$$: $$(5\sqrt{2})^2+(5\sqrt{2})^2=100$$.
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Quantitative :: Problem solving :: Algebra :: D01-44 [#permalink]

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14 Dec 2013, 19:41
$$x^2+y^2=100$$. 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|.
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Re: Quantitative :: Problem solving :: Algebra :: D01-44 [#permalink]

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14 Dec 2013, 20:53
1
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1
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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|.

For option E: Why making so much complicated?

The max difference for |X| - |Y| will be 10 and minimum difference 0.

Whether the difference is 3, 5, 8, it doesnt matter at all. since they all will come under the above range, possibly making the given equation valid.

To solve in 15 secs: Just check for option in which X or Y is greater than 10. Only C satisfies that.
Re: Quantitative :: Problem solving :: Algebra :: D01-44   [#permalink] 14 Dec 2013, 20:53

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# GMAT Diagnostic Test Question 44

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