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# If a and b are non-zero integers and |a| + |b| = 32, what is

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If a and b are non-zero integers and |a| + |b| = 32, what is  [#permalink]

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21 Feb 2012, 21:00
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75% (hard)

Question Stats:

63% (02:28) correct 37% (02:50) wrong based on 168 sessions

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If a and b are non-zero integers and |a| + |b| = 32, what is ab?

(1) -4a – 12b = 0
(2) |a| – |b| = 16
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Joined: 02 Sep 2009
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21 Feb 2012, 22:09
If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) $$-4x-12y=0$$ --> $$x=-3y$$ --> $$x$$ and $$y$$ have opposite signs --> so either $$|x|=x$$ and $$|y|=-y$$ OR $$|x|=-x$$ and $$|y|=y$$ --> either $$|x|+|y|=-x+y=3y+y=4y=32$$: $$y=8$$, $$x=-24$$, $$xy=-24*8$$ OR $$|x|+|y|=x-y=-3y-y=-4y=32$$: $$y=-8$$, $$x=24$$, $$xy=-24*8$$, same answer. Sufficient.

(2) $$|x| - |y| = 16$$. Sum this one with th equations given in the stem --> $$2|x|=48$$ --> $$|x|=24$$, $$|y|=8$$. $$xy=-24*8$$ (x and y have opposite sign) or $$xy=24*8$$ (x and y have the same sign). Multiple choices. Not sufficient.

For hard inequality and absolute value questions with detailed solutions check this: inequality-and-absolute-value-questions-from-my-collection-86939-40.html

Hope it helps.
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Re: If a and b are non-zero integers and |a| + |b| = 32, what is  [#permalink]

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22 Feb 2012, 19:37
i am not able to view the solutions for hard questions link tat yu ve shared above..
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Re: If a and b are non-zero integers and |a| + |b| = 32, what is  [#permalink]

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22 Feb 2012, 22:11
dvinoth86 wrote:
i am not able to view the solutions for hard questions link tat yu ve shared above..

Works fine with me... Do you mean that the link itself is broken, or you cannot find the solutions there? Each question has a link below it which leads to the solution, or you can just go to pages 2 and 3 where all the explanations are.

Let me know if this works.
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Re: If a and b are non-zero integers and |a| + |b| = 32, what is  [#permalink]

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22 Feb 2012, 22:16
Perfect Bunuel...that is the way I solved it too. But a slight error, cos its DS I did not completely solve it, assumed St 2 would be sufficient, but seen your solution....it indeed has multiple possibilities. For DS I believe I have to be very careful and do solve most of it before answering.thanks
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Re: If a and b are non-zero integers and |a| + |b| = 32, what is  [#permalink]

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09 Aug 2017, 07:12
Bunuel wrote:
If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) $$-4x-12y=0$$ --> $$x=-3y$$ --> $$x$$ and $$y$$ have opposite signs --> so either $$|x|=x$$ and $$|y|=-y$$ OR $$|x|=-x$$ and $$|y|=y$$ --> either $$|x|+|y|=-x+y=3y+y=4y=32$$: $$y=8$$, $$x=-24$$, $$xy=-24*8$$ OR $$|x|+|y|=x-y=-3y-y=-4y=32$$: $$y=-8$$, $$x=24$$, $$xy=-24*8$$, same answer. Sufficient.

(2) $$|x| - |y| = 16$$. Sum this one with th equations given in the stem --> $$2|x|=48$$ --> $$|x|=24$$, $$|y|=8$$. $$xy=-24*8$$ (x and y have opposite sign) or $$xy=24*8$$ (x and y have the same sign). Multiple choices. Not sufficient.

For hard inequality and absolute value questions with detailed solutions check this: http://gmatclub.com/forum/inequality-an ... 39-40.html

Hope it helps.

Hi Bunuel,
I guess there's some typo because of which your second statement looks faulty.
|x|= 24 and |y| = 8
So there will be 4 different set of values of x and y (When x and y have same sign, when x and y have different sign)
The values of xy will be 42 and -42.
That is why statement 2 is not sufficient.
I guess you have missed a negative sign in one of 24*8

Let me know if I'm wrong.
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Re: If a and b are non-zero integers and |a| + |b| = 32, what is  [#permalink]

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09 Aug 2017, 07:25
dvinoth86 wrote:
If a and b are non-zero integers and |a| + |b| = 32, what is ab?

(1) -4a – 12b = 0
(2) |a| – |b| = 16

a, b ≠ 0
|a| + |b| = 32
a*b = ?

1) -4a - 12b = 0
=> a = -3b
=> a = 24, b = -8
OR a = -24, b = 8
a*b = -24*8
Sufficient.

2) |a| - |b| = 16
a = 20, b = 4
a = -20, b = 4
a = 18, b = 2
Insufficient.

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Re: If a and b are non-zero integers and |a| + |b| = 32, what is   [#permalink] 09 Aug 2017, 07:25
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