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CAT DS: Pls suggest flaw in reasoning:

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shriwantchoudhary
 Post subject: CAT DS: Pls suggest flaw in reasoning:
 Post Posted: Tue Oct 11, 2011 2:00 pm 
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Students


Posts: 6
DS From CAT-2 (MGMAT)

If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x – 12y = 0

(2) |x| – |y| = 16

Consider the question stem: |x| + |y| = 32
Does this equation not mean the following simultaneous equations:
x + y = 32
-x -y = 32
-x + y = 32
x -y = 32

Now using Statement -1 we have x = -3y using the info from the q stem and statement -1 we can deduce that:

y = +/-8 & y = +/-16 for these values of y we can get corresponding four different values for x i.e. x = +/- 24 & +/-48

But then a question comes, does the original question stem get satisfied with all set of values of x & y?

we see that only two pairs of x,y satisfy the question stem hence xy is obtained. so Statement-1 is sufficient.
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700+
 Post subject: Re: CAT DS: Pls suggest flaw in reasoning:
 Post Posted: Tue Oct 11, 2011 7:26 pm 
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Students


Posts: 23
Location: Bangalore
Let me try helping you out with this one

According to the question |x| + |y| = 32. Lets just keep it like this for now. We just need to remember that |x| is the absolute value of x & it is always positive.

According to statement one, -4x – 12y = 0 i.e. x = -3y

Lets make a table

----y--------x--------Is |x| + |y| = 32?--------xy--------
----8------(-24)-------------Yes-------------(-192)------
---(-8)------24--------------Yes-------------(-192)------
----16-----(-48)------------- No---------------NA-------
---(-16)----(48)--------------No---------------NA-------

Since the question is asking for the value of xy, from the above table it can b seen that the value of xy is -192.

Therefore A is sufficient.

We need not consider values where y = + or - 16 because it doesn't satisfy both the conditions |x| + |y| = 32 & x = (-3y).

Hope I was able to clear your doubt

Changes shown in Blue color


Last edited by 700+ on Wed Oct 12, 2011 4:34 pm, edited 1 time in total.

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shriwantchoudhary
 Post subject: Re: CAT DS: Pls suggest flaw in reasoning:
 Post Posted: Wed Oct 12, 2011 3:27 pm 
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Students


Posts: 6
"We need not consider values where y = + or - 16 because it doesn't satisfy the condition |x| + |y| = 32."


I suspected the same thing.

Thanks,
SC
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jnelson0612
 Post subject: Re: CAT DS: Pls suggest flaw in reasoning:
 Post Posted: Sun Nov 20, 2011 12:26 am 
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ManhattanGMAT Staff


Posts: 1857
shriwantchoudhary wrote:
"We need not consider values where y = + or - 16 because it doesn't satisfy the condition |x| + |y| = 32."


I suspected the same thing.

Thanks,
SC


Correct! :-)

_________________
Jamie Nelson
ManhattanGMAT Instructor
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