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Absolute Value

by joyseychow » Tue Feb 02, 2010 8:50 pm
If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x - 12y = 0

(2) |x| - |y| = 16


[spoiler]OA is A. Am I missing something here? Why stmt 1 is sufficient? [/spoiler]
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by fibbonnaci » Tue Feb 02, 2010 10:22 pm
please post the question properly. mathematical symbols are not clear.
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by harsh.champ » Tue Feb 02, 2010 10:55 pm
joyseychow wrote:If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x - 12y = 0

(2) |x| - |y| = 16


[spoiler]OA is A. Am I missing something here? Why stmt 1 is sufficient? [/spoiler]
______________________
I think joyseychow meant + instead of the question mark sign(?) .On the keyboard if you hold on to the Fn key while pressing the (?) key you get a +,so i guess that was the original intention.
Alternatively,if you quote joyseychow's post,you can see that the original equations were
(1) (-)4x (-)12y =0

(2) |x| (minus) |y| = 16

________________________

I guess it would be okay to proceed using the above assumptions.
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by harsh.champ » Tue Feb 02, 2010 11:11 pm
fibbonnaci - Just try quoting the question posted by joyseychow.There is some problem with it.In the quoted text, you see that the question appears correct with proper mathematical symbols.Then copy the text and paste it below.Then click on the "Submit" button.You will see that the symbols change and we see a (?) sign instead of the +/- sign.I think there is some problem with the forum and it is needed to bring this to the notice of BEAT THE GMAT TEAM.
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by harsh.champ » Tue Feb 02, 2010 11:18 pm
joyseychow wrote:If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x - 12y = 0

(2) |x| - |y| = 16


[spoiler]OA is A. Am I missing something here? Why stmt 1 is sufficient? [/spoiler]
_____________________
So, I think the question reduces to:-

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

(1) -4x-12y = 0

(2) |x| (minus) |y| = 16


Soln:-Now for x and y to be non-zero integers we have the following sets
(1,31);(2,30)...........(29,3);(30,2);(31,1) ------ [Total=31]
Taking both the positive and negative signs of x and y,we have 31x4 solns.

Statement 1:It gives x=-3y that means we have y=-8,x=24 and y=8,x=-24.In both the cases,the product xy remains the same.
Statement 2: |x| - |y|=16 gives four solutions , x=+24,y=-8;x=+24,y=+8;x=-24,y=-8;x=-24,y=+8.Over here the product is varying.
Hence , only statement (1) is sufficient for answering the question.

I guess it clears your doubt. :)
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by fibbonnaci » Tue Feb 02, 2010 11:31 pm
harsh.champ wrote:fibbonnaci - Just try quoting the question posted by joyseychow.There is some problem with it.In the quoted text, you see that the question appears correct with proper mathematical symbols.Then copy the text and paste it below.Then click on the "Submit" button.You will see that the symbols change and we see a (?) sign instead of the +/- sign.I think there is some problem with the forum and it is needed to bring this to the notice of BEAT THE GMAT TEAM.
hey harsh.champ, i will take this up with the BTG team. this is a genuine concern for the group, and i am sure we will fix it soon
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by thephoenix » Tue Feb 02, 2010 11:42 pm
joyseychow wrote:If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x - 12y = 0

(2) |x| - |y| = 16


[spoiler]OA is A. Am I missing something here? Why stmt 1 is sufficient? [/spoiler]
s1)----->X=-3Y
==>IF Y<0, X>0
IF Y>0;X<0

FROM QUESTION

lXl + lYl=32
PUT X=-3Y--->3Y+Y=32---->lYl=8 AND lXl=24---->Y=+OR-8 AND X=+OR-24

NOW WE KNW THAT X=-3Y
---> IF Y=-8 ---->X=24 (WHICH IS TRUE AS PER THE EQN GIVEN IN Q)----->XY=-8*24
IF Y=+8----->X=-24----->XY=-8*24
IF X=24---->Y=-8---->XY=-8*24
AND IF X=-24---->Y=8---->XY=-8*24

HENCE FOR ALL THE POSSIBLE CASE SOLN IS SAME I.E -8*24
HENCE SUFF
S2)
WE HAVE TWO EQN
I.E
lXl+lYl=32
AND lXl-lYl=16
SOLVING X=+-24 AND Y=+-8

NOW IF X=24 ; FOR BTH Y=+-8 WE ARE GETTING lXl+lYl=32 AND lXl-lYl=16 BUT
XY =24*8 OR -8*24
SAME WITH X=-24

HENCE TWO ANS
HENCE INSUFF
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by DavidP » Wed Feb 03, 2010 1:32 am
Hi harsh.champ and fibbonnaci. Thanks for sharing the problem with the special minus sign. I just fixed the problem and confirmed that the minus sign appears correctly in my browser. Can you please let me know if it looks OK in your browser? Thanks!
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by sanju09 » Wed Feb 03, 2010 1:34 am
joyseychow wrote:If x and y are non-zero integers and |x| + |y| = 32, what is xy?

(1) -4x - 12y = 0

(2) |x| - |y| = 16


[spoiler]OA is A. Am I missing something here? Why stmt 1 is sufficient? [/spoiler]
(1) -4x - 12y = 0 implies that x = -3 y implies that x y < 0 and |x| = 3 |y|.

With the help of the stem we can draw that |x| = 24 and |y| = 8, either way, x y = -192.

So, sufficient.
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by fibbonnaci » Wed Feb 03, 2010 1:38 am
yup David, the minus sign appears fine in my browser.
Thanks a lot!
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by harsh.champ » Wed Feb 03, 2010 2:18 am
fibbonnaci wrote:
harsh.champ wrote:fibbonnaci - Just try quoting the question posted by joyseychow.There is some problem with it.In the quoted text, you see that the question appears correct with proper mathematical symbols.Then copy the text and paste it below.Then click on the "Submit" button.You will see that the symbols change and we see a (?) sign instead of the +/- sign.I think there is some problem with the forum and it is needed to bring this to the notice of BEAT THE GMAT TEAM.
hey harsh.champ, i will take this up with the BTG team. this is a genuine concern for the group, and i am sure we will fix it soon
hey fibbonnaci,
Thanks for looking into the matter.
The same problem crept up in another forum thread.
https://www.beatthegmat.com/ps-q-pls-ans ... tml#219793
I don't know if it is a bug,but it needs to be rectified as improper representation of a question leads to huge time waste of
beat the gmat community members.
Last edited by harsh.champ on Wed Feb 03, 2010 2:24 am, edited 1 time in total.
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by harsh.champ » Wed Feb 03, 2010 2:22 am
DavidP wrote:Hi harsh.champ and fibbonnaci. Thanks for sharing the problem with the special minus sign. I just fixed the problem and confirmed that the minus sign appears correctly in my browser. Can you please let me know if it looks OK in your browser? Thanks!
I would like to know what was the reason behind it as the same problem has surfaced in other threads of this forum also.
[https://www.beatthegmat.com/ps-q-pls-ans ... tml#219793]
Is this some bug or something??
Does it pertain to any specific browser you are using??I personally use firefox.
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by DavidP » Wed Feb 03, 2010 3:09 am
The problem is that you used some special character that looks like - rather than the actual - (dash) character when you entered the text for the formulas. This is a pretty common thing.

Our browsers should recognize these special characters and display them properly because many people use the special characters. Unfortunately, most browsers don't recognize the special characters and so they show a mess.

I fixed the bug by making BTG's forum software replace any special dash character with the normal dash character.
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