I think I must have been sleeping when this was taught in the 7th grade 
- Whats the rule to solve two eqs with two or more abs variables?
- Whats the rule to solve two eqs with two or more abs variables?- Attachments
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Source: Beat The GMAT — Data Sufficiency |
i think the answer should be C
the solution goes like this:
|x|+|y|=32
|x|-|y|=16
==>2|x|=48 or |x|=24
Hence x can be 24 or -24;
also x = -3y;
hence if x =24 then y = -8
and if x = -24 then y = 8
either way xy = -(24* 8)
Hence answer is c
Correct me if i am wrong
the solution goes like this:
|x|+|y|=32
|x|-|y|=16
==>2|x|=48 or |x|=24
Hence x can be 24 or -24;
also x = -3y;
hence if x =24 then y = -8
and if x = -24 then y = 8
either way xy = -(24* 8)
Hence answer is c
Correct me if i am wrong
Oh well I stopped calculating XY when I chose E. God knows when I will star getting things as asked in the Question.
When ever I read |X|, I also keep in my mind that its the distance from 0 on the number line towards either side
(1)
|X| + |Y| =32
X=-3Y
|3Y| + |Y| =32 -> |Y| = 8
Y = 8 X =-24
Y =-8 X= 24
XY =-192 both ways B, C & E out
(2)
|X| + |Y| =32
|X| - |Y| =16
|X|= 24
X=24 means |Y|=8, Y =8 /-8 XY =192/-192
X =-24 means |Y| =8, Y =8/ -8 XY=192/-192
We have both 192 and -192. Can't be D
Hence A.
Probably there is more to it as you asked how to solve two equations involving two equations with absolute variables. Let us know
When ever I read |X|, I also keep in my mind that its the distance from 0 on the number line towards either side
(1)
|X| + |Y| =32
X=-3Y
|3Y| + |Y| =32 -> |Y| = 8
Y = 8 X =-24
Y =-8 X= 24
XY =-192 both ways B, C & E out
(2)
|X| + |Y| =32
|X| - |Y| =16
|X|= 24
X=24 means |Y|=8, Y =8 /-8 XY =192/-192
X =-24 means |Y| =8, Y =8/ -8 XY=192/-192
We have both 192 and -192. Can't be D
Hence A.
Probably there is more to it as you asked how to solve two equations involving two equations with absolute variables. Let us know
