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# How many solutions are there for |x-1|-y=-5 and |x-1|+

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CEO
Joined: 15 Aug 2003
Posts: 3454
How many solutions are there for |x-1|-y=-5 and |x-1|+ [#permalink]

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06 Dec 2003, 14:51
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1.How many solutions are there for |x-1|-y=-5 and |x-1|+ |y-5|=1

a.0
b.1
c.2
d 3
e. 4

Last edited by Praetorian on 08 Dec 2003, 00:57, edited 1 time in total.
Director
Joined: 28 Oct 2003
Posts: 501
Location: 55405

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06 Dec 2003, 16:12
Praet--

That's a fantastic question. I tried to simplify and I just got a bee's nest. I ha ve no idea. I wonder if I missed something obvious.

-5(|x-1| + |y-5|)= |x-1|-y
-5|x-1| -5|y-5|= |x-1|-y
-6|x-1| -5|y-5|=-y
-6|x-1| =5|y-5|-y
GMAT Instructor
Joined: 07 Jul 2003
Posts: 770
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE

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07 Dec 2003, 06:05
praetorian123 wrote:
1.How many solutions are there for |x-1|-y=-5 and |x-1|+ |y-5|=1

a.0
b.1
c.2
d 3
e. 4

This is a good problem:

_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

CEO
Joined: 15 Aug 2003
Posts: 3454

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07 Dec 2003, 06:28
praetorian123 wrote:
1.How many solutions are there for |x-1|-y=-5 and |x-1|+ |y-5|=1

a.0
b.1
c.2
d 3
e. 4

heres what i get .
|x-1|-y=-5 ........(1)

2. |x-1|+ |y-5|=1 .....(2)

from (1) , |x-1|= y-5
Substitute in equation (2).
y-5 + |y-5| = 1
|y-5| = 6 - y

therefore,
y-5 = - (6-y) , which gives no solution
y -5 = 6- y , which gives ... y = 11/2

Substitute back in (1)

|x-1|-y=-5

|x-1|= y-5

x-1 = - y+5

i. x = -y + 6

= -11/2 + 6

= 1/5

ii. x-1 = y-5

x = y -4

= 11/2 - 4

x = 3/2

in other words, we have two solutions.

1. x = 1/5 , y= 11/2
2. x= 3/2 , y=11/2

did i do this right?

thanks
praetorian
GMAT Instructor
Joined: 07 Jul 2003
Posts: 770
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE

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09 Dec 2003, 05:13
praetorian123 wrote:
is my solution ok?

That is essentially how I solved it, but I didn't take ALL of the steps. Remember, we only needed to know how many solutions there were, not what the solutions actually are!
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

Re: PS : Modulus   [#permalink] 09 Dec 2003, 05:13
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