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Praetorian
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[#21] 2 Min. Challenge : Solutions II 17 Mar 2004, 09:32
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1. Time yourself
2. Solve this as fast as you can.
3. Write your solution here , and please mention your time.


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



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[#21] 2 Min. Challenge : Solutions II 17 Mar 2004, 09:52
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A ??


For |x-1|+ |y-5|=1 to be true

x= 0 and y= 5
or
x=1 and y =6

If we apply the same values for |x-1|-y=-5
the equation doesn't get satisfied.

took 2 mins.
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BG
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[#21] 2 Min. Challenge : Solutions II 17 Mar 2004, 09:55
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Think there are 4. i can not understand if it should be separate solutions or common for both equations. Time >4 min. solutions to the first are X=1 Y=5, to the second (X=1,Y=6), (X=2,Y=5),(X=0,Y=5)
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[#21] 2 Min. Challenge : Solutions II Updated on: 17 Mar 2004, 10:03
Originally posted by Makky07 on 17 Mar 2004, 09:56.
Last edited by Makky07 on 17 Mar 2004, 10:03, edited 2 times in total.
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B ?
Looking at the second equation, the absolute value of x-1 and y-5 must be positive sum to 1 e.g. 1 + 0 = 1 OR 0 + 1 = 1 OR 0.5 + 0.5 = 1

So, from the second equation, x = 1 and y = 6 OR x = 2 and y = 5 OR x = 1.5 and y = 5.5

Plug those values back into the first equation and you find that only x=1.5 and y=5.5 solves the equation.

I think I'm missing something but I can't think of what it is.
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[#21] 2 Min. Challenge : Solutions II 17 Mar 2004, 09:59
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Dear Praetorian

Thanks for posting such a good question!

My guess is B

There is one and only solution (0.5, 5.5)


Time: much more than 2 mins.
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[#21] 2 Min. Challenge : Solutions II 17 Mar 2004, 10:00
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Answer is C. I took about 2 minutes.

This is how I did it.

|X-1| = Y-5
and
|X-1| = 1 - |Y-5|
so 1-|Y-5| = Y-5
1 = Y-5 + |Y-5|
if Y = 5.5 then this equation is satisfied
so
|X-1| = 0.5
only X = 1.5 or X = 0.5 satisfies this equation.
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[#21] 2 Min. Challenge : Solutions II 17 Mar 2004, 10:03
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Nice anandnk! You took such a straightforward approach.
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[#21] 2 Min. Challenge : Solutions II 17 Mar 2004, 20:32
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praetorian123
1. Time yourself
2. Solve this as fast as you can.
3. Write your solution here , and please mention your time.


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


C is the correct answer.

On your GMAT, you only need to know HOW many solutions. So, we dont need actual values. But, for the benefit of the guys , here is a complete solution.


1. |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



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