[#21] 2 Min. Challenge : Solutions II

Question

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

Geethu · Answer

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.

BG · Answer

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)

Makky07 · Answer

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.

kpadma · Answer

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.

anandnk · Answer

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.

Makky07 · Answer

Nice anandnk! You took such a straightforward approach.

Praetorian · Answer

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

[#21] 2 Min. Challenge : Solutions II

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards