MGMAT Tought Question Bank Problem - Equations, Inequalities

[miss.t.gould]

Is |x| < 1 ?

(1) |x + 1| = 2|x - 1|

(2) |x - 3| > 0

My approach for this is

I was able to rephrase the stmt to -1 < x < 1, and realize that stmt (2) was insufficient as it yields x>3 x<3....

BUT I have no idea how to handle Stmt (2), and to be honest I didn't really understand the explanation provided in the question bank. Can someone please explain to me how to approach Stmt(1)?

My exam is next Friday, so would appreciate a response in the next few days.
Thanks

[arora.sumit88]

My take on this is:

Statement 1: |x+1| = 2|x-1|

Can be broken down into two cases:

a. x + 1 = 2(x-1)
b. x + 1 = -2(x-1)

solving a:
x + 1= 2x - 2
-x = -3
x = 3

solving b:
x + 1 = -2x +2
3x =1
x = 1/3

|X|=|3|<1..No
|1/3|<1.. Yes

1. Not sufficient

2. |X-3|>0
x - 3 >0 or x-3<0
Again |X|<1 can be yes or no while testing different values.
Not sufficient.

Combining 1 and 2

We get |X|=1/3 <1 Yes. So Ans is "C"..

[jnelson0612]

Nice work arora!

[sitsmeagain]

My take on this is:

Statement 1: |x+1| = 2|x-1|

Can be broken down into two cases:

a. x + 1 = 2(x-1)
b. x + 1 = -2(x-1)

solving a:
x + 1= 2x - 2
-x = -3
x = 3

solving b:
x + 1 = -2x +2
3x =1
x = 1/3

|X|=|3|<1..No
|1/3|<1.. Yes

1. Not sufficient

2. |X-3|>0
x - 3 >0 or x-3<0
Again |X|<1 can be yes or no while testing different values.
Not sufficient.

Combining 1 and 2

We get |X|=1/3 <1 Yes. So Ans is "C"..

Hello,
For statement 1 , i got X = 1/3 or X = 3 ==> not sufficient
For Statement 2, i got X < 3 or X > 3 , Can you provide number examples here?
For X>3, i take 4 , hence |4| < 1 , NO
For X<3 i take -2, hence |2| < 1 , NO... Isnt this sufficient?
Should i also consider 0 for X< 3 , which would be |0| < 1, Yes.. hence insufficient ??


How do igo forward for statement 2?

And how does Statement (1)+ (2) give x = 1/3 ??

Regards,
Mustu

[tim]

For statement 2 you just need to plug in something between -1 and 1, as you did with 0. Once you have the two statements together, here's what you know:

it's either 1/3 or 3
AND
it's not 3

this means it has to be 1/3, so we know that |x|<1