GMAT Club - m11#16

Question

Which of the following represents the range for all x which satisfy |1 - x| < 1 ?

A. (-1, 1)
B. (-1, 2)
C. (0, 1)
D. (0, 2)
E. (1, 2)

alpha_plus_gamma · Answer

-1< 1-x < 1

x<2, x> 0

D.

x2suresh · Answer

say 1-x =y |y|<1 means -----> y values must be between -1 and 1 when y>0 --> y<1 --> 1-x<1 --> x>0 when y<0 --> -y<1 --> y>-1 --> 1-x>-1 --> x<2 (0,2) is it clear

arjtryarjtry · Answer

hmmm.... i went to the basics.. and it struck me suddenly thanks suresh... cos ur explanation reinforced what i thought. in maths when u discover something u feel like.... :band

..

icandy · Answer

When ever you see modulo you have two possibilities

(1-x) < 1 & -(1-x) < 1

If you solve both of them, 0<x<2 is what you will get.

Twoone · Answer

Yep,

x> 2 and x < 0.

so it is in between 0 and 2. so, (0,2).

So IMO is D

lsmv479 · Answer

Mathematicians usually think of absolute value as a measure of distance (more abstractly, a metric)

abs(a-b) is the distance from a to b (or vice versa)

abs(b) = abs(b-0) is the distance from b to zero

To find the values that satisfy the equation

abs(1-x) <1

we want to find all values whose distance from 1 is less than 1.

Think visually using the number line and visualize all the values that are less than 1 unit from the number 1

(0,2) is obviously those values

AndreG · Answer

Which of the following represents the range for all  X  which satisfy  |1 - X| \lt 1  ?

* (-1, 1)
 * (-1, 2)
 * (0, 1)
 * (0, 2)
 * (1, 2)

Answer:
 The correct answer is D.

Explanation:
 If  X \ge 1  , then the inequality turns into  X - 1 \lt 1  or  X \lt 2  . If  X \lt 1  , then the inequality turns into  1 - X \lt 1  or  X \gt 0  . Combine the intervals to get the answer.

My problem:
 |1-2|=1 not smaller than 1 ... ???

Bunuel · Answer

|1-x|<{1} --> key point is x=1 (key points are the values of x when absolute values equal to zero), thus two ranges to check: x<1 --> |1-x|=1-x and |1-x|<{1} becomes: 1-x<{1} --> x>0 ; x\geq{1} --> |1-x|=-1+x and |1-x|<{1} becomes: -1+x<{1} --> x<2 ; So |1-x|<{1} holds true for 0

AndreG · Answer

Thanks for the quick reply! 
Your explanation with the key-point value is very helpful!

Also, I was not aware, that if they talk about "range" the values given are excluded (hence  0<x<2  )

Thanks
André

bblast · Answer

quoting bunuel :

" I guess (0,2) should be changed to 0<x<2 (as well as all other options) to avoid confusion whether 0 and 2 are inclusive in the range. "

This correction is needed IMO. when we say (0,2) we mean than the numbers are included.
Also another alternative would be to change the question to |1-x|<=1

anujkch · Answer

I was able to get to the equation 
2> x > 0

but it will be wrong to say (0,2) as this will include 0 and 2 as well where as x not equal to 0 or 2.

Please comment

GMAT Club - m11#16

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