Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 10 Mar 2014, 05:42

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is |x| + |x -1| = 1? (1) x 0 (2) x 1

Author Message
TAGS:
Manager
Status: Persevering
Joined: 15 May 2013
Posts: 219
Location: India
GMAT Date: 08-02-2013
GPA: 3.7
WE: Consulting (Consulting)
Followers: 0

Kudos [?]: 43 [0], given: 34

Re: Is |x| + |x -1| = 1? (1) x 0 (2) x 1 [#permalink]  18 Aug 2013, 05:15
btg9788 wrote:
Shouldn't it be mandatory that X is an integer? Or that is assumed implicitly?

No you should not assume it to be a integer, if it is not mentioned. The problem here is the range is such that even if you pick a non integer value, you will get the answer as 1.

After combining we have 0<=x<=1

For example if x=0.33

|0.3|+|1-0.3|=.3+.7=1 . Hope it is clear
_________________

--It's one thing to get defeated, but another to accept it.

Manager
Joined: 31 Mar 2013
Posts: 64
Followers: 0

Kudos [?]: 7 [0], given: 74

Re: Is |x| + |x -1| = 1? (1) x 0 (2) x 1 [#permalink]  29 Sep 2013, 12:20
Bunuel wrote:
samark wrote:
Bunuel,

I am confused here..
"B. 0<=x<=1 --> x-x+1=1 --> 1=1. Which means that for ANY value from the range 0<=x<=1, equation |x| + |x -1| = 1 holds true."

I am confused that how first x is +ive and second one -ve...after we take condition 0<=x<=1?
Pls, explain.

Thanks!

We know that for |x|:
When x\leq{0}, then |x|=-x;
When x\geq{0}, then |x|=x.

We have |x| + |x -1| = 1.

Now for the range: 0\leq{x}\leq{1} --> |x|=x (as x in given range is positive) and |x-1|=-(x-1)=-x+1 (as expression x-1 in the given range is negative, to check this try some x from this range, let x=-0.5 then x-1=0.5-1=-0.5=negative). So |x| + |x -1| = 1 in this range becomes: x-x+1=1 --> 1=1, which is true. That means that for ANY value from the range 0\leq{x}\leq{1}, equation |x| + |x -1| = 1 holds true.

Hope it's clear.

Bunuel, I have a question on the part in red. Shouldn't it actually be:

We know that for |x|:
When x<{0}, then |x|=-x; (I have changed the "less than or equal to" to only "less than")
When x\geq{0}, then |x|=x.

Because we should consider 2 cases -
a) greater than or equal to zero
AND
b) less than zero. [Not less than or equal to zero]

In the part B of your solution we are also considering the case where x=1, right? If this is the case, how can |x-1| be -x +1? At x=1, I am guessing |x-1| = x-1.
Math Expert
Joined: 02 Sep 2009
Posts: 16862
Followers: 2777

Kudos [?]: 17628 [0], given: 2232

Re: Is |x| + |x -1| = 1? (1) x 0 (2) x 1 [#permalink]  29 Sep 2013, 12:24
Expert's post
emailmkarthik wrote:
Bunuel wrote:
samark wrote:
Bunuel,

I am confused here..
"B. 0<=x<=1 --> x-x+1=1 --> 1=1. Which means that for ANY value from the range 0<=x<=1, equation |x| + |x -1| = 1 holds true."

I am confused that how first x is +ive and second one -ve...after we take condition 0<=x<=1?
Pls, explain.

Thanks!

We know that for |x|:
When x\leq{0}, then |x|=-x;
When x\geq{0}, then |x|=x.

We have |x| + |x -1| = 1.

Now for the range: 0\leq{x}\leq{1} --> |x|=x (as x in given range is positive) and |x-1|=-(x-1)=-x+1 (as expression x-1 in the given range is negative, to check this try some x from this range, let x=-0.5 then x-1=0.5-1=-0.5=negative). So |x| + |x -1| = 1 in this range becomes: x-x+1=1 --> 1=1, which is true. That means that for ANY value from the range 0\leq{x}\leq{1}, equation |x| + |x -1| = 1 holds true.

Hope it's clear.

Bunuel, I have a question on the part in red. Shouldn't it actually be:

We know that for |x|:
When x<{0}, then |x|=-x; (I have changed the "less than or equal to" to only "less than")
When x\geq{0}, then |x|=x.

Because we should consider 2 cases -
a) greater than or equal to zero
AND
b) less than zero. [Not less than or equal to zero]

In the part B of your solution we are also considering the case where x=1, right? If this is the case, how can |x-1| be -x +1? At x=1, I am guessing |x-1| = x-1.

No, it works with = sign as well: |0|=0=-0.

If x=1, then |x-1|=0 and -x+1=0 too.
_________________
Manager
Joined: 31 Mar 2013
Posts: 64
Followers: 0

Kudos [?]: 7 [0], given: 74

Re: Is |x| + |x -1| = 1? (1) x 0 (2) x 1 [#permalink]  29 Sep 2013, 20:21
I didn't know this. Thanks for clarifying, Bunuel!
Re: Is |x| + |x -1| = 1? (1) x 0 (2) x 1   [#permalink] 29 Sep 2013, 20:21
Similar topics Replies Last post
Similar
Topics:
If x≠0, is |x| <1? (1) x^2<1 (2) |x| < 1/x 8 03 Jul 2006, 11:01
Is x=0 (1) x+1>0 (2) x= -x 3 23 Oct 2008, 14:45
4 If x 0, is x^2 / |x| < 1? 10 14 Dec 2009, 00:03
1 If x 0, is x^2/|x| < 1? 6 03 Jan 2010, 06:14
9 If x#0, is x^2/|x| < 1? 12 08 Sep 2010, 10:51
Display posts from previous: Sort by