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

 It is currently 29 Nov 2015, 08:07

### 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?

Author Message
TAGS:
Manager
Status: Persevering
Joined: 15 May 2013
Posts: 225
Location: India
GMAT Date: 08-02-2013
GPA: 3.7
WE: Consulting (Consulting)
Followers: 1

Kudos [?]: 71 [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: 68
Location: United States
Followers: 0

Kudos [?]: 21 [0], given: 109

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: 30395
Followers: 5096

Kudos [?]: 57456 [0], given: 8813

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: 68
Location: United States
Followers: 0

Kudos [?]: 21 [0], given: 109

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!
Manager
Joined: 07 May 2013
Posts: 109
Followers: 0

Kudos [?]: 14 [0], given: 1

Re: Is |x| + |x -1| = 1? (1) x 0 (2) x 1 [#permalink]  04 Jun 2014, 04:40
wow! That is a lot of discussion. My solution will baffle you all.
Basically he is asking if the sum of the distance between 0 and x & x and 1 equal to one.

<-------><-------->
-----------------0---------x----------1-------------

I.E x must lie between 0 and 1
That condition is only satisfied when we combine the two. Hence answer is C.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 7309
Followers: 385

Kudos [?]: 93 [0], given: 0

Re: Is |x| + |x -1| = 1? [#permalink]  19 Jun 2015, 01:39
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Intern
Joined: 17 Jun 2015
Posts: 5
Location: United States
Followers: 0

Kudos [?]: 0 [0], given: 14

Re: Is |x| + |x -1| = 1? [#permalink]  03 Jul 2015, 09:37
I would choose the graphical method for this problem.

Statements 1 and 2 are clearly insufficient on their own. However taken together we see that x lies between 1 and 0.
|x| represents distance from Zero and |x-1| represents distance from 1.

now |x|+|x-1| represents total distance between 1 and 0.

This is always 1.

Regards
Sunil Natraj
Manager
Joined: 07 Apr 2015
Posts: 187
Followers: 1

Kudos [?]: 40 [0], given: 185

Re: Is |x| + |x -1| = 1? [#permalink]  04 Jul 2015, 05:00
cheetarah1980 wrote:
I got C. I plugged in numbers for each statement.
If x=0, then true. If x=1, then true. If x=2, then not true. S1 not sufficient
If x=1, then true. If x=-2, then not true. S2 not sufficient
if x is between 0 and 1 inclusive that means we plug in fractions (plus we already know that it's true for 0 and 1). No matter what fraction x represents 1-x will always give the value needed to add to x to make it = 1. Thus C is sufficient.

Exactly the way I did it, just confused by the huge discussion around this if that is sufficient enough....?!
Intern
Joined: 20 Apr 2015
Posts: 5
Followers: 0

Kudos [?]: 0 [0], given: 26

Re: Is |x| + |x -1| = 1? [#permalink]  10 Oct 2015, 20:21
Bunuel wrote:
Economist wrote:
Hi Bunuel,
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.

we cannot derive anything in this interval, does it mean that all values in this interval satisfy the equation ? This is something new for me...do you have any links for this? I thought, since we cannot derive anything, this interval is also out of scope.

Though, I got the answer by some quick number substitutions.

Well knew that this part needs more explanation.

When $$x$$ is in the range $$0\leq{x}\leq{1}$$, equation $$|x|+|x-1|=1$$ will become: $$x-x+1=1$$ --> $$1=1$$. Which is true, indeed $$1=1$$. But what does that mean? This means that when $$x$$ is in this range, equation takes the form of $$x-x+1=1$$ and value of $$x$$ does not affects the equation as it cancels out. OR in other words any $$x$$ from this range makes equation to hold true.

You can try some number picking from this range to see that.

Hope it's clear. Please tell me if it needs more clarification.

BTW what answer did you get?

hii Bunuel i am not able to understand how do you decide the check points for such question .
Intern
Joined: 06 Oct 2013
Posts: 25
Location: United Kingdom
WE: Engineering (Consulting)
Followers: 0

Kudos [?]: 12 [0], given: 32

Re: Is |x| + |x -1| = 1? [#permalink]  07 Nov 2015, 03:52
Bunuel wrote:
This one is very tricky!

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

Q is $$|x| + |x -1| = 1$$. Let's check when this equation holds true. We should consider three ranges (as there are two check points $$x=0$$ and $$x=1$$):

A. $$x<0$$ --> $$-x-x+1=1$$ --> $$x=0$$, but this solution is not valid as we are checking the range $$x<0$$;

B. $$0\leq{x}\leq{1}$$ -->$$x-x+1=1$$ --> $$1=1$$, which is true. That means that for ANY value from the range $$0\leq{x}\leq{1}$$, equation $$|x| + |x -1| = 1$$ holds true.

C. $$x>1$$ --> $$x+x-1=1$$ --> $$x=1$$, but this solution is not valid as we are checking the range $$x>1$$.

So we get that equation $$|x| + |x -1| = 1$$ holds true ONLY in the range $$0\leq{x}\leq{1}$$.

Statements:
(1) $$x\geq{0}$$. Not sufficient, as $$x$$ must be also $$\leq{1}$$;
(2) $$x\leq{1}$$. Not sufficient, as $$x$$ must be also $$\geq{0}$$;

(1)+(2) $$0\leq{x}\leq{1}$$, exactly the range we needed. Sufficient.

Bunuel,

highlighted part: if $$x<=0--->-x-x+1=1-----> x=0$$. then it becomes valid, right ?. then doesn't it change our Answer?

or when we have to consider "equal sign". $$x<=0,0<x<1 ( or ) x<0, 0<=x<1$$
VP
Joined: 08 Jul 2010
Posts: 1007
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 32

Kudos [?]: 679 [0], given: 39

Re: Is |x| + |x -1| = 1? [#permalink]  07 Nov 2015, 05:36
Expert's post
mendelay wrote:
Is |x| + |x -1| = 1?

(1) x ≥ 0
(2) x ≤ 1

For Such questions the first and most important question is TO THINK, for what vale of x, will |x| + |x -1| = 1 be true

The ranges of values to be checked are
1) between 0 and 1
2) between 0 and -1
3) Greater than 1
4) Less than -1

After a few hit and trial you may comfortably arrive at the range 0 ≤ x ≤ 1 for which the above expression will be correct

Statement 1: x ≥ 0

x may be between 0 and 1 (Answer to the question 'YES') OR
x may be Greater than 1 (Answer to the question 'NO')
NOT SUFFICIENT

Statement 2: x ≤ 1

x may be between 0 and 1 (Answer to the question 'YES') OR
x may be Less than 0 (Answer to the question 'NO')
NOT SUFFICIENT

Combining the two Statements
x ≥ 0 and x ≤ 1
i.e. 0 ≤ x ≤ 1
SUFFICIENT

_________________

Prosper!!!

GMATinsight

Bhoopendra Singh and Dr.Sushma Jha

e-mail: info@GMATinsight.com
Call us : +91-9999687183 / 9891333772

http://www.GMATinsight.com/testimonials.html

Contact for One-on-One LIVE Online (SKYPE Based) Quant/Verbal FREE Demo Class

______________________________________________________
Please press the if you appreciate this post !!

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 295
GPA: 3.82
Followers: 10

Kudos [?]: 81 [0], given: 0

Re: Is |x| + |x -1| = 1? [#permalink]  10 Nov 2015, 10:17
Expert's post
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is |x| + |x -1| = 1?

(1) x ≥ 0
(2) x ≤ 1

If we modify the question, the range becomes 0≤x≤1, and the answer becomes (C), as the range of conditions 1 and 2 is 0≤x≤1

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 20% off coupon code for GMAT Club members.
Unlimited Access to over 120 free video lessons - try it yourself

Re: Is |x| + |x -1| = 1?   [#permalink] 10 Nov 2015, 10:17

Go to page   Previous    1   2   [ 32 posts ]

Similar topics Replies Last post
Similar
Topics:
6 Is x = 1? 5 19 Jun 2015, 00:55
1 Is x = 1? 4 06 Feb 2015, 06:21
25 Is x=1? 5 18 Jun 2013, 08:16
2 Is 1 > |x - 1| ? 5 14 Jul 2010, 05:36
6 Is |x| + |x - 1| = 1? 8 22 Jan 2010, 06:42
Display posts from previous: Sort by