GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Jun 2019, 00:24 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Which of the following is satisfied with |x-4|+|x-3|<2?

Author Message
TAGS:

Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7472
GMAT 1: 760 Q51 V42 GPA: 3.82
Which of the following is satisfied with |x-4|+|x-3|<2?  [#permalink]

Show Tags

1
28 00:00

Difficulty:   45% (medium)

Question Stats: 68% (01:54) correct 32% (01:54) wrong based on 900 sessions

HideShow timer Statistics

Which of the following is satisfied with |x-4|+|x-3|<2?

A. 1<x<5
B. 2<x<5
C. 2.5<x<4.5
D. 2.5<x<4
E. 3<x<4

_________________

Originally posted by MathRevolution on 27 Jan 2016, 18:24.
Last edited by chetan2u on 30 Jan 2016, 07:21, edited 3 times in total.
Reformatted the question.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7472
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Which of the following is satisfied with |x-4|+|x-3|<2?  [#permalink]

Show Tags

7
18
Which of the following is satisfied with |x-4|+|x-3|<2?

A. 1<x<5 B. 2<x<5 C. 2.5<x<4.5 D. 2.5<x<4 E. 3<x<4

--> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<2 -> |x-4+x-3|<2 -> |2x-7|<2, -2<2x-7<2, 5<2x<9, 5/2<x<9/2 -> 2.5<x<4.5
_________________
CEO  S
Joined: 20 Mar 2014
Posts: 2622
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Which of the following is satisfied with |x-4|+|x-3|<2?  [#permalink]

Show Tags

2
4
MathRevolution wrote:
Which of the following is satisfied with |x-4|+|x-3|<2?

A. 1<x<5 B. 2<x<5 C. 2.5<x<4.5 D. 2.5<x<4 E. 3<x<4

* A solution will be posted in two days.

Remember that |x-a| represents distance of x from 'a'. As mentioned in the question,

|x-4|+|x-3|<2 simply means that you need to find the range of 'x' such that distance of x from 4 + distance of x from 3 < 2.

Refer to the attached image, you realize that the distance 'y' when it is in between 3 and 4 will always be <2. For regions x<3 or x>4, the sum of the distances of 'y' from 3 and 4 will be <2 only when

y+1+y<2 ---> 2y+1<2 ---> y<0.5 or in other words, range of x is ---> 2.5 < x < 4.5

Attachment: 2016-01-27_20-50-35.jpg [ 6.25 KiB | Viewed 5941 times ]

C is thus the correct answer.

Alternate solution: using POE to arrive at the correct answer.

Once you know that the sum of the distances of x from 3 and 4 must be < 2,

A. 1<x<5 . Try with x=1.5. Clearly the distance of 1.5 from 3 and 4 will be >2. Eliminate.

B. 2<x<5 . Take x=2.1. Again, the distances of 2.1 from 3 and 4 (=0.9 and 1.9 respectively) will sum to > 2. Hence Eliminate.

C. 2.5<x<4.5. Works for all possible values. Keep.

D. 2.5<x<4. Take x=4.2. The distances of 4.2 from 3 and 4 (=1.2 and 0.2 respectively) will sum to < 2 but this value is NOT in the given range, thus incomplete range. Hence Eliminate.

E. 3<x<4. Take x=2.6. It works for the given sums of the distances < 2 but is not in the given range, thus incomplete range. Hence eliminate.

C is thus the correct answer.

Hope this helps.
General Discussion
Manager  B
Joined: 24 Jul 2014
Posts: 89
Location: India
WE: Information Technology (Computer Software)
Re: Which of the following is satisfied with |x-4|+|x-3|<2?  [#permalink]

Show Tags

1
If we put x=2.51 , 2.501 ...
|x-4|+|x-3| = 1.98 , 1.998 ..... just below 2

Again if we put x= 4.49,4.499.....
|x-4|+|x-3|=1.98,1.998 ... just below 2

So Range should be
2.5<x<4.5

_________________
The Mind ~ Muscle Connection
My GMAT Journey is Complete.Going to start the MBA in Information Management from 2016
Good Luck everyone.
Intern  Joined: 03 Feb 2016
Posts: 10
Re: Which of the following is satisfied with |x-4|+|x-3|<2?  [#permalink]

Show Tags

4
Given the modules |x-4| and |x-3|, we have 2 key points (4 and 3) which give us 3 cases:

1. x<3
-x+4-x+3<2 --> $$x<\frac{5}{2}$$ -->2.5<x<3 Solution is valid.

2. 3$$\leq{x}$$<4

-x+4+x-3<2 --> 1<2 Solution is valid.

3. 4$$\leq{x}$$

x-4+x-3<2 --> x$$\leq\frac{9}{2}$$ --> x$$\leq4.5$$ Solution is valid.

Therefore x must belong to the interval 2.5<x$$\leq{4.5}$$ to satisfy the given in-equation.
Manager  S
Status: Gmat lover
Joined: 27 Mar 2017
Posts: 84
Location: India
Schools: IIMA , IIMA PGPX"18
GMAT 1: 710 Q49 V39 GPA: 3.91
Re: Which of the following is satisfied with |x-4|+|x-3|<2?  [#permalink]

Show Tags

A. 1<x<5
B. 2<x<5
C. 2.5<x<4.5
D. 2.5<x<4
E. 3<x<4
_________________
_________________
Rules for posting in verbal Gmat forum, read it before posting anything in verbal forum
Giving me + 1 kudos if my post is valuable with you The more you like my post, the more you share to other's need.

“The great secret of true success, of true happiness, is this: the man or woman who asks for no return, the perfectly unselfish person, is the most successful.”
-Swami Vivekananda
Manager  B
Joined: 29 May 2017
Posts: 128
Location: Pakistan
Concentration: Social Entrepreneurship, Sustainability
Re: Which of the following is satisfied with |x-4|+|x-3|<2?  [#permalink]

Show Tags

FelixM wrote:
Given the modules |x-4| and |x-3|, we have 2 key points (4 and 3) which give us 3 cases:

1. x<3
-x+4-x+3<2 --> $$x<\frac{5}{2}$$ -->2.5<x<3 Solution is valid.

2. 3$$\leq{x}$$<4

-x+4+x-3<2 --> 1<2 Solution is valid.

3. 4$$\leq{x}$$

x-4+x-3<2 --> x$$\leq\frac{9}{2}$$ --> x$$\leq4.5$$ Solution is valid.

Therefore x must belong to the interval 2.5<x$$\leq{4.5}$$ to satisfy the given in-equation.

Hi....

I need to learn this key point method......can you send some links please?

regards
Manager  B
Joined: 25 Nov 2017
Posts: 86
Location: India
GMAT 1: 590 Q47 V25 GMAT 2: 660 Q50 V29 GPA: 3.56
Re: Which of the following is satisfied with |x-4|+|x-3|<2?  [#permalink]

Show Tags

MathRevolution wrote:
Which of the following is satisfied with |x-4|+|x-3|<2?

A. 1<x<5 B. 2<x<5 C. 2.5<x<4.5 D. 2.5<x<4 E. 3<x<4

--> If there is addition when there are 2 absolute values, you can just ignore the middle. That is, |x-4|+|x-3|<2 -> |x-4+x-3|<2 -> |2x-7|<2, -2<2x-7<2, 5<2x<9, 5/2<x<9/2 -> 2.5<x<4.5

Hello MathRevolution ,

If there is addition when there are 2 absolute values, you can just ignore the middle
Is this because lal+lbl>=la+bl ? Re: Which of the following is satisfied with |x-4|+|x-3|<2?   [#permalink] 20 Oct 2018, 05:55
Display posts from previous: Sort by

Which of the following is satisfied with |x-4|+|x-3|<2?  