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CEO  V
Joined: 03 Jun 2019
Posts: 2931
Location: India
GMAT 1: 690 Q50 V34 WE: Engineering (Transportation)
How many integer values of x satisfy the equation |x-3|+|x-20|<17?  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 65% (01:57) correct 35% (02:00) wrong based on 208 sessions

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How many integer values of x satisfy the equation |x-3|+|x-20|<17?

A. 2
B. 4
C. 0
D. 1
E. 3

_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10497
Location: Pune, India
Re: How many integer values of x satisfy the equation |x-3|+|x-20|<17?  [#permalink]

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3
4
Kinshook wrote:
How many integer values of x satisfy the equation |x-3|+|x-20|<17?

A. 2
B. 4
C. 0
D. 1
E. 3

|x - 3| + |x - 20| signifies sum of 'distance from 3' and 'distance from 20'. Note that distance between 3 and 20 is 17. So whichever point we take on the number line, the sum of the distance will be at least 17. So the sum will never be less than 17.

Check:
https://www.veritasprep.com/blog/2011/0 ... s-part-ii/
https://www.veritasprep.com/blog/2016/1 ... -part-iii/
_________________
Karishma
Veritas Prep GMAT Instructor

##### General Discussion
Senior Manager  P
Joined: 09 Jun 2014
Posts: 329
Location: India
Concentration: General Management, Operations
How many integer values of x satisfy the equation |x-3|+|x-20|<17?  [#permalink]

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Kinshook wrote:
How many integer values of x satisfy the equation |x-3|+|x-20|<17?

A. 2
B. 4
C. 0
D. 1
E. 3

|x - 3| + |x - 20| signifies sum of 'distance from 3' and 'distance from 20'. Note that distance between 3 and 20 is 17. So whichever point we take on the number line, the sum of the distance will be at least 17. So the sum will never be less than 17.

Check:
https://www.veritasprep.com/blog/2011/0 ... s-part-ii/
https://www.veritasprep.com/blog/2016/1 ... -part-iii/

I generally go for the convetional approach wherein I start taking the modulus out after finding critical points and its really time
consuming.

I tried reading this a few times.However,I am not be able to understand 100% .

|x - 3| + |x - 20| signifies sum of 'distance from 3' and 'distance from 20'.

>> I interpret x is some point which is at a distance 3 and 20 from number number line based on the blog link you sent.

Next you wrote ,
Note that distance between 3 and 20 is 17...

>>Does this mean x lies somewhere between 3 and 20 inclusive.

So whichever point we take on the number line, the sum of the distance will be at least 17
>> say we take x=5 then |x-3|=2 and |x-20| = 15 so sum is 17 ??
is this what we are trying to interpret ?

I am sorry.I just want to be crystal clear with this new concept.

I will re-read your blogs multiple times so to understand and grasp the concept better.

Thanks
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10497
Location: Pune, India
Re: How many integer values of x satisfy the equation |x-3|+|x-20|<17?  [#permalink]

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prabsahi wrote:
Kinshook wrote:
How many integer values of x satisfy the equation |x-3|+|x-20|<17?

A. 2
B. 4
C. 0
D. 1
E. 3

|x - 3| + |x - 20| signifies sum of 'distance from 3' and 'distance from 20'. Note that distance between 3 and 20 is 17. So whichever point we take on the number line, the sum of the distance will be at least 17. So the sum will never be less than 17.

Check:
https://www.veritasprep.com/blog/2011/0 ... s-part-ii/
https://www.veritasprep.com/blog/2016/1 ... -part-iii/

I generally go for the convetional approach wherein I start taking the modulus out after finding critical points and its really time
consuming.

I tried reading this a few times.However,I am not be able to understand 100% .

|x - 3| + |x - 20| signifies sum of 'distance from 3' and 'distance from 20'.

>> I interpret x is some point which is at a distance 3 and 20 from number number line based on the blog link you sent.

Next you wrote ,
Note that distance between 3 and 20 is 17...

>>Does this mean x lies somewhere between 3 and 20 inclusive.

So whichever point we take on the number line, the sum of the distance will be at least 17
>> say we take x=5 then |x-3|=2 and |x-20| = 15 so sum is 17 ??
is this what we are trying to interpret ?

I am sorry.I just want to be crystal clear with this new concept.

I will re-read your blogs multiple times so to understand and grasp the concept better.

Thanks

IF you are new to this concept, start from here: https://www.veritasprep.com/blog/2011/0 ... edore-did/
Then go on to the two posts mentioned above.
_________________
Karishma
Veritas Prep GMAT Instructor

Senior Manager  P
Joined: 09 Jun 2014
Posts: 329
Location: India
Concentration: General Management, Operations
How many integer values of x satisfy the equation |x-3|+|x-20|<17?  [#permalink]

### Show Tags

prabsahi wrote:
How many integer values of x satisfy the equation |x-3|+|x-20|<17?

A. 2
B. 4
C. 0
D. 1
E. 3

|x - 3| + |x - 20| signifies sum of 'distance from 3' and 'distance from 20'. Note that distance between 3 and 20 is 17. So whichever point we take on the number line, the sum of the distance will be at least 17. So the sum will never be less than 17.

Check:
https://www.veritasprep.com/blog/2011/0 ... s-part-ii/
https://www.veritasprep.com/blog/2016/1 ... -part-iii/

I generally go for the convetional approach wherein I start taking the modulus out after finding critical points and its really time
consuming.

I tried reading this a few times.However,I am not be able to understand 100% .

|x - 3| + |x - 20| signifies sum of 'distance from 3' and 'distance from 20'.

>> I interpret x is some point which is at a distance 3 and 20 from number number line based on the blog link you sent.

Next you wrote ,
Note that distance between 3 and 20 is 17...

>>Does this mean x lies somewhere between 3 and 20 inclusive.

So whichever point we take on the number line, the sum of the distance will be at least 17
>> say we take x=5 then |x-3|=2 and |x-20| = 15 so sum is 17 ??
is this what we are trying to interpret ?

I am sorry.I just want to be crystal clear with this new concept.

I will re-read your blogs multiple times so to understand and grasp the concept better.

Thanks

IF you are new to this concept, start from here: https://www.veritasprep.com/blog/2011/0 ... edore-did/
Then go on to the two posts mentioned above.[/quote]

Thanks Karishma,though I read the blog but I am not new to this concept.

The way you have applied here without solving the equations is something that I need to get better at.

Thanks a lot though,the other two blogs that you have written (In fact all your blogs) are a gem.
Intern  Joined: 27 May 2017
Posts: 1
Re: How many integer values of x satisfy the equation |x-3|+|x-20|<17?  [#permalink]

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I understood the Veritas logic , but can someone please solve this using the conventional(critical points ) method too . I am stuck at a point .

Thanks. Intern  B
Joined: 05 Sep 2018
Posts: 11
GMAT 1: 610 Q44 V30 How many integer values of x satisfy the equation |x-3|+|x-20|<17?  [#permalink]

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Ok. Here is the conventional method ( though lengthy one).

Firstly plot the zero points. In this case we have 2 points i.e. 3 & 20
With these 2 points we have 3 regions a) x<3 b)3<=x<20 c) x>=20

a) x<3
The equation becomes 3-x+20-x < 17
=> 2x>6
=> x>3 However this does not satisfies initial condition (x<3) so No solution.

b) 3<=x<20
The equation becomes x-3+20-x<17
=> the x cancels out; we do not have any solution.

c) x>=20
The equation becomes x-3+x-20< 17
=> 2x<40
=> x<20 Again the solution does not satisfies initial condition (x>= 20). Hence no solution

_________________
No Option to DIE. It's DO or DO. How many integer values of x satisfy the equation |x-3|+|x-20|<17?   [#permalink] 08 Aug 2019, 01:49

# How many integer values of x satisfy the equation |x-3|+|x-20|<17?  