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If x is 200 units away from 50 on a number line, what is the distance

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If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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New post 05 Jul 2018, 22:46
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If x is 200 units away from 50 on a number line, what is the distance between x and z?
(1) Distance between 50 and z is 100.
(2) \(xz>0\)


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_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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New post Updated on: 05 Jul 2018, 23:48
chetan2u wrote:
If x is 200 units away from 50 on a number line, what is the distance between x and z?
(1) Distance between 50 and z is 100.
(2) \(xz>0\)


New question


There are 2 cases when x is 200 units away from 50 on a number line.
Number line:-(-150)---------0---------(Reference=50)-----------------(x=250)----

Statement-1:-
Distance between 50 and z is 100.
Number line:-(x=-150)----(z=-50)-----0---------(Reference=50)-------(z=150)----------(x=250)----
Now,distance between x and z:-
1.|x-z|=|-150-(-50)|=|-150+50|=|-100|=100 unit
2.|x-z|=|250-150|=|100|=100 unit
3.|x-z|=|-150-150|=|-300|=300 unit
4.|x-z|=|250-(-50)|=|300|=300 unit
So, insufficient
Statement-2:-
\(xz>0\)
x has two positions but there is no info available on z.
So, insufficient.
combining, we have both x and z same polar sign so that xz>0
1.|x-z|=|-150-(-50)|=|-150+50|=|-100|=100 unit
2.|x-z|=|250-150|=|100|=100 unit
So, sufficient.

Ans. (C)
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PKN

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Originally posted by PKN on 05 Jul 2018, 23:17.
Last edited by PKN on 05 Jul 2018, 23:48, edited 1 time in total.
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Re: If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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New post 05 Jul 2018, 23:18
chetan2u wrote:
If x is 200 units away from 50 on a number line, what is the distance between x and z?
(1) Distance between 50 and z is 100.
(2) \(xz>0\)


New question



Given x is 200 units away from 50 on the number line, x can be on the right or left of 50, we do not know,

hence x = 250 or x = -150 on the number line

.......(-150)................................0.................(50)....................................(250)

we need to find distance between x & z or l x - z l

Statement 1: Distance between 50 and z is 100.

Hence , we have


.......(-150).............(-50)...................0.................(50).......................(150).............(250)

z = -50 or z = 150

we get l x - z l = 300 or 100

Statement 1 alone is Not Sufficient.


Statement 2: x*z > 0

Hence x & z have the same sign, either both are positive or both are negative.

However we do not know value of z. Hence Statement 2 is Not Sufficient.


Combining 1 & 2, we get

if x & z both are positive, then x & z both lie on the right of 50

0.................(50).......................(150).............(250)

x = 250 & z = 150

hence l x - z l = 100

if x & z both are negative, then x & z both lie on the left of 0

.......(-150).............(-50)...................0.................(50)

x = -150 & z = -50

hence l x - z l = 100

Both cases give the same value for l x - z l

We get that Combining the 2 statements is Sufficient.




Answer C.



Thanks,
GyM
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Re: If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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New post 05 Jul 2018, 23:23
PKN wrote:
chetan2u wrote:
If x is 200 units away from 50 on a number line, what is the distance between x and z?
(1) Distance between 50 and z is 100.
(2) \(xz>0\)


New question


There are 2 cases when x is 200 units away from 50 on a number line.
Number line:-(-150)---------0---------(Reference=50)-----------------(x=250)----

Statement-1:-
Distance between 50 and z is 100.
Number line:-(x=-150)----(z=-50)-----0---------(Reference=50)-------(z=150)----------(x=250)----
Now,distance between x and z:-
1.|x-z|=|-150-(-50)|=|-150+50|=|-100|=100 unit
2.|x-z|=|250-150|=|100|=100 unit
Statement-2:-
\(xz>0\)
x has two positions but there is no info available on z.
So, insufficient.

Ans. (A)



We need to consider two more cases

3.|x-z|=|250-(-50)|=|250+50|=|300|=300 unit

4.|x-z|=|-150-150|=|-300|=300 unit



Cheers!
GyM
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Re: If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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New post 05 Jul 2018, 23:40
GyMrAT wrote:
PKN wrote:
chetan2u wrote:
If x is 200 units away from 50 on a number line, what is the distance between x and z?
(1) Distance between 50 and z is 100.
(2) \(xz>0\)


New question


There are 2 cases when x is 200 units away from 50 on a number line.
Number line:-(-150)---------0---------(Reference=50)-----------------(x=250)----

Statement-1:-
Distance between 50 and z is 100.
Number line:-(x=-150)----(z=-50)-----0---------(Reference=50)-------(z=150)----------(x=250)----
Now,distance between x and z:-
1.|x-z|=|-150-(-50)|=|-150+50|=|-100|=100 unit
2.|x-z|=|250-150|=|100|=100 unit
Statement-2:-
\(xz>0\)
x has two positions but there is no info available on z.
So, insufficient.

Ans. (A)



We need to consider two more cases

3.|x-z|=|250-(-50)|=|250+50|=|300|=300 unit

4.|x-z|=|-150-150|=|-300|=300 unit



Cheers!
GyM


Thanks gym, I missed to consider the cases pertaining to left & right of number line. I considered two cases separately since both are not intersecting each other. I thought we couldn't combine.
Good learning.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

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Posts: 7029
Re: If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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New post 05 Jul 2018, 23:41
good GyMrAT
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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New post 05 Jul 2018, 23:56
PKN wrote:

Thanks gym, I missed to consider the cases pertaining to left & right of number line. I considered two cases separately since both are not intersecting each other. I thought we couldn't combine.
Good learning.



You are welcome! One trick i utilize on DS is to visualize the question maker as a mischievous person, chuckling quietly & waiting for you to commit a mistake. Don't let him or her have the last laugh. In this case with all due respect it is chetan2u :grin:

Have a nice day!

GyM
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Re: If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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New post 05 Jul 2018, 23:57
chetan2u wrote:
good GyMrAT



Thank you Sire!! Appreciate your encouragement.
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If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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New post 06 Jul 2018, 00:03
GyMrAT wrote:
PKN wrote:

You are welcome! One trick i utilize on DS is to visualize the question maker as a mischievous person, chuckling quietly & waiting for you to commit a mistake. Don't let him or her have the last laugh. In this case with all due respect it is chetan2u :grin:

Have a nice day!

GyM


Great question chetan2u sir , Nice lines & valuable tips GyMrAT.
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

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Joined: 02 Aug 2009
Posts: 7029
Re: If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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New post 06 Jul 2018, 00:21
GyMrAT wrote:
PKN wrote:

Thanks gym, I missed to consider the cases pertaining to left & right of number line. I considered two cases separately since both are not intersecting each other. I thought we couldn't combine.
Good learning.



You are welcome! One trick i utilize on DS is to visualize the question maker as a mischievous person, chuckling quietly & waiting for you to commit a mistake. Don't let him or her have the last laugh. In this case with all due respect it is chetan2u :grin:

Have a nice day!

GyM



GyMrAT It is the best technique to follow in DS..
Imagine the same in ACTUALs, I am sure you and anyone else too would do really good in DS.

PKN thanks, usually dont find you missing out on catching tricks
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If x is 200 units away from 50 on a number line, what is the distance &nbs [#permalink] 06 Jul 2018, 00:21
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