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

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Math Expert
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Posts: 7764
If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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05 Jul 2018, 23:46
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45% (medium)

Question Stats:

72% (01:45) correct 28% (01:28) wrong based on 32 sessions

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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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Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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Updated on: 06 Jul 2018, 00:48
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)
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine

Originally posted by PKN on 06 Jul 2018, 00:17.
Last edited by PKN on 06 Jul 2018, 00:48, edited 1 time in total.
Director
Joined: 14 Dec 2017
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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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06 Jul 2018, 00:18
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.

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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06 Jul 2018, 00:23
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
_________________
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
Re: If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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06 Jul 2018, 00:40
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
Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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06 Jul 2018, 00:41
Director
Joined: 14 Dec 2017
Posts: 517
Location: India
Re: If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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06 Jul 2018, 00:56
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

Have a nice day!

GyM
_________________
Director
Joined: 14 Dec 2017
Posts: 517
Location: India
Re: If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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06 Jul 2018, 00:57
chetan2u wrote:
good GyMrAT

Thank you Sire!! Appreciate your encouragement.
_________________
VP
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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06 Jul 2018, 01:03
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

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
Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: If x is 200 units away from 50 on a number line, what is the distance  [#permalink]

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06 Jul 2018, 01:21
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

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
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Re: If x is 200 units away from 50 on a number line, what is the distance   [#permalink] 06 Jul 2018, 01:21
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