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R, S, T, and U are points on a line, and U is the midpoint of line

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R, S, T, and U are points on a line, and U is the midpoint of line  [#permalink]

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New post 08 Dec 2011, 23:12
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R, S, T, and U are points on a line, and U is the midpoint of line segment ST. If the lengths of line segments RS, RT, and ST are 20, 4, and 24, respectively. What is the length of line segment RU?

A. 6
B. 8
C. 12
D. 14
E. 16

What is the quickest way to solve such a problem? I did get the correct answer but got it after a lot of time. How would one solve this problem quickly and efficiently? Please help.
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Re: R, S, T, and U are points on a line, and U is the midpoint of line  [#permalink]

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New post 08 Dec 2011, 23:32
ST = 24, RT = 4, RS = 20 => this should tell you the order of the points on the number line as S, U, R, T (because any other ordering will violate at least one of the equations)

ST = SU + UT = 2UT = 24
=> UT = 12
=> UR + RT = 12 => UR = 12 - RT = 12 -4 = 8
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Re: R, S, T, and U are points on a line, and U is the midpoint of line  [#permalink]

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New post 09 Dec 2011, 02:46
30 sec. by drawing the line.
Just draw the line as guided placing U in the middle.
Straight away you know that UT=12 =>RT=4 So, UT-RT=UR=12-4=8
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Re: R, S, T, and U are points on a line, and U is the midpoint of line  [#permalink]

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New post 09 Dec 2011, 03:25
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siddharthmuzumdar wrote:
R, S, T, and U are points on a line, and U is the midpoint of line segment ST. If the lengths of line segments RS, RT, and ST are 20, 4, and 24, respectively. What is the length of line segment RU?

A. 6
B. 8
C. 12
D. 14
E. 16

What is the quickest way to solve such a problem? I did get the correct answer but got it after a lot of time. How would one solve this problem quickly and efficiently? Please help.


Yes, the quickest way is drawing the line.
U is the mid point of ST so I draw a line segment ST and U in the middle. Length of ST is 24 so length of SU and UT must be 12 each.
Attachment:
Ques3.jpg
Ques3.jpg [ 4.34 KiB | Viewed 6944 times ]

Now we need to place R. RS = 20 and RT = 4 which means that R is closer to T than to S. So it cannot be on the left of S. It can also not be on the right of T because then RS must be greater than 24. So R must be in between S and T, closer to T.
Attachment:
Ques4.jpg
Ques4.jpg [ 5.37 KiB | Viewed 6949 times ]


Length of RU = 20 - 12 = 8
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Re: R, S, T, and U are points on a line, and U is the midpoint of line  [#permalink]

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New post 29 Mar 2015, 08:07
1
siddharthmuzumdar wrote:
R, S, T, and U are points on a line, and U is the midpoint of line segment ST. If the lengths of line segments RS, RT, and ST are 20, 4, and 24, respectively. What is the length of line segment RU?

A. 6
B. 8
C. 12
D. 14
E. 16

What is the quickest way to solve such a problem? I did get the correct answer but got it after a lot of time. How would one solve this problem quickly and efficiently? Please help.


Given that RS = 20, RT = 4 and ST = 24.
We can see that ST = RS + RT.
Hence R is in between S and T.
Also, U is the mid point of ST.
So, SU = UT = 12
Hence R has to be in between U and T (otherwise it will not satisfy given conditions).
So, UT = 12 and RT = 4
Hence RU = UT - RT
= 12 - 4
= 8

Hence option (B).

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R, S, T, and U are points on a line, and U is the midpoint of line  [#permalink]

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New post Updated on: 16 Apr 2018, 12:46
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Top Contributor
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siddharthmuzumdar wrote:
R, S, T, and U are points on a line, and U is the midpoint of line segment ST. If the lengths of line segments RS, RT, and ST are 20, 4, and 24, respectively. What is the length of line segment RU?

A. 6
B. 8
C. 12
D. 14
E. 16



Here's my step-by-step solution:

U is the midpoint of line segment ST, and the length of line segment ST is 24.
So, we get the following:
Image

This means that SU and UT both have length 12:
Image

The length of line segment RT is 4
There are two possible locations for R:
Case a:
Image
In case a, the length of line segment SR is 28, but the question tells us that line segment SR has length 20.
So, R cannot be in the above location.

Case b:
Image
In case b, the length of line segment SR is 20...PERFECT
Now that we've determined R's location, we can find the length of RU.

Image
RU must have length 8

Answer: B

Cheers,
Brent
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Originally posted by GMATPrepNow on 29 Sep 2016, 08:39.
Last edited by GMATPrepNow on 16 Apr 2018, 12:46, edited 1 time in total.
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Re: R, S, T, and U are points on a line, and U is the midpoint of line  [#permalink]

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New post 27 Feb 2017, 04:57
On the x-axis, if S is at 0, then U is at 12, R is at 20 and T is at 24. Therefore RU = SR - SU = 20 -12 = 8. Option B
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Re: R, S, T, and U are points on a line  [#permalink]

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New post 06 May 2017, 20:35
With the given RS, RT, and ST are 20, 4, and 24 and U being the mid point of ST, we can say that the points are aligned as

S U R T
total length of ST=24, since U is mid point SU = 12
SR = 20, so RU = RS-SU
=20-12
=8
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Re: R, S, T, and U are points on a line  [#permalink]

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New post 06 May 2017, 22:20
amathews wrote:
R, S, T, and U are points on a line, and U is the midpoint of line segment ST. If the lengths of line segments RS, RT, and ST are 20, 4, and 24, respectively. What is the length of line segment RU?

A. 6
B. 8
C. 12
D. 14
E. 16



Just draw the figure as attached

Answer: Option B
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123.jpg [ 44.38 KiB | Viewed 3214 times ]


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Re: R, S, T, and U are points on a line, and U is the midpoint of line  [#permalink]

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Re: R, S, T, and U are points on a line, and U is the midpoint of line   [#permalink] 18 Sep 2018, 22:07
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