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Manager  Joined: 12 Oct 2011
Posts: 169
R, S, T, and U are points on a line, and U is the midpoint of line  [#permalink]

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8 00:00

Difficulty:   25% (medium)

Question Stats: 78% (02:04) correct 22% (02:13) wrong based on 391 sessions

### HideShow timer Statistics 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.
Intern  Joined: 23 Sep 2011
Posts: 46
Location: Singapore
Concentration: Finance, Entrepreneurship
GPA: 3.44
WE: Information Technology (Investment Banking)
Re: R, S, T, and U are points on a line, and U is the midpoint of line  [#permalink]

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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
Manager  Joined: 13 May 2011
Posts: 217
WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
Re: R, S, T, and U are points on a line, and U is the midpoint of line  [#permalink]

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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
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9433
Location: Pune, India
Re: R, S, T, and U are points on a line, and U is the midpoint of line  [#permalink]

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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.

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 [ 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 [ 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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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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Joined: 12 Sep 2015
Posts: 3847
R, S, T, and U are points on a line, and U is the midpoint of line  [#permalink]

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2
Top Contributor
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

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: This means that SU and UT both have length 12: The length of line segment RT is 4
There are two possible locations for R:
Case a: 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: 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. RU must have length 8

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.
Director  S
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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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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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GMAT Mentors Manager  S
Joined: 05 Nov 2016
Posts: 85
Re: R, S, T, and U are points on a line  [#permalink]

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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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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

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File comment: www.GMATinsight.com 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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