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

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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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B
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BrentGMATPrepNow
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Re: R, S, T, and U are points on a line, and U is the midpoint of line [#permalink] New post   Updated on: 26 May 2021, 05:55
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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:


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

Answer: B

Cheers,
Brent

Originally posted by BrentGMATPrepNow on 29 Sep 2016, 08:39.
Last edited by BrentGMATPrepNow on 26 May 2021, 05:55, edited 2 times in total.
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donkadsw
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Re: R, S, T, and U are points on a line, and U is the midpoint of line [#permalink] 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] 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] 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 19070 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 18992 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] New post   29 Mar 2015, 08:07
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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.


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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Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: https://www.optimus-prep.com/gmat-on-demand-course
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Re: R, S, T, and U are points on a line, and U is the midpoint of line [#permalink] 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, and U is the midpoint of line [#permalink] New post   06 May 2017, 20:35
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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, and U is the midpoint of line [#permalink] New post   06 May 2017, 22:20
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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

Answer: Option B
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File comment: www.GMATinsight.com
123.jpg
123.jpg [ 44.38 KiB | Viewed 14877 times ]

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Re: R, S, T, and U are points on a line, and U is the midpoint of line [#permalink] New post   11 Sep 2023, 16:52
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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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