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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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Re: R, S, T, and U are points on a line, and U is the midpoint of line [#permalink]
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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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 19518 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 19435 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]
1
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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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Re: R, S, T, and U are points on a line, and U is the midpoint of line [#permalink]
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]
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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]
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

Attachments

File comment: www.GMATinsight.com

123.jpg [ 44.38 KiB | Viewed 15305 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]
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