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by abhasjha » Fri Aug 01, 2014 11:44 am
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

can someone please help me in drawing the diagram and solve the question for me .....
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by BShubh » Fri Aug 01, 2014 12:05 pm
Since U is mid point of seg ST and ST is 24, then UT will be 12.
and since SR is 20 and RT is 4...RU should be 8
Please see attached image. Hope this makes sense.[/img]
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by Brent@GMATPrepNow » Fri Aug 01, 2014 2:58 pm
abhasjha 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
Brent Hanneson - Creator of GMATPrepNow.com
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