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08 Dec 2011, 23:12
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
82% (01:56) correct
18%
(02:08)
wrong
based on 600
sessions
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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
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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Updated on: 26 May 2021, 05:55
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.
Last edited by BrentGMATPrepNow on 26 May 2021, 05:55, edited 2 times in total.
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siddharthmuzumdar
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
General Discussion
08 Dec 2011, 23:32
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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
ST = SU + UT = 2UT = 24
=> UT = 12
=> UR + RT = 12 => UR = 12 - RT = 12 -4 = 8
