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abhasjha: Master | Next Rank: 500 Posts; Posts: 379; Joined: Tue Sep 30, 2008 7:17 am; Location: NY; Thanked: 28 times; Followed by:11 members

gprep -4 ps

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 .....

https://graceeducation1613.wordpress.co ... questions/

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Source: Beat The GMAT — Problem Solving | Fri Aug 01, 2014 11:44 am

BShubh: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Thu Aug 29, 2013 3:37 pm; Thanked: 1 times

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

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:

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: