If A, B, and C are distinct points on the number line. Is th

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eitijan: Master | Next Rank: 500 Posts; Posts: 157; Joined: Sat Jan 30, 2016 5:55 am; Thanked: 1 times

by eitijan » Tue Apr 12, 2016 4:33 am

If A, B, and C are distinct points on the number line. Is the length of the line segment AB less than 10?

(1) The sum of the lengths of line segments AC and BC is 10

(2) The sum of the lengths of line segments AB and AC is more than 10

IMO B

Experts, please comment.

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Source: Beat The GMAT — Data Sufficiency | Tue Apr 12, 2016 4:33 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Apr 12, 2016 5:18 am

eitijan wrote:If A, B, and C are distinct points on the number line. Is the length of the line segment AB less than 10?

(1) The sum of the lengths of line segments AC and BC is 10

(2) The sum of the lengths of line segments AB and AC is more than 10

The average test-taker will assume that the points must be in alphabetic order:
A...B...C
Be sure to try NON-ALPHABETIC orderings.
The following cases satisfy both statements.

Case 1:
A=0..............B=8....C=9
Here:
AC+BC = 10, satisfying Statement 1.
AB+AC > 10, satisfying Statement 2.
In this case, AB < 10.

Case 2:
A=0...............C=8.............B=10
Here:
AC+BC = 10, satisfying Statement 1.
AB+AC > 10, satisfying Statement 2.
In this case, AB = 10.

Since the answer is YES in Case 1 but NO in Case 2, the two statements combined are INSUFFICIENT.

The correct answer is E.

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OptimusPrep: Master | Next Rank: 500 Posts; Posts: 410; Joined: Fri Mar 13, 2015 3:36 amFollowed by: 8 members; Location: Worldwide; Thanked: 120 times; GMAT Score:770

by OptimusPrep » Wed Apr 13, 2016 8:18 pm

eitijan wrote:If A, B, and C are distinct points on the number line. Is the length of the line segment AB less than 10?

(1) The sum of the lengths of line segments AC and BC is 10

(2) The sum of the lengths of line segments AB and AC is more than 10

IMO B

Experts, please comment.

Given: A, B, C are distinct points on the number line
Required: Is AB < 10

Statement 1: The sum of the lengths of line segments AC and BC is 10
We can place the points on the line in the following ways
Case 1:
----A-----B----C-----
In this case, since AC + BC = 10, hence AB < 10
Case 2:
----A-----C----B----
In this case, AC + BC = 10
Hence AB = 10
Two different answers,
Insufficient

Statement 2: The sum of the lengths of line segments AB and AC is more than 10
Again let us take the two cases

Case 1:
----A----B----C----
We are given that AB + AC > 10
Nothing can be said about AB

Case 2:
----A----C----B----
We are given that AB + AC > 10
Again, nothing can be said about AB.
Insufficient

Correct Option: E

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Matt@VeritasPrep: GMAT Instructor; Posts: 2630; Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members; Location: East Bay all the way; Thanked: 625 times; GMAT Score:780

by Matt@VeritasPrep » Fri Apr 15, 2016 1:18 pm

Another conceptual way of thinking about it:

Length of AC = x
Length of BC = y
Length of AB = z

S1: x + y = 10
S2: x + z > 10

We can conclude that z > y, but we can't conclude that z < 10. (In fact, since z = x + y is one immediate possibility -- if C is in between A and B on the number line, we'd have to have z = x + y -- z = 10 is certainly possible.)

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