A, B, C, and D are points on a line. If C is the midpoint of

[BTGmoderatorDC]

A, B, C, and D are points on a line. If C is the midpoint of line segment AB and if D is the midpoint of line segment CB, is the length of line segment DB greater than 5?

1) The length of line segment AC is greater than 8
2) The length of line segment CD is greater than 6

OA B

Source: Official Guide

[deloitte247]

The given line = AB
Midpoint of AB = C =>AC = BC = AB/2
Midpoint of CB = D => CD = BD = BC/2
Where BC = AB/2
$$\frac{AB}{2}=\frac{AB}{2}\cdot\frac{1}{2}=\frac{AB}{4}$$
Question: is the length of line segment DB greater than 5?
DB>5

Statement 1: The length of the line segment AC is greater than 8.
DB = BC/2 = AB/4 = AC/2
If AC>6 = 6/2 = 3, then DB>3 which means that DB can either = 4 (i.e less than 5) or 5 (i.e equal to 5) or 6 (i.e greater than 5).
Therefore, statement 1 is NOT SUFFICIENT

Statement 2: The length of the line segment CD is greater than 6.
BD = CD; so, if CD>6, definitely, BD>6. This means that the length of the line segment DB is greater than 5, hence, statement 2 alone is SUFFICIENT.

The answer is therefore option B.

Thanks

[Brent@GMATPrepNow]

A, B, C, and D are points on a line. If C is the midpoint of line segment AB and if D is the midpoint of line segment CB, is the length of line segment DB greater than 5?

1) The length of line segment AC is greater than 8
2) The length of line segment CD is greater than 6

OA B

Source: Official Guide

Given: A, B, C, and D are points on a line. If C is the midpoint of line segment AB and if D is the midpoint of line segment CB
When we sketch this information we get the following:

Notice that the two blue bars of equal length represent AC = CB, and the two red bars of equal length represent CD = DB.

Aside: The 4 points could also be arranged as B..D..C......A, but that doesn't change the answer to the question

Target question: Is the length of line segment DB greater than 5?

Statement 1: The length of line segment AC is greater than 8
There are several scenarios that satisfy statement 1. Here are two:
Case a: AC = 9.

In this case, the answer to the target question is NO, line segment DB is NOT greater than 5

Case b: AC = 14.

In this case, the answer to the target question is YES, line segment DB IS greater than 5

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The length of line segment CD is greater than 6

Since CD = DB, we can conclude that line segment DB IS greater than 6, which means line segment DB IS greater than 5
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent