# Number Line

## Arithmetic: Number Line

Read the following SAT test question and then select the correct answer.

Work all math problems by reading the question carefully and identifying the bottom line.  Assess your options for solving the problem and choose the most efficient method to attack the problem.  When you have an answer, loop back to make sure that it satisfies the bottom line.

A, B, C, and D are points on a line, with D the midpoint of segment . The lengths of segments  , and are 10, 2, and 12, respectively. What is the length of segment ?

Bottom Line: distance A to D

Assess your Options:  Drawing out the situation will give you a visual to understand the situation.

Attack the Problem:  Start with what you know.  You have a lot of points named, but the first information that you are given is that D is the midpoint between B and C. Now you are given three lengths.  You can’t label the ones involving A yet, but you can label the length from B to C.  Remember that D is the midpoint, and you will also know the lengths of B to D and D to C. Now go back to those other lengths you were given that involved point A.  Point A is 2 units away from C and 10 units away from B.  The only possible location for A is between B and C, but closer to C. Now that you have all your points labeled, it is time to go back and look for your bottom line.  What is the distance from A to DD to C was 6 units, and A to C was 2 units, so what is 6 minus 2?  The answer is 4.  (You could also use B to A is 10 and subtract the length of B to D, 6, and get the same answer of 4.)

Loop Back:  You solved for the distance from A to D, so you are ready to check your answers.

(A) 2
(B) 4
(C) 6
(D) 10
(E) 12

The correct answer is (B).

On sat.collegeboard.org, 61% of the responses were correct.

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