SAT Question of the Day June 09 2013

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

A.     2

B.     4

C.     6

D.     10

E.     12

This is a reading comprehension question as much as it is a mathematical question.

Notice that the assumption that the points are in order from A to B to C to D is challenged by the statement that D is actually exactly in the middle between B and C.

Now, what we want to do is create a diagram that will help us solve the important question – what is the distance between A and D?

Lets start with what we know to be true – D is in the middle between B and C.

Draw a line and two points on it and name them B and C (for the sake of simplicity let’s call the left one B and the right one C). Mark the middle of the segment as point D.

Now point A can be either on the left side of B, between B and D, between D and C, or on the right side of C.

(A)—B—(A)—D—(A)—C—(A)

Now, let us look on the distances between the points: BC is 12 – so BD=DC=6 We know AB is 10 – which places A either on the left of B or between D and C (10 is not far enough from B to be on the other side of C). We also know that the distance between A and C is 2 units – this leaves us only one option –  A is between D and C – and is located 4 units from D.

B——D—-A–C

46% out of 150,000 got it right.

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