Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

In the figure above, the length of line A B is 2 times x and the length of line B C is 3 times x. If a point is chosen at random from line A C, what is the probability that the point will lie on line B C?

(A) 2 over 5

(B) 1 over 2

(C) 3 over 5

(D) 2 over 3

(E) 5 over 6 

正确答案>>>

The correct answer is C

Explanation

The probability that a point chosen from line A C will lie on line B C is the ratio of the length of line B C to the length of line A C. The length of line A B is 2 times x and the length of line B C is 3 times x, so the length of line A C is 5 times x. Therefore, the ratio of the length of line B C to the length of line A C is (3 times x) over (5 times x) = 3 over 5.