Question 60 Answer and Explanation _ACT June 2016 Form 72F Math Section

60. Distinct points A, B, C, and D are collinear, and B is between A and C. For D to be between A and C such that AD + DB + BC = AC, which of statements I–IV below must be true?

(Note: If B is between A and C, then AB + BC = AC.)

I. AD = DB

II. AD = BC

III. B is between D and C

IV. D is between B and C

F. I only

G. III only

H. I and III only

J. II and IV only

K. None of the statements must be true.

Answer and Explanation

Your Answer is

Correct Answer is G

Explanation

Because B is in the middle of AC, so AB+BC=AC. And because AD+DB+BC=AC, so AB=AD+DB. So D is in the middle of AB. So only the third statement is true. Choose G.