SAT Math Multiple Choice Practice Question 407: Answer and Explanation
Note: Figure not drawn to scale.
If AB > CD, which of the following must be true?
I. AB > BC
II. AC > BD
III.AC > CD
A. I only
B. II only
C. III only
D. II and III only
E. I, II, and III
Correct Answer: D
D You should have noticed several things about this question. First, the figure was not drawn to scale. So a good first step would be to redraw the figure to comply with the condition ( > ). Second, the question asks which of the following must be true. Must is an important word—if it were which of the following could be true, you'd change your analysis completely. So, redrawing the figure, you'd get something like this:
In this figure, is clearly larger than . Because plugging in numbers makes the distance more concrete, you might have made AB = 3 and CD = 2, for example. Because you don't know the length of BD, however, you'd have to leave it alone. Now, let's check the conditions. Option I: Well, this could be true, but it doesn't have to be. So, option I is out. This allows you to eliminate A and E. Option II: If you let AB = 3 and CD = 2, AC = 3 + BC while BD = BC + 2. No matter what BC is, AC > BD. Option II is true. This allows you to eliminate C, which does not include Option II. We still need to check one more. Option III: If AB > CD, and AC > AB, then AC > CD. Option III is true; therefore, D is the answer.