# SAT Math Multiple Choice Practice Question 407: Answer and Explanation

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**Question: 407**

**11.**

__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

**Explanation:**

**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.