SAT Math Multiple Choice Practice Question 328: Answer and Explanation

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Question: 328

20. Every car at a certain dealership is either a convertible, a sedan, or both. If one-fifth of the convertibles are also sedans and one-third of the sedans are also convertibles, which of the following could be the total number of cars at the dealership?

A. 28
B. 29
C. 30
D. 31
E. 32

Correct Answer: A


A Set up a Venn diagram to visualize the information.

Notice that the number of sedans must equal the number of convertibles. Say the number of convertible sedans is x. If this is the number of sedans, then there must be 3x sedans in total, and of these are not convertibles. Similarly, if x is the number of convertibles, then there must be 5x convertibles altogether, and of these are not sedans. So now your diagram can look like this:

So there must be a total of cars at the dealership. The only choice that is a multiple of 7 is (A): 28.

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