SAT Math Multiple Choice Practice Question 188: Answer and Explanation

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Question: 188

12. For all numbers a and b, let a # b be defined as ab. Which of the following is equal to (3 # 2) - (2 # 3)?

I.4 # 0

II.1 # 3

III.2 # 1

A. I only
B. II only
C. III only
D. I and II
E. I and III

Correct Answer: D

Explanation:

D. Break this problem into a few different parts: a # b = ab, 3 # 2 = 32 = 9, and 2 # 3 = 23 = (2)(2)(2) = 8. So, (3 # 2) - (2 # 3) = 9 - 8 = 1. Now you need to check I, II, and III to see which, if any, of them are equal to 1. Because any number raised to the 0 power equals 1, 4 # 0 = 40 = 1, making Option I true. Therefore, Choices (A), (D), or (E) may be the answer. Option II is true because 1 # 3 = 13 = 1, so Choice (D) must be the answer. You can check Option III just to be sure: 2 # 1 = 21 = 2.

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