SAT Math Multiple Choice Practice Question 220: Answer and Explanation

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Question: 220

22. For any two real numbers p and q, define pGq as follows: pGq = p + q - 3. Which of the following equations are true?

I.pGq = qGp

II.3Gq = q

III.(pGq)Gr = pG(qGr)

A. I only
B. I and II
C. I and III
D. I, II, and III
E. none of the above

Correct Answer: D

Explanation:

D. Pick numbers and plug them in. Try p = 5 and q = 8. 5G8 = 5 + 8 - 3 = 10 and 8G5 = 8 + 5 - 3 = 10, so Option I seems to be true. 3G8 = 3 + 8 - 3 = 8, so Option II is true also. You've eliminated Choices (A), (C), and (E). To test Option III, let r = 4. (5G8)G4 = (5 + 8 - 3)G4 = 10G4 = 10 + 4 - 3 = 11, and 5G(8G4) = 5G(8 + 4 - 3) = 5G9 = 5 + 9 - 3 = 11, so Option III works as well. Choice (D) is the one you want.

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