SAT Math Multiple Choice Practice Question 212: Answer and Explanation

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Question: 212

14. Which of the following is true for all values of a and b?

I.ab |ab|

II.|a + b| = |a| + |b|

III.|a - b| = |b - a|

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

Correct Answer: C

Explanation:

C. When in doubt, plug in numbers! For absolute value problems, you probably want to mix up positive and negative numbers so that you know you aren't missing any obvious special cases. To test Option I, use a = 3 and b = -4. That seems to be true because -12 12. You can also plug in a pair of positive numbers and a pair of negative numbers to double-check. Onwards to Option II! Check out a = -2 and b = 5. |-2 + 5| = |3| = 3, and |-2| + |5| = 2 + 5 = 7, so Option II doesn't work. You already know that Choices (B) and (D) won't work. Testing Option III, try out a = 3 and b = -4. |3 - (-4)| = |3 + 4| = 7, and |-4 - 3| = |-7| = 7, so Option III works! Choice (C) is the right answer.

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