SAT Math Multiple Choice Practice Question 60: Answer and Explanation

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Question: 60

16. If and , then b could be

A. -8
B. -7
C. -6
D. 7
E. 8

Correct Answer: C

Explanation:

C. In case you didn't already know, this question is tough. When a problem looks complicated, start with the simplest part you can see. In this case, the simplest part is . If you make a positive, the result must be less than 3. So a could be a number like 1, 2, 2.3, or 1/8, or it could be the negative versions of any of these numbers. So what can't a be? It can't be 3 or bigger than 3, and it can't be -3 or less than -3.

Okay, now it's time to tackle . Start by plugging Choice (A), b = -8, into the equation. Then . If you try some possible a values, you see that you can't make this equation equal less than 4. The same thing happens when you plug in Choices (B), (D), and (E). But if you try Choice (C), you get . Now if you let a = -2.5, or any number between -2 and -3, the answer is less than 4.

This question is a lot of work. On the real SAT, you probably want to skip a problem if it looks this time-consuming. Save your energy for easier problems, and go back to the really complex ones if you have time after you answer all the other questions.

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