SAT Math Multiple Choice Question 653: Answer and Explanation

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Test Information

Question: 653

8. If Images and Images, what is the value of b - a?

  • A. -2
  • B. 2
  • C. 4
  • D. 8

Correct Answer: B

Explanation:

B

Advanced Mathematics (exponents) MEDIUM

Images

Substitute Images

(Law #3 from Chapter 9, Lesson 9):

Images

Cross-multiply:

x2 = 16

Take the square root:

x = ±4

Recall the other equation:

Images

Law #6 from Chapter 9, Lesson 9:

xb-a = 16

Substitute x = ±4:

(±4)b-a = 16

Notice that both 42 = 16 and

(-4)2 = 16, therefore:

b - a = 2

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