SAT Math Multiple Choice Question 765: Answer and Explanation

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Question: 765

15. For how many distinct integer values of n is (n 1 2)(n + 8) negative?

  • A. Four
  • B. Five
  • C. Six
  • D. Seven

Correct Answer: B



Algebra (quantitative reasoning) MEDIUM-HARD

First, we should notice the fact that n + 8 must be greater than n + 2, no matter the value of n. Next, we should notice that, in order for the product of two numbers to be negative, one of those numbers must be positive and the other one negative. Obviously, the greater number is the positive one, and the lesser one is the negative one.


n + 2 < 0 and n + 8 > 0

Solve each inequality for n:

n < -2 and n > -8

Since n must have an integer value and must satisfy the inequalities above, it can take only the values -7, -6, -5, -4, and -3.

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