SAT Math Multiple Choice Practice Question 107: Answer and Explanation

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Question: 107

19. The factors of a positive number n are all the positive numbers that n can be divided by without leaving a remainder; this includes 1 and n itself. For example, the factors of 10 are 1, 2, 5, and 10. How many positive numbers less than 50 have an odd number of factors?

A. 0
B. 1
C. 7
D. 16
E. 49

Correct Answer: C

Explanation:

C. Usually, factors come in pairs. For example, in the case of 10 you have 1 × 10 and 2 × 5. The only way to end up without a pair is if one of the factors involves the same number twice. You have the same number twice only if the number is a perfect square. Take 16, for example. You have 1 × 16, 2 × 8, and 4 × 4, which makes only 5 factors, an odd number. So how many positive perfect squares are less than 50? There are 7 such numbers: 49, 36, 25, 16, 9, 4, and 1.

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