College Math Placement Test College Math Placement Test Number Theory 3

Question 1

Which of the following is NOT a factor of 84?

Accepted Answer

18

Answer

84 = 2²×3×7 has only one factor of 3, but 18 = 2×3² requires two factors of 3, so 18 does not divide 84.

Question 2

The product of two consecutive even integers is 168. What are the integers?

Accepted Answer

12 and 14

Answer

12 × 14 = 168, so the two consecutive even integers are 12 and 14.

Question 3

If p is a prime number greater than 2, which of the following must be odd?

Accepted Answer

p²

Answer

Any prime greater than 2 is odd, and the square of an odd number is always odd.

Question 4

What is GCD(120, 180)?

Accepted Answer

60

Answer

120 = 2³×3×5 and 180 = 2²×3²×5, so GCD = 2²×3×5 = 60.

Question 5

Which of the following numbers is a perfect square?

Accepted Answer

144

Answer

144 = 12², making it a perfect square, while 50, 72, and 200 are not.

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