Consider a positive odd integer n. Let X = twice the number of factors of n, and let Y = the number of factors of 2n. Which of the following must be true?
Answer A: X = 4
Answer B: X Y
Answer C: Y X
Answer D : X = Y
Answer E :There is not enough information to solve the problem.

Please Answer and Explain the Question, Thank You.

Question

Consider a positive odd integer n. Let X = twice the number of factors of n, and let Y = the number of factors of 2n. Which of the following must be true?
Answer A: X = 4
Answer B: X > Y
Answer C: Y > X
Answer D : X = Y
Answer E :There is not enough information to solve the problem.

Please Answer and Explain the Question, Thank You.

anonymous · Answer

Consider an odd n with factors 1, a, b, ab. Then 2n has factors 1, 2, a, b, 2a, 2b, ab, 2ab. Notice that 2n has twice as many factors as n. This argument extends for any number of factors in the original n, and works because none of the factors of n are even. So X = Y, for all n.  So I understand now Thank You, to no one in particular.