1991 AHSME Problems/Problem 14
Problem
If is the cube of a positive integer and is the number of positive integers that are divisors of , then could be
(A) (B) (C) (D) (E)
Solution 1: Number Sense
Solution by e_power_pi_times_i
Notice that if is expressed in the form , then the number of positive divisors of is . Checking through all the answer choices, the only one that is in the form is .
Solution 2: Answer Choices
Solution by e_power_pi_times_i
Since the divisors are from , then the answer must be something in (mod ). Since and are the same (mod ), as well as and , is the only answer left.
See also
1991 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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