81. If n is an integer greater than 1, and n is not a prime number, then which of the following must be true?
(A) n is the sum of three prime numbers
(B) n is the difference between 2 even numbers
(C) n is the difference between one even number and one odd number
(D) n is the product of one even number and one odd number
(E) n is the product of prime numbers
OA[spoiler]: E[/spoiler]
I initially picked D as my answer since the first four numbers that meet the condition would be 4, 6, 8, 9. I don't think the question is specific enough--but perhaps someone can point out where I am wrong here.
86. If 5x^2 has two different prime factors, at most how many different prime factors does x have?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
[spoiler]OA: B[/spoiler]
I took this to mean, since 5x^2 has two prime factors, they must be 5 and x^2. Thus x^2 is prime. Thus x would only have one prime factor. What is wrong with my reasoning here?
87. How many positive integers, from 2 to 100, inclusive, are not divisible by odd integers greater than 1?
(A) 5
(B) 6
(C) 8
(D) 10
(E) 50
[spoiler]OA: B[/spoiler]
I attempted to first find all the different integers divisible by 3, 5, 7, 9, and 11 but this was pretty time consuming. Any other ideas?
(A) n is the sum of three prime numbers
(B) n is the difference between 2 even numbers
(C) n is the difference between one even number and one odd number
(D) n is the product of one even number and one odd number
(E) n is the product of prime numbers
OA[spoiler]: E[/spoiler]
I initially picked D as my answer since the first four numbers that meet the condition would be 4, 6, 8, 9. I don't think the question is specific enough--but perhaps someone can point out where I am wrong here.
86. If 5x^2 has two different prime factors, at most how many different prime factors does x have?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
[spoiler]OA: B[/spoiler]
I took this to mean, since 5x^2 has two prime factors, they must be 5 and x^2. Thus x^2 is prime. Thus x would only have one prime factor. What is wrong with my reasoning here?
87. How many positive integers, from 2 to 100, inclusive, are not divisible by odd integers greater than 1?
(A) 5
(B) 6
(C) 8
(D) 10
(E) 50
[spoiler]OA: B[/spoiler]
I attempted to first find all the different integers divisible by 3, 5, 7, 9, and 11 but this was pretty time consuming. Any other ideas?
