1. In the land of Noom, all nouns are 4-letter words with consonants at the beginning and end and a repeated vowel (a, e, i, o, or u) in the middle. How many such words are possible?

2. How many positive three-digit integers are there in which the sum of its three digits is odd?

3. How many non-empty subsets containing only prime numbers does the set {1,2,3,4,5,6,7} have?

4. What two-digit number has exactly 9 factors?

5. How many factors of 1200 can be divided by 15 without a remainder?

6. When the positive integers with exactly three positive divisors are listed in ascending order, what is the fifth number listed?

7. N is the smallest positive integer that is divisible by every 1-digit positive integer. How many positive factors does N have?

8. Call a positive integer kinda-prime if it has a prime number of positive integer divisors. If there are 168 prime numbers less than 1000, how many kinda-prime positive integers are there less than 1000?

Oofrence Apr 24, 2019