Special Populations Flashcards
7 cards from real AMC 12 practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.
Read the first 7 Special Populations flashcards as text
How many prime numbers are less than 50?
Answer: 15
The primes are 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47, which is 15 numbers.
What is the sum of the first 10 triangular numbers (1, 3, 6, 10, ...)?
Answer: 220
The sum of the first n triangular numbers is n(n+1)(n+2)/6, giving 10·11·12/6 = 220.
What is the smallest perfect number greater than 6?
Answer: 28
28 = 1+2+4+7+14, the sum of its proper divisors.
How many perfect squares are between 1 and 200, inclusive?
Answer: 14
Squares 1^2 through 14^2 = 196 are at most 200, while 15^2 = 225 is too large.
How many three-digit positive integers are palindromes?
Answer: 90
The first digit has 9 choices (1-9) and the middle digit has 10, giving 90.
If F1 = F2 = 1 and F(n) = F(n-1) + F(n-2), what is F10?
Answer: 55
The sequence runs 1,1,2,3,5,8,13,21,34,55, so F10 = 55.
How many integers from 1 to 100 are both perfect squares and perfect cubes?
Answer: 2
Such numbers are sixth powers: 1 and 64.
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