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 positive integers at most 100 are relatively prime to 100?
Answer: 40
φ(100) = 100(1 - 1/2)(1 - 1/5) = 40.
How many positive divisors does 360 have?
Answer: 24
360 = 2^3·3^2·5, so it has (3+1)(2+1)(1+1) = 24 divisors.
How many integers from 1 to 1000 are divisible by 3 or 5?
Answer: 467
333 + 200 - 66 = 467 by inclusion-exclusion.
How many trailing zeros does 100! have?
Answer: 24
Counting factors of 5 gives floor(100/5) + floor(100/25) = 20 + 4 = 24.
What is the sum of the first 20 odd positive integers?
Answer: 400
The sum of the first n odd numbers is n^2 = 400.
How many lattice points (x, y) with integer coordinates lie on the circle x^2 + y^2 = 25?
Answer: 12
The points are (±5,0), (0,±5), (±3,±4), and (±4,±3), which is 12 in all.
What is the largest prime factor of 1001?
Answer: 13
1001 = 7·11·13.
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