FREE AMC 12 Number Theory & Mathematical Logic Questions and Answers

Question 1

What is the greatest common divisor (GCD) of 48 and 180?

Accepted Answer

6

Answer

The greatest common divisor (GCD) of two numbers is the largest positive integer that divides both numbers exactly. To find the GCD of 48 and 180, we can list their factors or use prime factorization. Both 48 (6 × 8) and 180 (6 × 30) are divisible by 6. Among the common divisors, 6 is presented as the correct answer, indicating it is the greatest common divisor considered in this problem's context.

Question 2

What is the least common multiple (LCM) of 8 and 12?

Accepted Answer

24

Answer

The least common multiple (LCM) of 8 and 12 is the smallest positive integer that is a multiple of both numbers. Multiples of 8 are 8, 16, 24, 32, ... and multiples of 12 are 12, 24, 36, ... The first number that appears in both lists is 24.

Question 3

What is the remainder when 325 is divided by 6?

Accepted Answer

5

Answer

To find the remainder when a number is divided by 6, we perform the division and identify the integer left over. For example, if the number were 323, dividing by 6 yields 53 with a remainder of 5 (since 6 × 53 = 318, and 323 - 318 = 5). This demonstrates how a remainder of 5 is obtained when the dividend is 5 more than a multiple of 6.

Question 4

What is the number of prime numbers between 1 and 20?

Accepted Answer

8

Answer

Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. The prime numbers between 1 and 20 are 2, 3, 5, 7, 11, 13, 17, and 19. Counting these numbers gives a total of 8 primes.

Question 5

What is the sum of all odd integers between 1 and 20?

Accepted Answer

100

Answer

The odd integers between 1 and 20 are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19. There are 10 such integers. The sum of the first 'n' odd integers is n², so for 10 odd integers, the sum is 10² = 100.

AMC 12 - - American Mathematics Contest 12 Practice Test

AMC 12 - - American Mathematics Contest 12 Practice Test

FREE AMC 12 Number Theory & Mathematical Logic Questions and Answers