Math STEM AMC8 Quiz

What is the total number of positive divisors of the product 10 x 14 x 21?

• 12

• 18

• 36

• 30

• 24

Answer explanation

To find the total number of positive divisors of 10 x 14 x 21, first factor each number: 10 = 2^1 x 5^1, 14 = 2^1 x 7^1, 21 = 3^1 x 7^1. The product is 2^2 x 3^1 x 5^1 x 7^2. The total divisors formula is (2+1)(1+1)(1+1)(2+1) = 36. Thus, the answer is 36.

How many of the positive integers from 1 to 10,000 do not have an odd number of factors?

• 100

• 300

• 1000

• 9900

• 5000

How many positive factors of 288 are also multiples of 4?

• 5

• 7

• 10

• 12

• 14

How many positive integer factors of 432 are perfect squares?

• 3

• 6

• 12

• 20

• 2

Find the value of a positive integer x such that the (x + 72) = y²    and (x + 49) = z².

• 0

• 9

• 72

• 49

• 12

Tags

CCSS.HSA-REI.B.4B

The sum of two prime numbers is 39. What is the sum of the reciprocals of these two prime numbers?

• 1/39

• 39/74

• 2/39

• 74

• 30

The difference between two prime numbers is 77. What is the value of their product?

• 77

• 11

• 155

• 158

• 1/77

Tags

CCSS.6.EE.A.1

• 5

• 0.5

• 7.5

• 11

• 3

• 5

• 1

• 2

• 6

Tags

CCSS.8.EE.C.7B

• 2.5: 3.5: 1

• 1: 25: 35

• 25: 14: 35

• 35: 14: 4

• 3.5: 14: 0.4