Prime Numbers and Ratios

The video tutorial covers four math problems. Problem 106 involves solving for the present number of teachers using student-teacher ratios and algebraic manipulation. Problem 107 requires finding the smallest integer n for which 25^n is greater than 5^12, focusing on exponent inequalities and base conversion. Problem 108 explores properties of prime numbers, particularly their sums and differences, to determine true statements. Problem 109 involves comparing different expressions to identify the one with a different value, emphasizing fraction operations and algebraic evaluation.

If the current student-to-teacher ratio is 30:1, and both students and teachers increase, what is the new ratio?

• 25:1

• 35:1

• 20:1

• 30:1

What is the present number of teachers if the student-to-teacher ratio is 30:1?

• 15

• 10

• 25

• 20

How can you express 25 in terms of a power of 5?

• 5^1

• 5^4

• 5^2

• 5^3

What is the smallest integer n for which 25^n is greater than 5^12?

• 8

• 7

• 6

• 5

Which of the following statements about prime numbers greater than 2 is true?

• Their sum is always odd.

• Their difference is always odd.

• Their sum is always even.

• Their product is always even.

If x and y are different prime numbers greater than 2, what can be said about x divided by y?

• It is always an integer.

• It is always less than 1.

• It is never an integer.

• It is always greater than 1.

What is the result of adding two odd prime numbers greater than 2?

• A prime number

• A composite number

• An even number

• An odd number

Which expression does not have the same value as the others?

• 5/3

• 1/3 + 1/3 + 1/3 + 1/3 + 1/3

• 1/3 * (1 + 1 + 1 + 1 + 1)

• (1 + 2 + 3 + 4 + 5) / 3

What is the value of 1/3 times the sum of five ones?

• 5

• 5/3

• 1

• 3

If you add 1/3 to itself five times, what is the result?

• 3

• 5

• 1

• 5/3