Integer Values and Divisibility Concepts

The video tutorial explores a mathematical problem involving integers x and y, where y is between 7 and 16, and x/y equals 2/5. The instructor identifies possible integer values for y and calculates corresponding x values. The solution involves checking divisibility by 5 to ensure x remains an integer. Ultimately, two possible values for x are found, demonstrating the application of constraints and integer arithmetic.

What is the range of possible integer values for y given the constraint 7 < y < 16?

• 7, 8, 9, 10, 11, 12, 13, 14, 15

• 8, 9, 10, 11, 12, 13, 14, 15

• 9, 10, 11, 12, 13, 14, 15, 16

• 8, 9, 10, 11, 12, 13, 14, 15, 16

If x/y = 2/5, what is the expression for x in terms of y?

• x = 5/2y

• x = 5y/2

• x = 2y/5

• x = 2/5y

Why can't x be an integer when y = 8?

• Because 8 is not an integer

• Because 8 is not divisible by 2

• Because 8 is not divisible by 5

• Because 8 is greater than 7

What is the value of x when y = 10?

• x = 4

• x = 5

• x = 3

• x = 6

Which of the following values of y will make x an integer?

• 8 and 9

• 10 and 15

• 11 and 14

• 10 and 12

What is the value of x when y = 15?

• x = 5

• x = 4

• x = 6

• x = 3

How many possible integer values are there for x?

• One

• Two

• Four

• Three

What is the pattern observed when checking if x is an integer?

• x is an integer only when y is divisible by 5

• x is never an integer

• x is an integer only when y is divisible by 2

• x is always an integer

What is the result of 15 times 2/5?

• 7

• 6

• 8

• 5

Why is it unnecessary to test all values of y?

• Because only values divisible by 2 matter

• Because only values divisible by 5 matter

• Because all values of y are valid

• Because y must be greater than 16