Consecutive Integer Puzzles: Quadratics & Factoring Fun

1. The product of two consecutive integers is 72. What are the integers?

• 8 and 9

• 7 and 8

• 6 and 7

• 9 and 10

2. If the product of three consecutive integers is 120, what are the integers?

• 3, 4, 5

• 5, 6, 7

• 2, 3, 4

• 4, 5, 6

3. A rectangle's length is one more than its width. If the area is 30 square units, find the dimensions of the rectangle.

• Width: 4 units, Length: 5 units

• Width: 6 units, Length: 7 units

• Width: 5 units, Length: 6 units

• Width: 3 units, Length: 4 units

4. The product of two consecutive integers is equal to the square of the smaller integer. What are the integers?

• -1 and 0

• 2 and 3

• 0 and 1

• 1 and 2

5. The sum of two consecutive integers is 25. What are the integers?

• 8 and 9

• 14 and 15

• 12 and 13

• 10 and 11

6. If the product of two consecutive integers is 56, what are the integers?

• 7 and 8

• 8 and 9

• 5 and 6

• 6 and 7

7. A number and its consecutive integer have a product of 90. What is the number?

• 7

• 10

• 9

• 8

8. The area of a square is equal to the product of two consecutive integers. If the area is 36, what are the integers?

• 3 and 4

• 6 and 7

• 4 and 5

• 5 and 6

9. The product of two consecutive integers is 42. Write a quadratic equation to represent this situation and solve for the integers.

• 5 and 6

• 8 and 9

• 6 and 7 or -7 and -6

• -5 and -4

10. If the product of two consecutive integers is 20, factor the quadratic equation that represents this problem.

• (n + 4)(n - 5)

• (n + 5)(n - 4)

• (n + 1)(n - 21)

• (n + 2)(n - 10)