Question

If 2 times the sum of two consecutive even numbers is greater than 94, what is the smallest possible value of the larger number?

Answer 1

26

Explanation:

Define the variables:

• 2n = first even number
• 2n + 2 = consecutive even number

Given information:

• 2 times the sum of two consecutive even numbers is greater than 94

Create an inequality from the defined variables and the given information:

⇒ 2(2n + 2n + 2) > 94

Solve the inequality:

⇒ 2(4n + 2) > 94

⇒ 8n + 4 > 94

⇒ 8n > 90

⇒ n > 11.25

Therefore:

• 2n > 22.5
• 2n + 2 > 24.5

As 2n and 2n+2 are even numbers:

• smaller number (2n) ≥ 24
• larger number (2n + 2) ≥ 26

Therefore, the smallest possible value of the larger number is 26.