Question

Find all pairs of consecutive even positive integers, both of which are larger than 8, such that their sum is less than 25?

a) 10 and 12
b) 12 and 14
c) 14 and 16
d) 16 and 18

Answer 1

The only pair of consecutive even positive integers larger than 8 and with a sum less than 25 is 10 and 12.

Step-by-step explanation:

To find all pairs of consecutive even positive integers, both of which are larger than 8, such that their sum is less than 25, we need to first understand what consecutive even integers are. Consecutive even integers are numbers that differ by two and are both divisible by 2. Since they need to be greater than 8, our starting point would be 10. Now we will list the pairs and add them to ensure their sum is less than 25.

• 10 and 12: The sum is 10 + 12 = 22, which fulfills the condition.
• 12 and 14: The sum is 12 + 14 = 26, which does not fulfill the condition.
• Further pairs will have even larger sums, so we stop here as our sum limit is 25.

Therefore, the only pair that fulfills the condition is 10 and 12.