Question

Find the number of pairs of consecutive even positive integers both of which are smaller than 25 and their sum is more than 30.

1. 4
2. 3
3. 8
4. 10

Answer 1

Correct Answer - Option 1 : 4

Calculation:

Let x be the smaller of the two consecutive even positive integers. Then, the other even integer is x + 2.

It is given that both the integers are smaller than 25 and their sum is more than 30.

Therefore, 

⇒ x + 2 < 25 and x + (x + 2) > 30

⇒ x < 23 and 2x + 2 > 30

⇒ x < 23 and 2x > 28

⇒ x < 23 and x > 14

⇒ 14 < x < 23

⇒ x = 16, 18, 20, 22               [ x is an even integer]

Hence, the required pairs of consecutive even integers are (16, 18), (18, 20), (20, 22) and (22, 24)