Question

Find the number of pairs of consecutive even positive integers, both of which are greater than 5 such that their sum is less than 23.

• A. 6
• B. 4
• C. 3
• D. 5

Answer 1

The correct option is C

3

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

Since, both the integers are greater than 5,

$x>5$ ------(1)

Also, the sum of two integers is less than 23.

$\Rightarrow$ $x+(x+2)<23$

$\Rightarrow$ $2x<23–2$

$\Rightarrow$ $2x<21$

$\Rightarrow$ $x<10.5$ -------- (2)

From (1) and (2), we obtain $5<x<10.5$

Since, x is an even number; x can take the values 6, 8, 10

Thus, required possible pairs are (6, 8), (8, 10) and (10,12).