# Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23

**Solution:**

Let x be the smaller of the two consecutive even positive integers, then the other integer is (x + 2)

Since both the integers are larger than 5,

x > 5 ....(1)

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

x + (x + 2) < 23

⇒ 2x + 2 < 23

⇒ 2x < 21

⇒ x < 21/2

⇒ x < 10.5. ....(2)

From (1) and (2), we obtain

5 < x <10.5.

Since x is an even positive integer, then values of x are 6, 8 and 10

When When When

x = 6, the pair is (6, 8)

x = 8, the pair is (8, 10)

x = 10, the pair is (10, 12)

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

NCERT Solutions Class 11 Maths Chapter 6 Exercise 6.1 Question 24

## Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23

**Summary:**

A linear inequation x + (x + 2) < 23 can be formed. We have found that the required possible pairs are (6, 8), (8, 10) and (10, 12)