Find the pairs of consecutive odd positive integers both of which are

1.	Find the pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.
Answer» Let x be the smaller of the two consecutive odd positive integers, then the other is x + 2. According to the given conditions. x < 10, x + 2 < 10 and x + (x + 2) > 11 ⇒ x < 10, x < 8 and 2x > 9 x < 10, (∵ x < 8 automatically smallest of the lesser than) ... (1) and x > (9/2) ... (2) From (1) and (2), we get 9 (9/2) < x < 8 Also, x is an odd positive integer. x can take values 5 and 7. So, the required possible pairs will be (x, x + 2) = (5, 7), (7, 9)

Find the pairs of consecutive odd positive integers both of which are smaller than 10 such that their sum is more than 11.

Answer»

Let x be the smaller of the two consecutive odd positive integers, then the other is x + 2.

According to the given conditions.

x < 10, x + 2 < 10 and x + (x + 2) > 11

⇒ x < 10, x < 8

and 2x > 9

x < 10, (∵ x < 8 automatically smallest of the lesser than) ... (1)

and x > (9/2) ... (2)

From (1) and (2), we get 9

(9/2) < x < 8

Also, x is an odd positive integer. x can take values 5 and 7.

So, the required possible pairs will be (x, x + 2) = (5, 7), (7, 9)