Question

Find all pairs of consecutive odd positive integers both of which are smaller than 8 such that their sum is more than 10.

(a) (5,7)

(b) (3,5), (5,7)

(c) (3,5), (5,7), (7,9)

(d) (5,7), (7,9)

I got this question during an online exam.

My question comes from Algebraic Solutions of Linear Inequalities in One Variable and their Graphical Representation in section Linear Inequalities of Mathematics – Class 11

Answer 1

Right answer is (a) (5,7)

The explanation: Let two numbers be x and x+2.

x + x+2 >10 => 2x>8 => x>4

and x<8

and x+2<8 => x<6.

4<x<6 => x can be 5.

For x =5, x+2=7

So, Pairs of odd consecutive positive integers are (5,7).