Example 8 Find all pairs of consecutive odd natural numbers, both of which are larger than 10, such that their sum is less than 40. Let the smaller odd natural number be x Since the larger integer is consecutive odd, it will be x + 2 Given that, Both integers are larger than 10 i.e. x > 10 Since x > 10 & x > 8 x > 10 & x + 2 > 10 x > 10 – 2 x > 8 Sum of the numbers is less than 40 ∴ x + (x + 2) < 40 2x + 2 < 40 2x < 40 – 2 2x < 38 x < 19 Hence, x > 10 & x < 19 Natural numbers greater than 10 but less than 19 are 11, 12, 13, 14, 15, 16, 17, 18 Odd natural numbers are 11,13,15,17 Hence x = 11, 13, 15, 17 Hence, finding the possible pairs as follows. Possible pairs are (11, 13) , (13, 15) , (15, 17), (17, 19)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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