23. Find all pairs of consecutive odd positive integers both of which are smaller than
10 such that their sum is more than 11.
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Let x be the smaller of the two consecutive odd positive integers. Then, the other integer is x+2. Since both the integers are smaller than 10.
x + 2 < 10
⇒x < 10 − 2
⇒x < 8 ..... (i)
Also, the sum of the two integers is more than 11.
∴x + ( x + 2 ) > 11
⇒2x + 2 > 11
⇒2x > 11 − 2
⇒2x > 9
⇒x > 9/2
⇒x > 4.5 ...... (ii)
From (i) and (ii), we obtain
Since x is an odd number, x can take values, 5 and 7.
Thus, the required possible pairs are (5,7) and (7,9).
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