Determine all pairs of consecutive even positive integers, both of which are greater than 5 such that theirsum is less than 23.
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Determine all pairs of consecutive even positive integers, both of which are greater than 5 such that theirsum is less than 23.
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ANSWER
10 and 12
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Let x be the smaller of the two consecutive even positive integers, then the other even integer is x + 2.
Given x > 8 and x + (x + 2) < 25.
⇒ x > 8, and 2x + 2 < 25.
⇒ x > 8, 2x < 23
⇒ x > 8, x < 23/2
⇒ 8 < x < 23/2
⇒ x = 10,
∴ the required parity even integers is (10, 12)