The number of pairs of consecutive even positive integers, both of which are larger than 8 , such that their sum is less than 25 , is

Question

The number of pairs of consecutive even positive integers, both of which are larger than 8 , such that their sum is less than 25 , is (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

Let x be the smaller of two consecutive even positive integers. Then, the other even integer is x+2. text Given, x>8 text and x+x+2<25 ⇒ x>8 text and 2 x+2<25 ⇒ x>8 text and 2 x<23 ⇒ x>8 text and x<(23/2) ⇒ x=10 Hence, there exists only one pair of even integer (10,12).

Q. The number of pairs of consecutive even positive integers, both of which are larger than 8 , such that their sum is less than 25 , is

1

2

3

4

Let x be the smaller of 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 and 2x<23 ⇒x>8 and x<223​ ⇒x=10 Hence, there exists only one pair of even integer (10,12).