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Q24.    Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23.

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Let x be smaller of two consecutive even positive integers. Then the other integer is x+2.

Both integers are larger than 5.

\therefore \, \, \, x> 5

 Sum of both integers is less than 23.

\therefore \, \, \, x+(x+2)< 23

\Rightarrow \, \, \, (2x+2)< 23

\Rightarrow \, \, \, 2x< 23-2

\Rightarrow \, \, \, 2x< 21

\Rightarrow \, \, \, x< \frac{21}{2}

\Rightarrow \, \, \, x< 10.5

  We conclude  \, \, \, \, x< 10.5  and  \, \, \, x> 5  and x is even integer number.

  x can be 6,8,10.

The pairs of consecutive even positive integers are (6,8),(8,10),(10,12).

 

Posted by

seema garhwal

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