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Find all pairs of consecutive even positive integers, both of

Question

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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Find all pairs of consecutive even positive integers, both of which are larger than

5

such that their sum is less than

23

9 mins ago

Discuss this question LIVE

9 mins ago

Text solutionVerified

Let

x

be the smaller of the two consecutive even positive integers. Then, the other integer is

x + 2

Since both the integers are larger than

5

x > 5

.... (1)

Also, the sum of the two integers is less than

23

x + (x + 2) < 23

\Rightarrow 2 x + 2 < 23

\Rightarrow 2 x < 23 - 2

\Rightarrow 2 x < 21

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

\Rightarrow x < 10.5

..... (2)

From (1) and (2), we obtain

5 < x < 10.5

Since

x

is an even number,

x

can take the values

6, 8

and

10

Thus, the required possible pairs are

(6, 8), (8, 10)

and

(10, 12)

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Question Text	Find all pairs of consecutive even positive integers, both of which are larger than $5$ such that their sum is less than $23$ .
Answer Type	Text solution:1
Upvotes	150