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Question

Find the number of pairs of consecutive even positive integers, both of which are greater than 5 such that their sum is less than 23.


A

6

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B

(8, 10)

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C

(10, 12)

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D

(12, 14)

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Solution

The correct options are
A

6


B

(8, 10)


C

(10, 12)


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

Since, both the integers are greater than 5,

x>5 ------(1)

Also, the sum of two integers is less than 23.

x+(x+2)<23

2x<232

2x<21

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, 10

Thus, required possible pairs are (6, 8), (8, 10) and (10,12).


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