Consider two successive even numbers. If 10 is subtracted from 4 times the smaller one, then
the resulting value is smaller than 2 times the larger one. What is the maximum possible value
of the sum of the two successive even numbers?
Answers
Given : two successive even numbers. If 10 is subtracted from 4 times the smaller one, then the resulting value is smaller than 2 times the larger one.
To find : maximum possible value of the sum of the two successive even numbers
Solution:
Let say two successive even numbers.
2k & 2(k + 1)
Sum = 2k + 2(k + 1) = 4k +2
10 is subtracted from 4 times the smaller one, then the resulting value is smaller than 2 times the larger one
4 * 2k - 10 < 2 (2(k + 1))
Dividing by 2 on both sides
=> 4k - 5 < 2k + 2
=> 2k - 5 < 2
=> 2k < 7
=> k < 3.5
maximum possible value of k = 3
maximum possible value of the sum of the two successive even numbers
= 4k + 2 = 4(3) + 2 = 14
14 is maximum possible value of the sum of the two successive even numbers
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