Let N, x and y be positive integers such that N = x + y, 2 < x < 10 and 14 < y < 23. If N > 25, then how many distinct values are possible for N?
Explanation:
Given, 2 < x < 10
x can take any of the values from {3, 4, 5, 6, 7, 8, 9}
Also, 14 < y < 23
y can take any of the values from {15, 16, 17, 18, 19, 20, 21, 22}
The highest value N (i.e., x + y) can take = 9 + 22 = 31 (when x = 9; y = 22)
The lowest value N (i.e., x + y) can take = 3 + 15 = 18 (when x = 3; y = 15)
But, N = x + y > 25. Hence the different values of x + y are {31, 30, 29, 28, 27, 26}.
Hence, x + y, and thereby N can take 6 distinct values.
Hence, 6.
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.