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  • The number of ways of selecting two numbers a and <img alt="b, a \in\{2,4,6, \ldots, 100\}" src="https://entrancecorner.oncodecogs.com/gif.latex?b%2C%20a%20%5Cin%5C%7B2%2C4%2C6%2C%20%5Cldots%2C%201

The number of ways of selecting two numbers a and b, a \in\{2,4,6, \ldots, 100\} and b \in\{1,3,5, \ldots .99\} such that 2 is the remainder when a+b is divided by 23 is   

Option: 1

268


Option: 2

108


Option: 3

54


Option: 4

186


Answers (1)

best_answer

a+b= 25,          a+b= 71           a+b= 117           a+b= 163
a          b                    a       b                       a         b                         a            b
2         23                   2       69                    18        99                      64         99       
4          21                  4       67                    20       97                      66         97
\vdots                                  \vdots                                 \vdots                                     \vdots
24          1                 70       1                    100        17                    100            63
________                 __________           ____________              _______________
12 cases                   35 cases                   42 cases                        19 cases

Total ways = 12+35+42+19
                  = 108             

Posted by

Divya Prakash Singh

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