Question

The number of ways of selecting two numbers from the first $15$ natural numbers such that their sum is a multiple of $5$,is

• A. 20
• B. 36
• C. 21
• D. 16

Answer 1

Answer: (C)

21

The maximum sum when two numbers are selected from $1st$ $15$ natural numbers$=29$ (i.e when $15$ and $14$ are selected).
Hence multiples of $5$ in this case can only be $5,10,15,20,25$
No. of ways in which $2$ numbers are selected with sum $5=2(1,4and2,3)$
Similarly no. of ways of selecting $2$ numbers such that their sum $10=4$
no. of ways of selecting $2$ numbers such that their sum $15=7$
no. of ways of selecting $2$ numbers such that their sum $20=5$
no. of ways of selecting $2$ numbers such that their sum $25=3$
Therefore, total no. of ways such that sum is multiple of $5=(2+4+7+5+3)=21$
Hence, option 'C' is correct.