Question

17. Find the sum of all two-digit numbers which
when divided by 3 give 2 as remainder.
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Answer 1

Answer:

Step-by-step explanation:

First two digit number to fulfill the given condition is 11. Now each number with a gap of 3 will give a remainder 2 when divided by 3. Hence such numbers will form an arithmetic progression (AP) series containing numbers 11,14,17,20 and so on and last number of the series will be 98. As 98 - 11 = 87 and 87/3= 29 hence there will be a total of 30 ie 29 +1 numbers in the series. Now the sum total of the series will be

Count of numbers * (first number + last number) /2

so

30 * (11 +98)/2

15 * 109

1635, hence answer.