Question

The sum of all 2-digit numbers which leave remainder 1 when divided by 3 is
1) 1616
2)1602
3)1605
4)None of these
​

Answer 1

Answer:

1605

Step-by-step explanation:

the two digit numbers which leave remainder 1when divided by 3 are

10,13,16.....................31,34,37...... ......42,..........91 ,94,97

first term a= 10

common difference d= 3

last term l = 97

to calculate number of terms

a+(n-1) d= l

10+(n-1) d =97

(n-1) 3 =97-10

n-1 = 87÷3

n-1 = 29

n= 29+1=30

number of terms = 30

sum of these 30 terms = 30/2{a+l} using S= n/2{first term+last term}

= 30/2{10+97}

= 30/2×107

=15 × 107

= 1605

the answer is 1605