Question

Sum of all 3 digit number which are divisible by 3 but not divisible by 5

Answer 1

there are many numbers which are divisible by 3 but not divisible by5

ex:-123

351

Answer 2

The three digit numbers divisible by 3 form an AP with first term 102, last term 999 and common difference 3

So 999=102+(n-1)3

3n = 999-102+3 = 900

So n=300

Sum of all numbers= 300/2(102+999)

= 1,65,150

But this sequence also has some numbers which are multiples of 5 . These numbers will be multiples of 15 as the lcm of 3 and 5 is 15.

So these numbers also form an AP with first term 105, last term 990 and common difference 15

990=105+(n-1)15

15n = 990 -105+15=900

n=60

So sum = 60/2(105+990) = 32,850

So the required sum= 1,65,150 - 32,850

= 1,32,300

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