1.

How many numbers are only divisible by 3 in 1 to 200​

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Answer:

FIRST ,between 1 - 200

let we TAKE the no. Divisible by 3 = x

And no. Divisible by 7 = y

And no. Divisible by both 3 & 7 = z

Between 1 to 200 multiples of 3 are

3,6 ,9...............198

So using ARITHMETIC progression LAST tern relation.

L = a + (n-1)d..................................(1)

L = 198

a=3

d=3

We get n = 66 =x

Similarly for 7 we get , y= 28.

Now the we will find the no.s which are divisible by both 3 and 7 for that we determine the no. divisible by 21 = 3×7

21,42,63..........189

Using relation 1 we get z = 9

Last step is

No. Divisible by 3 or 7 b/w 1 - 200 = (no.s divisible by 3 ) + (no.s divisible by 7) - (no.s divisible by both)

= X+Y-Z

= 66+28-9 = 85

Numbers DIVINE by both 3 or 7 between 1 to 200 are 85.


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