how many even multiples of 3 are there between 50 and 100?
Thank you!
Here the first number after 50 divisible by 3 is 51. But that is odd.
The next number divisible by 3 is 54.
Hence the first term is 54.
Then the numbers increase by a common difference 6.
The last even number divisible by 3 less than 100 is 96.
So
96 = 54 + (n-1) 6
96-54 = (n-1)6
42 = (n-1)6
42/6= n-1
7 = n-1
7+1 = n
n = 8 ......Answer
Here the first number after 50 divisible by 3 is 51. But that is odd.
The next number divisible by 3 is 54.
Hence the first term is 54.
Then the numbers increase by a common difference 6.
The last even number divisible by 3 less than 100 is 96.
So
96 = 54 + (n-1) 6
96-54 = (n-1)6
42 = (n-1)6
42/6= n-1
7 = n-1
7+1 = n
n = 8 ......Answer
(Method 1)There are 10 multiples of 3 in 1- 30, So there are 10 multiples of 3 in 50 - 80. Then we count from 81.
81, 84, 87, 90, 93, 96, 99.
There are 17 multiples of 3 between 50 and 100.
Then we have 99 is not an even number.
51, 54, 57, 60..... , 96 <---- 16 numbers there.
Then we divide 16 by 2 which is 8
There are 8 even multiples of 3 between 50 and 100.
(Method 2) Even multiples of 3 must be divisible by 6 because those multiples of 3 are divisible by 2 and 3.
Starting from 54, we have
54, 60, 66, 72, 78, 84, 90, 96 Which is 8 numbers.