Question

How many numbers lie between 10 and 300, which when divided by 4 leaves a remainder 3?

Answer 1

The first number greater 10 which when divided by 4 leaves a remainder 3 is 11.
So, the next number will be 11 + 4 = 15
The other numbers in this will be = 15 + 4 = 19 ; 19 + 4 = 23 ; 23 + 4 = 27
So, the AP = 11, 15, 19, 23, 27, 32......
The last term of this AP will be 299.
We have to find the total numbers that lie between 10 and 300, which when divided by 4 leaves a remainder 3.
In fact we have to find 'n' that is the number of terms of the AP.
an = a + (n - 1)d
299 = 11 + (n -1)4
299 = 11 + 4n - 4
299 - 11 + 4 = 4n
292 = 4n
n = 292/4
n = 73
So, total 73 numbers lie between 10 to 300 which when divided by 4 leaves a remainder 3.