Question

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

A
71
B
72
C
73
D
74

Solution

## The correct option is C 73The 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 $$3.$$$$\Rightarrow$$  $$a_n = a + (n - 1)d$$Here, $$a_n=299,\,a=11$$ and $$d=4$$$$\Rightarrow$$  $$299 = 11 + (n -1)4$$$$\Rightarrow$$  $$299 = 11 + 4n - 4$$$$\Rightarrow$$  $$299 - 11 + 4 = 4n$$$$\Rightarrow$$  $$292 = 4n$$$$\Rightarrow$$  $$n =\dfrac{292}{4}$$$$\therefore$$  $$n = 73$$So, total $$73$$ numbers lie between $$10$$ to $$300$$ which when divided by $$4$$ leaves a remainder $$3.$$Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More