CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

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


A
71
loader
B
72
loader
C
73
loader
D
74
loader

Solution

The correct option is C 73
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 $$3.$$
$$\Rightarrow$$  $$a_n = a + (n - 1)d$$
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
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image