Question

How many numbers less than 500, when divided by 11, gives 3 as a remainder ?

Answer 1

The first integer will be 3=(7∗0+3). Now keep on adding 7 to this until 100.

eg(7∗0)+3=3;3+7=10;10+7=17;17+7=23 and so on

result = 3,10,17,24,31,38,45,52,59,66,73,80,87,94

i.e. 14 numbers

Another approach can be using Arithmetic Progression

start from 3 and then increment each by 7.

So we are getting an AP with a=3and d=7. We need to find the number of elements in our AP i.e. 'n' but first we must know the last element of our AP 'a(n)'

Now,a(n)=(floor(100/7)∗7)+3=(13∗7)+3=(91+3)=94

so the AP becomes 3 10 17 ..... 94. To calculate the number of elements in this AP is

a(n)=a+(n−1)∗d or n=(a(n)−a)/d+1=(94−3)/7+1=13+1=14 elements (ans)

Answer 2

hey friend....

the ans is 46.