Question

Which of the following is not a leap year?
$\left( a \right)$ 600
$\left( b \right)$ 700
$\left( c \right)$ 800
$\left( d \right)$ 1010

Answer 1

Hint: In this particular type of question use the concept that leap year is a divisible by 4 but any other year is not divisible by 4 and in a leap year the number of days is one more than the number of days in any other year which is not a leap year so use these concepts to reach the solution of the question.

Complete step-by-step answer:
As we know that in a particular year there are a total 365 days.
But in a leap year there is one more day compared to any ordinary year so the total number of days in a leap year is (365 + 1) = 366 days.
And a leap year comes after every 3 year i.e. 4 year is a leap year.
For example- if we start from 1, so 1^st, 2^nd and 3^rd are ordinary years and 4^th is a leap year.
As we see that 1, 2 and 3 are not divisible by 4 but 4 is divisible by 4, so a leap year is always divisible by 4.
So we can say that all the years which are divisible by 4 are leap years, in other words we can say that leap years is the set of years which is divisible by 4.
So the set of years which is divisible by 4 is,
Years = {4, 8, 12, 16, 20, 24, 28, 32, ................................}
Now we have to find out from the given options which is not a leap year.
So we have to check one by one
Option (a) = 600.
So divide 600 by 4 we have,
$ \Rightarrow \dfrac{{600}}{4} = 150$
So it is a leap year.
Option (b) = 700.
So divide 700 by 4 we have,
$ \Rightarrow \dfrac{{700}}{4} = 175$
So it is a leap year.
Option (c) = 800.
So divide 800 by 4 we have,
$ \Rightarrow \dfrac{{800}}{4} = 200$
So it is a leap year.
Option (d) = 1010.
So divide 1010 by 4 we have,
$ \Rightarrow \dfrac{{1010}}{4} = 252.5$
So it is not a divisor of 4
So it is not a leap year.
So it is the required answer.
Hence option (D) is the correct answer.

Note – Whenever we face such types of questions the key concept we have to remember is that always recall the number of days in a leap year then construct the set of years which is only leap years then check which divisibility rule it follows then check the options one by one we will get the required answer.