how many leap years are there in 100 years?(say between 1600 and 1700)?

Question

by arith.progression :a=1600 ,d=4,l=1696 i got the answer as 25 leap years...but in aptitude book it was given 24...please clear this.........

1600 must also be included only then it will be hundred years....isn't it

Answer 1

"between 1600 and 1700"

So you have to start from 1601 and stop at 1699!

That is from 1604 to 1696

a= 1604, d = 4
a + (n-1)d = 1696
1604 + (n-1)4 = 1696

(n-1)*4 = 92
n-1 = 23
n = 24

A Tip regarding such problems:
Generally , leap years are divisible by four, but century years are special, they must also be divisible by 400. The year 2000 was a leap year.
1600 is a leap , but 1700 is NOT a leap year.

Answer 2

The answer depends on whether the 'century' is divisible by 400 or not! 1600 and 2000 were leap years but 1700, 1800, 1900 were not.
Your example includes 101 years - 1600 is year 1, 1601 is year 2 etc
From 1900 to 1999 there are 24 leap years 1904,1908....1996 (24*4) but from 1901 to 2000 there are 25. 1904 (4*1) to 2000 (4*25)

Answer 3

Earth takes little more than 365 days to revolve round the sun. Leap years are introduced to correct for the same. Though every fourth year is a leap year, earth takes little less than 365 + 1/4 days to revolve. So to correct it, leap year is skipped every 100 years till 400 years. In short, there are 97 leap years in every block of 400 years.

To make it more clear, year 4, 8, 12, 16, ... are leap years but not year 100, 200, 300. But again year 400 is a leap year.

Between years 1600 and 1700, year 1600 is a leap year, but 1700 is not. Also year 1604, 1608, 1612, ... till 1696 are leap years. Thus there are 25 leap years between 1600 and 1700. But that is not so between 1300 and 1400. Here neither 1300 nor 1400 is a leap year. So there are 24 leap years between 1300 and 1400.

Answer 4

Since 'between' does not include 1700 as a leap year, then 1600 must also not be considered as a leap year. When that word 'between so and so' comes, then 'so and so' should not be considered as part of the group. So, you must start from 1601 and end at 1699.

a = 1604, d = 4, l = 1696 is correct.

Let n be the number of leap years.

1604 + 4(n - 1) = 1696
4n - 4 = 92
4n = 96
n = 24

24 leap years.

Answer 5

The ACTUAL number of days in a year should be only
365 days 5 hours 56 minutes & 24 seconds.
For easy calculation purposes the number of days in a
year is taken as 365 and the remaining time of
5 hours 56 minutes & 24 seconds
is taken as 6 hours i.e., one fourth of a day and adjusted in
the name of LEAP YEAR in every fourth year.
As there is an EXCESS ADJUSTMENT of
3 minutes & 36 Seconds
which is nothing but
1/400th of a DAY
this ACCUMULATED ONE DAY IS BEING ADJUSTED ONCE IN EVERY 400 YEARS
i.e., in the years 1600, 2000,2400 and so on.
ANSWER:
As 1600 is not a LEAP YEAR there were only 24 leap years BETWEEN 1600 and1700 - exclusive of 1700 starting from 1604 and ending with1696.

Answer 6

Leap Years Between 1900 And 2000

Answer 7

1696 - 1600 = 96/4 = 24

Answer 8

It is said that leap years b/w 1600 & 1700 .So neither 1600 will be included nor 1700 . you will have to count it from 1604, 1608 _______ 1696 .
When you will count , you will get 24 as the ans.

Answer 9

If you are taking 1600-1700 as an example, I have a better idea. Take 1601-1701 as an example. The answer should be same as the no. of leap years in a century never changes.

So the leap years would be:
1604,1608,1612,1616,1620,1624,1628,
1632,1636,1640,1644,1648,1652,1656,
1660,1664,1668,1672,1676,1680,1684,
1688,1692,1696,1700.
i.e, 25 leap years.
It proves that the answer in the book is wrong, misprint,etc.

Answer 10

arithmetic progression
L = a + (n - 1)d

Exclusive between or inclusive between?
If between means not including 1600 and 1700, then a = 1604.

If a = 1604, d = 4, and L = 1696, then
1696 = 1604 + (n - 1)(4)
92 = (n - 1)(4)
92 / 4 = n - 1
23 = n - 1
23 + 1 = n
24 = n