Aptitude - Calendar - Discussion

1.Odd Days: Number of days more than the complete number of weeks in a given perios is the number of odd days during that period.

2. Leap Year: Every year which is divisible by 4 is called a leap year. Thus, each one of the years 1992, 96, 2004, 2008 etc is a leap year.

Every 4th century is a leap year but no other century is a leap year. Thus each one 400, 800, 1200, 2000 etc are is a leap year. None of 1900, 2010, 2020, 2100 etcis a leap year.

An year which is not a leap year is called an ordinery year.

3. (i) An ordinary year has 365 days

(ii) A leap year has 366 days

4. Counting of Odd days

(i) 1 ordinary year = 365 days= (52weeks + 1day)

An ordinary year has 1 odd day

(ii) 1 Leap year =366 days= (52weeks + 2days)

A leap year has 2 odd days

(iii) 100 years= 76 ordinary years + 24 leap years

= [(76x52)weeks + 76days] + [(24x52)weeks + 48 days)

=5200weeks + 124days

=(5217weeks + 5days)

Therefore 100 years contain 5 odd days

200 years contain 10 and therefore 3 odd days

300 years contain 15 and therefore 1 odd day

400 years contain (20+1) and therefore 0 odd days

Similarly, each one of 800, 1200, 1600, 2000 etc contain 0 odd days

Remark: (7n+m) odd days, where m<7 days=" 1">
5.Counting Days:

We have : Sunday for 0 odd days; Monday for 1 odd day; Tuesday of 2 odd days and so on

So in that way U will get the number of Odd day s in mulitiple of 400 years :0 odd days

19.8.2015 was a wednesday.

Solution:

I. Take the year part and split it into two parts (ie) 2014 & 2015
II. 2014 ...... Can be splited into 2000 years and 14 years.
III. Odd days calculation: since 2000 is a leap century (2000/400 =50) year so 0 odd day.
...>(14 /4= quotient =3 ,remaider=2) gives;

Leap year =3 . Ordinary year =(14-3=11) 11.
.....>Odd days in 14 yrs= [(3*2=6)+(11*1=11)]=6+11=17
Therfore total no of odd days in 2014= 17.
IV. 19.8.2015

Odd days:
Jan Feb Mar Apr May Jun July Aug
31 28 31 30 31 30 31 19
Add all days= 231,
Therfore odd days upto 19.8.2015 = 231,
V.Total odd days = 17(from step III) + 231(from step IV).
=248 /7 = 3(Remainder =3, And quotient =35).

0 -sunday
1- monday
2- tuesday
3- wednesday
4- thursday
5- friday
6- saturday

Therfore answer is Wednesday.

Notes:
Century leap years =400 , 800,1200,1600 ,2000,2400. That is a year which is divisible by 400.
100 is not a leap year eventhough it is divisible 4. Centuary year should be divisible by 400.

If number exist between 2000 to 2099 then apply formula like
Example 5 april, 2020.

1) Take last 2 digit 20
2) 20+20/4-1=>20+5-1=>4
3) Follow this series
0 For jan
3 For feb
3 For mar
6 For april
1 For may
4 For june
6 For july
2 For aug
5 For sep
0 For oct
3 For nov
5 For dec

4) Check the code for april= 6 that means month=6 then date=gives a date in question like 5

5)(y+m+d) mod 7 (mod means take remainder)

6)(24+6+5)mod 7=>35mod 7=>means 0 Sunday.

@Gautam

Formula/Shortcut: Odd days in 1600 years = 0
Formula/Shortcut: Odd days in 400 years = 0

Therefore, 1600 + 400 = 2000.

2000 + { Jan (31). Feb(28). March(31) April 1st (1) }

(31 + 28 + 31 + 1) = 91 days 0 odd days.

Therefore On 1st April, 2001 it was Sunday.

From this data, we can find that

In April, 2001 Wednesday falls on 4th, 11th, 18th and 25th.

Hope this will help you. Have a nice day!

2001-january-1 day is Monday.

So, 2001-April 1st is Sunday.
How is that possible?

Ans) Century code: 6 (2001)
Month code: 0 (January)
Year : 01
Leap years : 0
Date : 1
Total = 8.

So, finally 8÷7=1 (Monday) - January
April 1st = 30days + 0 + 3 + 1 = 34.

= 34÷7 = 6 odd days (Monday + 6odddays).
So, April 1st Sunday.
April 4th Wednesday.

Shortcut:

From 0(AJ),1(JO),2(My),3(Ag),4(FMrN),5(Jn)6(SD).

And 1-S,2-M,3-T,4-W,5-TH,6-FR,7 or 0- Sat.

finding day on 1/4/2001.

1+0+(2001-1900)+(2001-1900)/4.

1+0+101+25 ; 101/4=25.25 take the whole number (25 only).

127/7=18 reminder 1 which represents day Sunday.

This means that if Sunday is 1 then Wednesday is 4 therefore,
Option D is right.

Odd days means the leftover days.

I will explain with an example;
Find how many odd days are there in 25 days?

So, The answer would be 4.

How?
7 days means 1 complete week and in 25 days we have 3 complete weeks that is up to the 21st day.

The remaining 4 days are odd days because it is not a complete one week.

Guys it is easy to find solution to this problem by formula.

Day = Date+Month code+(x-1990)+(x-1990)/4.

Here given day is Wednesday it's code is 4 so now 4 = Date+0+101+25.

4 = Date+126.

You should get (date+126)/7 you should get 4 by trail and error method if you substitute any one day you will know the answer.

Simple method:
Use this formula:

Day +month.no +(x-1900)+(x-1900)/4.
let day=Sunday=1.
1+0+(2001-1900)+(2001-1900)/4.
1+0+101+25 ; 101/4=25.25 take the whole number (25 only).
127/7=18 reminder 1 which represents day Sunday.
This means that if Sunday is 1 then Wednesday is 4 therefore,
Option D is right.

Why 1600 and 400?

Because 1200 is min leap year 1300 in not leap year same 1400, 1500 also not a leap year 1600 is a leap year and the max leap year is 2000. Therefore all problems we get 1600.

Here, 2001 = 1600 + 400 (1600 is leap year so 0 odd day & 400 is also leap year therefore 0 odd days).