Latest TCS Aptitude Question SOLUTION: last day of the any century can not be end with which day?

100 years contain= 5 odd days
200 years contain = 3 odd days
300 years contain = 1 odd days
400 years contain = 0 odd days
the cycle is repeated
so century can not end with Tuesday , Thursday , Saturday .

First day of century can be
Sunday, Monday, Wednesday or Friday and not Tuesday,Thursday or saturday.

So last day of century can not be
Monday, wednesday or Friday.

december 31 , 2000 is sunday
december 31 , 2100 is friday
december 31 , 2200 is wednesday
december 31 , 2300 is monday
Again december 31 , 2400 is sunday

This cyclic order goes on.
If a century is leap year, its last day will be sunday.

Nandita:- tueday thursday saturday is the correct ans

First a leap year is a year which has 1 day more than a normal year. A year is a leap year if:
1. it is divisable by 4 and not divisable by 100
or
2. it is divisable by 100 and divisable by 400

in a century there are 25 leap years if it ends with a leap year
and there are 24 leap years if it does not

if there are 25 leap years in a century then the "shift" in days is ((365*100)+25) mod 7 = 6 if there are 24 leap years then the "shift" is ((365*100)+24) mod 7 = 5

this shift is the difference in days on the same date
for instance if a day x is a monday the day x+5 would be a friday ( because friday is 5 days away from monday) this goes back as well so the day x-2 is saturday (which is 2 days back from monday)
notice that x+7 is actually the same day x (so 7 days after a monday comes again a monday)

so now that we said all that stuff lets look at the 1st of jan
on the first year of a century
if the first day of a century is x the first day of the next century will be (according to the shift mentioned earlier):
x-1 (which is the same as x+6) if the century ends with a leap year
x-2 (which is the same as x+5) if the century doesn't end with a leap year

now lets take some starting year of a century which ends with a leap year for example 1901 (because the 20th century ends with 2000 and that is a leap year)
...
1901 starts with day x (first day of next cent. we substract 1)
2001 starts with day x-1 (first day of next cent we substract 2)
2101 starts with day x-3 (first day of next cent we substract 2)
2201 starts with day x-5 (first day of next cent we substract 2)
2301 starts with day x-7 (we substract 1 for the next...)
...
this repeats itself int the past and future
in 2301 we have the exact same situation as in 1901 as far as days go.
so we see now that the days x-2 x-4 and x-6 can not start
a century and knowing that 1901 started with a tuesday
we know that x-2 = sunday x-4 = friday and x-6=wednesday
can not start a century and the days preeceding sun fri and wed cannot end it and those are sat thur and tue.

So we conclude that tuesday thursday and saturday can not end a century.

I know i've made this freakin complicated but i believe its ok, dont hesitate to check mistakes are possible :P


P.S. Thursday can end 2099 but the officially last day of 21century is 31. dec 2100 and it is a friday

first days of century will be thursday-tuesday-sunday-friday this is a cycle
so the last days of century cant become these days..
so ans is thurs,tues,sun,fri

evry1 is giving different answers.. which solution is correct??