what is the year??!!..(puzzle)?

Question

there are five friends. josh says that his birthdate is 31st desember 1878.
rick says his bd is 14th november 1902.
derik says his bd is 12th july 1898.
usha says her bd is 29th february 1900.
mike says his bd is 15th may 1904.
now, in which year will the sum of their ages be equal to a prime number between 175 and 240?

im stuck in a quiz by this one damn question!.plz if anyone can solve this out?

Answer 1

The Julian Calendar was reformed by Pope Gregory in 1582 because the year had gotten out of step with the seasons by ten days. The reason was that the old calendar contained a leap year every four years without exception, making the average year slightly too long, 365.25 days to be exact.

Earth's (seasonal) year is actually closer to 365.2422 days. Gregory did two things: he skipped ten days in the month of October to bring the calendar back to where it should be, then added a rule that only century years divisible by 400 would be leap years. So every four years since 1584 have been leap years *except* for 1700, 1800 and 1900 - and Usha could not have been born on 2/29/1900 because that day did not exist.

Answer 2

The prime numbers between 175 and 240 are:

179 181 191 193 197 199 211 223 227 229 233 239.

The difference in the ages is 1904- each age. 26 + 2 + 6 + 4+0=38. So it is 38 + whatever year it is between the range of 175 and 240. Since there are 5 of them the sum of their ages excluding the 38 years must be a multiple of 5. the prime number is 193, which should give you the year.

Answer 3

The difficulty (and, I suspect, the answer to the quiz) is that Usha is lying! 1900 was not a leap year, so she could not have been born on 29 Feb that year!

(The prime numbers between 175 and 240 are:

179 181 191 193 197 199 211 223 227 229
233 239 - From a little program called Sieve.exe which uses the Sieve of Erastothenes http://www.fpx.de/fp/Software/Sieve.html )

Let's approach the problem with the assumption that Usha meant 28th February. You will find that, because nobody shares a birthday, in any one year, the sum of their ages spans five years in a continuous sequence (in 1905, for example, the sum of their ages on each day would run from 38 on 1st January to 43 on 31st December), so at certain times in their lives the sum of their ages would equal all of the primes in turn! Hence there is no UNIQUE solution to the problem EXCEPT the one of invalid data!

My expectation is that, in quizzes like this which look incredibly complicated, you will find one piece of information which invalidates the problem, making the answer very simple. What is being tested is not your ability to find all the primes or to work out the ages on every particular date in a year to find which number fits but your ability to look at and evaluate a problem BEFORE you waste time on calculation!

Answer 4

On the year the youngest turns 1 add all thier ages together. (in 1905 josh is 27, rick is 3, derik is 7, usha is 5, and mike is 1) thats 43.
Now add 5 (one year for each person)(along with one to the year to keep track of it) to the sum of thier ages untill it equals a prime number between 175 and 240 (179 181 191 193 197 199 211 223 227 229 233 239)

The answer is 1935 in which thier ages will add up to 193

Answer 5

The answer is not unique. For example, on 1-1-1936, the age of Josh, Rick, Derik, Usha, and Mike are 57, 33, 37, 35, and 31, respectively. Summation result of this numbers is 193, a prime number. You can check that on 1-1-1942 the sum of their ages is 223, also a prime number.

Answer 6

Sorry I'm lazy to count because I use a tedious method. here goes:
Get all the prime numbers between 175 - 240
Let's say this prime no is A
Let the year we wish to know be x
The equation is A = 5x - (1878+1902+1898+1900+1904)
Just substitute the Prime nos into A and you can get the answers.
I dunno what to do with the day and month