I am currently teaching myself some maths but I have found these two questions on the internet, and I'm completely stuck.
The questions are:
1.A man whose birthday was January 1st died on Feb 9th 1992. He was years of age in the year for some interger . In what year was he born?
2. If and are both prime numbers, find, with justification, all possible values of .
I think that question 1 is to do with quadratics and you can tell that if is , then would be which looks to be the most sensible, although I do not know where to go. Question 2 I don't really know where to start.
These are both really nagging me and I cannot get the answers.
Thanks so much for any help given!
Good. You might also note that if x= 45, then which cannot be right because he died before that. If x= 43, then which would mean that when he died, in 1992, he was 43+ (1992- 1849)= 43+ 143= 186 years old! Now, if he was 44 in 1936, when was he born?
p must not be 2 or 7 since, in that case, would be divisible by 2 or 7 respectively.Question 2 I don't really know where to start.
These are both really nagging me and I cannot get the answers.
Thanks so much for any help given!
Question 1:
Observation 1: hence maximum possible integers whose squares are less than 1992 are atmost 44. Now lets consider the simplest case of 1 for a man to be 1 year old on 1 AD he as to be born on 1 Jan 0 AD the he would be 1992 year of age when he died which would be absurd.
So for any AD the man has to be born AD to be x years old and given that he died on 1992 only practical solution can be obtained if choose an year closer to 1992 so choosing the year 1936 we have . So the man should be born on 1936 - 44 = 1892 AD. So he was just over 100 years old when he died which is practically possible.
Kalyan.
Ok thanks so much! I understand question 1. Is there a more elegant answer for question 1 or would trial and error be a good answer?
I'm still not all that sure on question 2 though. I don't quite understand why some steps are being done? for example:
surely and therefore not divisable by 3?
Thanks very much!