Six children P, Q, R, S, T and U, were all born on the same day of the year, but each was born in a different year during a single six-year period.
P is older than R.
Q is older than both S and T.
U is two years older than S.
P was born either in 2007 or in 2008.
The oldest children was born in 2005.
If T is older than S, which of the following must be true ?
I. Q was born in 2005.
II. T was born in 2006.
III. P was born in 2008.
Solution
If the eldest child was born in 2005, then all the children were born in the years ranging from 2005 to 2010.
Case 1: P was born in 2007.
As U is 2 years older than S, U was either born in 2008 or 2006.
Case 1A: U was born in 2008. S was born in 2010. As P is older than R, R must be born in 2009. Also, as Q is older than T, T must be born in 2006 and Q must be born in 2005.
Case 1B: U was born in 2006. S was born 2 years later i.e. 2008. Now, Q must be older than S which means that Q was born in 2005. R and T are born in either 2009 or 2010.
Case 2: P was born in 2008.
As U is 2 years older than S, U was either born in 2005 or 2007.
Case 2A: U was born in 2005. S was born in 2007. As Q is older than S, Q was born in 2006. R and T are born in either of 2009 or 2010.
Case 2B: U was born in 2007 so S was born in 2009. As P is older than R, R must be born in 2010. And as Q is older than T, Q must be born in 2005 and T must be born in 2006.
The possibilities when T is older than S are cases 1A and 2B.
In both the cases Q was born in 2005 and T was born in 2006.
So, only I and II statements are definitely true.
