12. The combined age of Alice and Bob is 39 . The combined age of Bob and Clare is 40 . The combined age of Clare and Dan is 38. The combined age of Dan and Eve is 44. The total of all five ages is 105 .
Which of the five is the youngest?
A Alice
B Bob
C Clare
D Dan
E Eve
12. D Let the ages of Alice, Bob, Clare, Dan and Eve be $a, b, c, d, e$ respectively.
So, for example, $b+c=40$ and $d+e=44$. Adding these gives
$b+c+d+e=84$. We are also told that $a+b+c+d+e=105$. The difference between these equations shows that $a=105-84=21$. Hence $b=39-21=18$ and, similarly, $c=40-18=22, d=38-22=16$ and $e=44-16=28$. So Dan is the youngest.