Let the five integers be a, b, c, d and e with a ≤ b ≤ c ≤ d ≤ e. The smallest total is 57, which is an odd number so b ≠ a. Similarly, the largest total is 83, which is also an odd number so d ≠ e. Hence we now have a \textless{} b ≤ c ≤ d \textless{} e and a + b = 57 and d + e = 83. Only one possible total remains and so b = c = d with c + d = 70. This gives c = d (= b) = 35 and therefore e, the largest integer, is 83 − 35 = 48 (whilst a = 22). 
Five positive integers (not necessarily all different) are written on five cards. Boris calculates the sum of the numbers on every pair of cards. He obtains only three different totals: 57, 70 and 83. What is the largest integer on any card? 
Options:
* $$35$$ 
* $$42$$ 
* $$48$$ 
* $$53$$ 
* $$82$$ 