Why You Wanna Trip on Me

Algebra Level 3

Given that a , b , c , d , e a, b, c, d, e and f f are distinct positive integers such that a < b < c < d < e < f a<b<c<d<e<f .

37 , 50 , 67 , 72 , 80 , 89 , 95 , 97 , 102 , 110 , 112 , 125 , 132 , 147 , 155 37, 50, 67, 72, 80, 89, 95, 97, 102, 110, 112, 125, 132, 147, 155

If the 15 pairwise sum of these numbers are listed above, what is the value of c + d c+d ?


The answer is 102.

Porames Vattanaprasan by Porames Vattanaprasan , 21, Thailand

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1 solution

Rajen Kapur
Sep 25, 2015

Sum of all the given 15 numbers is 1470. As these 15 sums comprise of 30 values of these 6 variables 5 apiece, sum of a + b + c + d + e + f = 1470 5 = 294 a + b + c + d + e + f = \dfrac{1470}{5} = 294 . Now as the numbers are in ascending order it may be inferred that a + b = 37 a + b = 37 and e + f = 155 e + f = 155 the sum of the two extreme values correspond to the given lowest and highest sums, 37 and 155, respectively, it may be concluded that the remaining middle terms add-up to c + d = 294 − 37 − 155 = 102 c + d = 294 - 37 - 155 = 102 .

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