A shipping clerk has five boxes of different but unknown weights each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight, in kg, of the heaviest box ?	Pick.
A) 60
B) 61
C) 64
D) Can't be determined
E) None
Explanation :   Two boxes are selected at at time and weighed together. Thus, the selection order does not matter and selecting box 1 and then box 2 is the same as selecting box 2 and then box 1. So this is a combination problem.   2 boxes can be selected from 5 boxes in 5C2 ways, i.e. 10 ways. The given list of weighings is 10 in number. So we can assume that all the possible combinations of boxes have been weighed. Lets assume that all boxes are lined as per increasing weights and named as b1, b2, b3, b4, b5. From the given list (Arranges in increasing order of weights) ,   what we have is b1 + b2 = 110, as b1 is the lightest and b2 is the next lightest box heavier than b1. So the sum of these two should be the minimum value in the list.   The second lightest sum of weights, the second value in the list, will be the sum of the b1 + b3 = 112.   Similarly, the maximum value in the list should be the sum of weights of b4 and b5, giving b4 + b5 = 121.   The second last heaviest will be b3 + b5 = 120.   Adding the 4 equations, we get, 2 b1 + 2 b3 + 2 b5 + b2 + b4 = 463 - Equation 1.   Sum of all the weights in the given list is 1160. This sum is the sum of each of the cases b1+b2, b1+b3, b1+b4, b1+b5, b2+b3, b2+b4, b2+b5, b3+b4, b3+b5, b4+b5. Thus sum of all this will be 4(b1 + b2 + b3 + b4 + b5) = 1160. Thus, b1 + b2 + b3 + b4 + b5 = 290 - Equation 2.   Subtracting equation 2 from equation 1, we get, b1 + b3 + b5 = 173.   We know that b1 + b3 = 112, So b5 = 173 - 112= 
<gadget id="calculator">173 - 112</gadget>
<output>61</output>
61= Desired answer.   Answer : 61
<result>B</result>
A shipping clerk has five boxes of different but unknown weights each weighing less than 100 kg. The clerk weighs the boxes in pairs. The weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121 kg. What is the weight, in kg, of the heaviest box ?