There are 5 boxes of different weights. They are weighed in pairs taken 2 at a time and the weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121. What is the sum of the weights of the 5 boxes ?  Choose the correct choice from the following answers
A) 250	B) 289	C) 290	D) 295	E) 305
Let the 5 boxes be a, b, c, d and e. The ten weights correspond to all the possible combinations of 2 weights out of 5.   On adding all the given weights, each boxes weight gets added 4 times:   a+b, a+c, a+d, a+e.   Similarly for b:   b+c, b+d, b+e and a+b (already included above)   Similarly for c, d and e.   Therefore, 110+112+113+114 .....+120+121 = 4* (a+b+c+d+e)   or, 4* (a+b+c+d+e) = 1156   or, (a+b+c+d+e) = 1156/4= 
<gadget id="calculator">1156/4</gadget>
<output>289</output>
289   ANSWER:289
<result>B</result>
There are 5 boxes of different weights. They are weighed in pairs taken 2 at a time and the weights obtained are 110, 112, 113, 114, 115, 116, 117, 118, 120 and 121. What is the sum of the weights of the 5 boxes ?