Q 5.
Number Theory
Level
3
Tushar wrote 4 different natural numbers. He chose three numbers at a time and added them each time. He got the sums as 115, 153, 169, 181. The largest of the numbers Tushar first wrote is ?
The answer is 91.
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Let the numbers be a, b, c, d where a < b < c < d
Obviously,
a + b + c = 115 ................. (I)
a + b + d = 153 .................. (II)
a + c + d = 169 .................. (III)
b + c + d = 181 .................. (IV)
Thus, using (I) & (II): c = d - 38. Using (I) & (IV): a = d - 66.
Substituting for a and c in (III): 3d - 104 = 169
whence, d = 273/3 = 91