What is the Min Number
Number Theory
Level
2
If a, b , c are three consecutive positive integers such that a< b < c. What is the smallest value of b such that (a+b+c) is divisible by both 5 and 7.
The answer is 35.
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1 solution
If a, b and c are consecutive then a = b -1 and c = b + 1 , hence a + b + c = 3b. Since it is given that the sum of the three integers is divisible by 7 and 5 the smallest sum is 35. But as the sum is also divisible by 3 the smallest integer value of b such that 3b = 35*k is when b = 35.