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Suppose that a and b are integers such that 3b = 8 - 2a.  How many of the first six positive integers must be divisors of 2b + 30?

 Jan 6, 2021
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There are 2 divisors(1,2)

Because subtracting an even number from another even number will always result in an even number, and 2a always has to be even. The only way fo 3b to be even is if b is even too. So b is any even number. 2b+30 can only guarantee the positive divisor 2 because we can find examples where it will not work for the other integers. Since b is and integer, 1 is already a lock. 

b=4 a=-2

3 wont work, 4 wont work, 5 wont work and 6 wont work.

 Jan 6, 2021
edited by MooMooooMooM  Jan 6, 2021

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