If mn=3(m+1)+n and m and n are integers, m could be any of the following values EXCEPT:
A
2
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B
3
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C
4
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D
5
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E
7
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Solution
The correct option is D5
First you need to solve for n. The reason you solve for n is that the answer choices list possible values for m, the other variable. IF you solve for n, then you can plug the possible values for m into the formula and see when you get a non-integer for n, since n must be an integer.
mn=3(m+1)+n
mn−n=3(m+1)
n(m−1)=3(m+1)
n=3(m+1)(m−1)
mn=3(m+3)(m−1)
2n=3(2+1)(2−1)=9
3n=3(3+1)(3−1)=6
4n=3(4+1)(4−1)=5
5n=3(5+1)(5−1)=184=92
7n=3(7+1)(7−1)=4
Only a value of 5 for m does not produce an integer for n