Question 308623
The three consecutive integers are N, N+1, and N+2.
{{{ N+(N+1)+(N+2)=k}}}
Solve for N.
{{{ 3N+3=k}}}
{{{ 3N=k-3}}}
{{{ N=(k-3)/3}}}
Now solve for N+2 which is the greatest of the three integers. 
{{{ N+2=(k-3)/3+6/3}}}
{{{ N+2=(k-3+6)/3}}}
{{{ N+2=(k+3)/3}}}
{{{ N+2=k/3+1}}}
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b) is the correct answer.