Question

If the sum of the last $3$ integers in a set of $7$ consecutive integers is $258$, what is the sum of the first $4$ integers?

• A. $230$
• B. $200$
• C. $250$
• D. $330$

Answer 1

Answer: (D)

$330$

Think of the set of integers as $n,(n+1),(n+2),(n+3),(n+4),(n+5)$, and $(n+6).(n+4)+(n+5)+(n+6)=3n+15=258$. Therefore, $n=81$. The sum of the first four integers is $81+82+83+84=330$.

Alternatively, the sum of the first four integers is $4n+6$. If $n=81$, then $4n+6=4\left(81\right)+6=330$.