Math Gold Medalist

Lor

2024 AMC 8 

Problem 4

When Yunji added all the integers from $1$ to $9$, she mistakenly left out a number. Her incorrect sum turned out to be a square number. What number did Yunji leave out?

$\textbf{(A) } 5\qquad\textbf{(B) } 6\qquad\textbf{(C) } 7\qquad\textbf{(D) } 8\qquad\textbf{(E) } 9$

Important Identities

1+2+…+9-x= square number

45-x=square number

square number =36

x=9

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   Solution