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2019 SAIMC keystage2-EMIC individual Question 3

xIMC · 2019 SAIMC keystage2-EMIC individual

Question 3

Each of three students $A$, $B$ and $C$ has a calculator and starts doing some operations at the same time. Student $A$ starts from $1509$ and adds $3$ at each step, student $B$ starts from $2019$ and subtracts $7$ at each step, while student $C$ starts from the number $X$ and adds $1$ at the first step, adds $2$ at the second step, adds $3$ at the third step and so on. If after $N$ steps the three students end up with the same result, then find the number $X$.