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ITMC 2018 Grade 8 National Preliminary set01 Question 28

ITMC · ITMC 2018 Grade 8 National Preliminary set01

Question 28

Answer-format rule: round a non-integer answer to the nearest integer. If the calculated answer has more than five digits, give its last five digits.

Integers $x,y>1$ make both $25/x$ and $61/y$ reduced fractions, and $25/x+61/y$ is an integer. How many ordered pairs $(x,y)$ are possible?