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AMO · 2027 · Grades 4-5 · Self-study SET 34 Question 11

AMO

Question 11

Read carefully: dividing two positive whole numbers by their GCD (HCF) leaves two co-prime numbers. For example, 50 and 70 have GCD 10; their underlying co-primes are 5 and 7, obtained by dividing both numbers by 10.

Now use this idea. Two numbers add to 1085 and have GCD 35. What is the average of their underlying co-prime numbers, rounded to the nearest whole number?

Use ordinary rounding: a fractional part of exactly 0.5 rounds up. Enter one whole number.