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Mary was 12 on her last birthday.

We need to express 1800 as the product of two factors, one of which (her age in months) is between twelve and thirteen times the other (her age in complete years).

These are 150 and 12 respectively.

Mary is now 150 months old, i.e. she was twelve on her last birthday and she is now 12 years 6 months old

This problem is taken from the UKMT Mathematical Challenges.