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UKMT Pink Kangaroo, 2025

Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Sami and Parnika are celebrating their birthday today. Sami notices that $\frac{1}{19}$ of Parnika's age is equal to $\frac{1}{17}$ of his age. The sum of their ages is greater than 40 and less than 100. How old is Parnika?

(A) $19$ (B) $34$ (C) $38$ (D) $57$ (E) $76$

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