Maths Olympiad Prep

Track / Stage 4 / 211 of 340 #471 of 1964

Problem 471

AMC 12 late, AIME early
Number theory Difficulty 4.8 Find the answer

G1.4 16 cards are marked from 1 to 16 and one is drawn at random. If the chance of it being a perfect square number is 1d\frac{1}{d}, find dd.

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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Official solution

Perfect square numbers are 1,4,9,161,4,9,16.
 Probability =416=1dd=4 \begin{array}{l} \text { Probability }=\frac{4}{16}=\frac{1}{d} \\ d=4 \end{array}

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.