Maths Olympiad Prep

Track / Stage 4 / 195 of 340 #455 of 1964

Problem 455

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.

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 and solution reproduced as published; topic, difficulty and ordering added by this site.