Problems And Answers PHIMO MOCK 2020 JUNIOR SECONDARY

21. How many positive integers \(x\) are there such that \(3x\) has \(3\) digits and \(4x\) has four digits?

22. An icosidodecahedron is a convex polyhedron with 20 triangular faces and 12 pentagonal faces. How many vertices does it have (see next page for figure)?

23. The surface area of a right rectangular prism (a box) is 48 square feet, and the sum of its length, width, and height is 13 feet. What is the length of the longest diagonal connecting two corners of the box?

24. What is the area of the largest circle contained in an equilateral triangle of area \(8\sqrt 3\).

25. A circle of radius 3 crosses the center of a square of side length. Find the positive diference between the area of the nonoverlapping portions of the figures.

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