Problem Statement A cylinder with radius 2 cm and height 8 cm is full of water. A second cylinder of radius 4 cm and height 8 cm is empty. If all of the water is poured from the first cylinder i...

Problem Statement In an art gallery, a 2 m high painting, $BT$, is mounted on a wall with its bottom edge 1 m above the floor. A spotlight is mounted at $S$, 3 m out from the wall and 4 m above ...

Problem Statement In the diagram, $\triangle ABC$ is right-angled at $C$. If $BD = 2x$, $DC = x$, and $\angle ADC = 2(\angle ABC)$, then the length of $AB$ is Problem Link Solution $$\te...

Problem Statement In the diagram, $YQZC$ is a rectangle with $YC = 8$ and $CZ = 15$. Equilateral triangles $ABC$ and $PQR$, each with side length 9, are positioned as shown with R and B on sides $...

Problem Statement Sylvia chose positive integers $a$, $b$ and $c$. Peter determined the value of $a + \dfrac{b}{c}$ and got an answer of 101. Paul determined the value of $\dfrac{a}{c} + b$ and go...

Problem Statement If $a$ and $b$ are positive integers such that $\dfrac{1}{a} + \dfrac{1}{2a} + \dfrac{1}{3a} = \dfrac{1}{b^2 - 2b}$, then the smallest possible value of $a+b$ is Problem Link ...

Problem Statement For certain real numbers $a$, $b$, and $c$, the polynomial $g(x) = x^3 + ax^2 + x + 10$ has three distinct roots, and each root of $g(x)$ is also a root of the polynomial $f(x) = ...

Problem Statement The polynomial $x^3-ax^2+bx-2010$ has three positive integer roots. What is the smallest possible value of $a$? Problem Link Solution $$f(x) = x^3-ax^2+bx-2010 = (x - r_1)...

Problem Statement The sum of the zeros, the product of the zeros, and the sum of the coefficients of the function $f(x)=ax^{2}+bx+c$ are equal. Their common value must also be which of the followin...

Problem Statement The quadratic equation $x^2+mx+n$ has roots twice those of $x^2+px+m$, and none of $m,n,$ and $p$ is zero. What is the value of $n/p$? Problem Link Solution $$f(x) = x^2+mx+...