BARC Quiz 3: Solution and Q&A

Quiz 3 - Part 1

1. Calculate $\sqrt{2 + \sqrt{2 + \sqrt{2 + \ldots}}}$
2. Find the product of roots of $\dfrac{x^{2002} + 4x^{2001}}{4x^{2000}} = 8$.
3. Aedan opened his science book and noticed that the product of the two pages in front of him was equal to 1122. What were the sum of the numbers of those pages?
4. If $x + y = 5$ and $xy = 6$, find the value of $x^3 + y^3$.

Quiz 3 - Part 2

1. A boy playing under the streetlight noticed that the length of shadow of his 5-foot stick erected vertically on the pavement, is 20 inches. He then challenge his friends to a P5.00 bet that he can determine the length of their stick by just measuring the shadow. Erected vertically on the same spot, the length of shadow of the longer stick is 32 inches. How long is it?
2. Find the term that is independent of $x$ in the expansion of $\left( 2 + \dfrac{3}{x^2} \right) \left( x - \dfrac{2}{x} \right)^6$.
3. If one root of the quadratic equation with integer coefficients is 3+4i, what is the constant term of the equation?

Quiz 3 - Part 3

1. $w$ varies jointly with $x$ and $y$ and inversely with the square of $z$. If $w = 12$ when $x = 3$, $y = 8$, and $z = 2$, find the constant of proportionality $k$.
2. At what price will a businessman mark a digital camera for sale that cost P6,000 in order that 20% discount can be offered on the marked price and still makes a profit of 25% of the selling price.
3. From a tank filled with 240 gallons of alcohol, 60 gallons are drawn off and the tank is filled up with water. Then 60 gallons of the mixture are removed and replaced with water, and so on. How many gallons of alcohol remain in the tank after 5 drawings of 60 gallons each are made?