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Bobbing For Apples

There are 5 white, 7 red and 8 black balls in a box. If you are blindly picking up balls from the box, what is the minimum number of balls you need to take out of the box to ensure that you have at least 2 balls of the same color?

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Always be Investing

Albert and Samuel are given $10,000 each by their grandparents. Albert puts his money into the stock market immediately, earning 5% interest each year. Samuel holds onto his money for 2 years, before also investing in the stock market at the same interest rate as Albert. After 4 years, how much more money does Albert have?

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Marvelous Markdown

A seller gives a 10% discount to a customer who pays cash. What is the marked price of an item for which the customer pays $225?

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Photo attributed to melburnian.

Cylindrical Tank

A rectangular tank 82 cm long, 37 cm wide and 75 cm deep has the same volume as a cylindrical tank. If the radius of the cylindrical tank is 30 cm, what is its height (in cm) ? [let π = 3.14]

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Share the Dough

John, Jack and Jason share an amount in the ratio of 4:3:7, respectively. If Jason received $32 more than Jack, what is the total amount they shared?

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Need for Speed

A car starts from a static position and accelerates uniformly until it reaches a certain speed. If five cars reach the following speeds in the given amounts of time, which car will have gone the farthest distance after 1 second?

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Bocce Ball

There are 5 white, 7 red and 8 black balls in a box. If you are blindly picking up balls from the box, what is the minimum number of balls you need to take out of the box to ensure that you have at least 2 balls of the same color?

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Length of the Hypotenuse

If the area and perimeter of a right triangle are 30 cm2 and 30 cm, respectively, what is the length of the hypotenuse (the side opposite the right angle)?

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Perimeter of a Square

What is the maximum perimeter of a square that can fit inside a circle of radius 5 cm?

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Grading Policies

In a certain course, the Professor has two different grading policies, from which he picks the best. The first policy is to put 40% and 60% weights, respectively, on the midterm and final exams. Under the second grading policy, these weights are 50% each. A student has scored 85% on the midterm, and needs to score at least x% on the final to make a B (a total of 82%). What is the value of x?

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