A researcher is attempting to predict the number of lions in an African habitat based on previous data. He has formed a regression equation which is: Y = 25 + 0.5X – 2ZX, where X is the number of years since the first population sample, and Z is the death rate of the lions. If it has been 10 years, and the death rate is 1 lion per year, what is the predicted number of lions in the habitat?

## The Matrix

It takes 6 minutes and 12 minutes, respectively, to run two computer programs when they are run one at a time. However, their speeds are reduced by 50% and 40%, respectively, if running in parallel. If a PC starts running the two programs together, how long will it take for them to finish?

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## Car Journey

Mark’s car began a journey from a point at 7 AM, traveling at 30 mph. At 8 AM Jason’s car started traveling from the same point at 40 mph in the same direction as Jason. At what time will Jason pass Mark?

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## Mind Games

X is a multiple of A. A is always even, and is always divisible by B. X is also never divisible by C. Which of the following statements must be true?

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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?