Percentage Practice Questions

Question 1 of 5 Hard

Two years ago, Arthur gave each of his five children 20 percent of his fortune to invest in any way they saw fit. In the first year, three of the children, Alice, Bob, and Carol, each earned a profit of 50 percent on their investments, while two of the children, Dave and Errol, lost 40 percent on their investments. In the second year, Alice and Bob each earned a 10 percent profit, Carol lost 60 percent, Dave earned 25 percent in profit, and Errol lost all the money he had remaining. What percentage of Arthur's fortune currently remains?

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Correct answer: A

Percentage problems involving unspecified amounts can usually be solved more easily by using the number $100$. If Arthur's fortune was originally $\$100$, each of his children received $\$20$.

Let's see what happened to each $\$20$ investment in the first year: 
Alice: $\$20 + \$10$ profit $= \$30$ 
Bob: $\$20 + \$10$ profit $= \$30$ 
Carol: $\$20 + \$10$ profit $= \$30$ 
Dave: $\$20 - \$8$ loss $= \$12$ 
Errol: $\$20 - \$8$ loss $= \$12$

We continue on with our new amounts in the second year: 
Alice: $\$30 + \$3$ profit $= \$33$ 
Bob: $\$30 + \$3$ profit $= \$33$ 
Carol: $\$30 - \$18$ loss $= \$12$ 
Dave: $\$12 + \$3$ profit $= \$15$ 
Errol: $\$12 - \$12 = 0$

At the end of two years, $\$33 + \$33 + \$12 + \$15 = \$93$ of the original $\$100$ remains.

The correct answer is A.

Question 2 of 5 Easy

A car dealership has 40 cars on the lot, 30% of which are silver. If the dealership receives a new shipment of 80 cars, 40% of which are not silver, what percent of the total number of cars are silver?

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Correct answer: E

This is a weighted average problem; we cannot simply average the percentage of silver cars for the two batches because each batch has a different number of cars.

The car dealership currently has $40$ cars, $30\%$ of which are silver. It receives $80$ new cars, $60\%$ of which are silver (the $40\%$ figure given in the problem refers to cars which are not silver). Note that the first batch represents $\frac{1}{3}$ of the total cars and the second batch represents $\frac{2}{3}$ of the total cars. Put differently, in the new total group there is $1$ first-batch car for every $2$ second-batch cars.

We can calculate the weighted average, weighting each percent according to the ratio of the number of cars represented by that percent:

$$\text{Weighted average} = \frac{1(30\%) + 2(60\%)}{3} = 50\%$$

Alternatively, you can calculate the actual number of silver cars and divide by the total number of cars. $40(0.3) + 80(0.6) = 12 + 48 = 60$. $\frac{60}{120} = 50\%$.

The correct answer is E.

Question 3 of 5 Medium

Paul's income is 40% less than Rex's income, Quentin's income is 20% less than Paul's income, and Sam's income is 40% less than Paul's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?

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Correct answer: A

Notice that Paul’s income is expressed as a percentage of Rex’s and that the other
two incomes are expressed as a percent of Paul’s. Lets assign a value of $100 to
Rex’s income. Paul’s income is 40% less than Rex's income, so (0.6)($100) =
$60. Quentin’s income is 20% less than Paul's income, so (0.8)($60) = $48. Sam’s
income is 40% less than Paul's income, so (0.6)($60) = $36. If Rex gives 60% of
his income, or $60, to Sam, and 40% of his income, or $40, to Quentin, then: Sam
would have $36 + $60 = $96 and Quentin would have $48 + $40 = $88. Quentin’s
income would now be $88/$96 = 11/12 that of Sam's.

Question 4 of 5 Medium

A school’s annual budget for the purchase of student computers increased by 60% this year over last year. If the price of student computers increased by 20% this year, then the number of computers it can purchase this year is what percent greater than the number of computers it purchased last year?

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Question 5 of 5 Medium

Boomtown urban planners expect the city’s population to increase by 10% per year over the next two years. If that projection were to come true, the population two years from now would be exactly double the population of one year ago. Which of the following is closest to the percent population increase in Boomtown over the last year?

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