ACT Math : Arithmetic

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #251 : Arithmetic

A set of cards were purchased for . If the store earned  profit on the sale, what was the original price of the cards? Round to the nearest hundredth.

Possible Answers:

Correct answer:

Explanation:

This question is really asking a hidden percentage change question. It really means, "The price changed from  to , signalling a  change." Thus, you can set up an equation like this:

Solving for , you get:

Example Question #11 : How To Find Amount Of Profit

The profit on a particular product per unit is measured as a percentage of the cost to produce that unit. If  units are produced at a total cost of , and sell for a total of , what was the profit per unit, as a percentage?

Possible Answers:

Correct answer:

Explanation:

Remember, percentage profit is a ratio between two numbers. The ratio stays the same whether the numbers reflect hundreds of units sold or just one unit (unless otherwise told). So to find our answer, we only need to calculate the overall profit percentage.

Example Question #11 : How To Find Amount Of Profit

In business, profit is defined as revenue minus expenses. A profit is often expressed as a percentage of total revenue.

A company posts a  profit for the first quarter of the new year, pleasing investors. If the total profits for the quarter were  what were the expenses for the company in that quarter? Round to the nearest dollar.

Possible Answers:

Correct answer:

Explanation:

If a profit of  represents , then we can calculate revenue as:

Now, subtract the profit from the total revenue to calculate expenses:

Thus, the quarterly expenses were .

Example Question #12 : How To Find Amount Of Profit

Manufacturing a particular product produces a profit of  for each unit produced. If the cost to produce a unit is , what is the profit percentage on each unit? Do not round until the final answer.

Possible Answers:

Correct answer:

Explanation:

Calculating a percentage profit is the same as calculating a percent change. To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative. 

Example Question #161 : Percentage

A particular product is sold for  per unit. If the cost to produce a unit is , what is the profit percentage on each unit? Do not round until your the answer.

Possible Answers:

Correct answer:

Explanation:

Calculating a percentage profit is the same as calculating a percent change. To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative. 

Example Question #161 : Percentage

A cassette tape sells for , and the producer receives a cut of  of each sale. If the producer spends  of the sale price in manufacturing and producing expenses, how much money is made on the sale of each tape?

Possible Answers:

Correct answer:

Explanation:

Calculating a percentage profit is the same as calculating a percent change. To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative. 

Example Question #11 : How To Find Amount Of Profit

A product sells for  dollars, and costs  dollars to produce. What is the profit on each sale, as a percentage?

Possible Answers:

There is not enough information to answer the question.

Correct answer:

Explanation:

Calculating a percentage profit is the same as calculating a percent change. To find percent change, subtract the "old" amount from the "new" amount, then divide the result by the "old" amount. The result is a percent increase if positive and a percent decrease if negative. 

Example Question #1 : Decimals With Fractions

When 5/11 is written as a decimal, what is the 100th digit to the right of the decimal point?

Possible Answers:

4

5

0

1

2

Correct answer:

5

Explanation:

When 5 is divided by 11, the decimal is 0.45 repeating, with a 5 in the hundreths place. The key here is to recognize that 100 is an even number, and the 5 in 0.45 is two places to the right of the decimal point (2 also being an even number).

Example Question #251 : Arithmetic

Find  the sum of the following:

 

Possible Answers:

Correct answer:

Explanation:

To get the decimal from a fraction, divide the numerator by the denominator

Example Question #252 : Arithmetic

Find the sum to the nearest hundredth:

Possible Answers:

Correct answer:

Explanation:

1. Convert the fractions to decimals by division:

2. Add the corresponding whole numbers to the decimals:

3. Add the two decimals:

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