ACT Math : Arithmetic

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1231 : Act Math

What is  of  of ?

Possible Answers:

Correct answer:

Explanation:

For percentage problems, the easiest way to start is by remembering that the word "of" is best translated as a multiplication, while the word "is" is best translated by an equals sign. Thus, for the information provided, we can write the equation:

Solving for , you get:

Alternatively you could first calculate  of , which is , and then calculate  of that, and you would arrive at the same answer.

Example Question #171 : Arithmetic

A computer originally sold for  dollars. Its price was reduced by  and then again by . What was the final sale price for the computer? Round to the nearest cent.

Possible Answers:

Correct answer:

Explanation:

The most common way to do a problem like this is to begin by applying the first discount, calculating the amount to be removed from the original price. This is done by multiplying the original price by . This gives you . This is then subtracted from  to give you . Once again, this new number is multiplied, now by . This gives you . When subtracted from , this gives you a final price of , or the rounded value of .

A simpler way to do this is to realize that the first price reduction makes the new price to be  of the original. The second will then make the price to be  of the intermediary price. Thus, you could easily compute:

Example Question #1241 : Act Math

 pound man has a body composition made up of  pounds of fat,  pounds of muscle, and the rest of other organs, fluid, etc. What is the percentage of his muscle composition (in comparison with his toal weight) if he increases his weight in body fat by ? Round to the nearest hundredth of a percent.

Possible Answers:

Correct answer:

Explanation:

As of right now, the man has  pounds of body fat. If this increases by , we he will gain  or  more pounds of body fat. This means that he will have a total of  pounds of body fat. Also, it means that his total weight will be  pounds. Therefore, his muscle, as a percent of his total weight will be:

 or 

Example Question #81 : Percentage

What is  of ?

If necessary, round to the nearest percentage.

Possible Answers:

Correct answer:

Explanation:

To calculate the percentage of a percent, convert both percentages to decimals and multiply:

Example Question #81 : Percentage

What percentage of  is ? Round your answer to the nearest whole percentage.

Possible Answers:

Correct answer:

Explanation:

To find what percentage  is of  simply divide  by . Thus we see that 

Example Question #175 : Arithmetic

Question 20

If Abraham’s collection in July is 40% of his collection at the end of December, how many stamps must have he obtained in December?

Possible Answers:

Correct answer:

Explanation:

Abraham’s collection in July is 97 stamps. If that is 40% of his collection at the end of the year, his album must have  stamps.

Thus, he would have to get stamps to have that happen.

Example Question #1 : How To Find The Amount Of Sales Tax

Beth purchased $21.25 worth of groceries. The sales tax rate is 7.5%. What was her total bill?

Possible Answers:

$21.93

$23.41

$22.84

$22.11

$23.79

Correct answer:

$22.84

Explanation:

The tax is calculated by 0.075 * 21.25 = 1.59375 or $1.59. So the total bill is the cost of items purchased plus tax, which is $21.25 + $1.59 = $22.84.

Example Question #1 : Sales Tax

The last week of August is tax-free week.  If the standard tax rate is 8.25%, how much money would a shopper save buying a $50 dress and a $30 pair of shoes during tax free week?

Possible Answers:

$2.47

$8.00

$7.25

$6.60

$4.13

Correct answer:

$6.60

Explanation:

Tax = Total Cost * 0.0825 = (50 + 30) * 0.0825 = (80) x 0.0825 = 6.6 = $6.60

Example Question #1 : How To Find The Amount Of Sales Tax

If a stick of deodorant costs $4.29 with a sales tax of 8.75%. What will the total cost of the item be?

(round to the nearest cent)

Possible Answers:

$6.47

$4.66

$4.37

$4.76

$4.67

Correct answer:

$4.67

Explanation:

To solve for the tax charged multiply 0.0875 by the sales price of $4.29.

This is $0.375375. Add this to the original amount of $4.29.

The answer is 4.665375. Rounded to the nearest cent is $4.67

Example Question #1 : How To Find The Amount Of Sales Tax

On a grocery shopping trip you spent $15 on meat, $5 on cheese, and $25 on produce.  If the total bill was $48.15, what is the rate of sales tax on the food?

Possible Answers:

0.7%

0.75%

6.5%

7%

7.5%

Correct answer:

7%

Explanation:

Tax = Total Bill - Cost of Food = 48.15 – (15 + 5 + 25) = $3.15

Percentage of Tax = Tax / Cost of Food = 3.15/ (15 + 5 + 25) = 3.15 / 45 = 0.07 = 7%

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