ACT Math : Arithmetic
Study concepts, example questions & explanations for ACT Math
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Example Questions
Example Question #31 : Percentage
A high school senior takes a survey of the entire senior class for a project. She's interested in seeing the distribution of what her peers decide to pursue in college. She came up with the following data:
The rest of the 
In this question, information about 5 groups of students is included but isn't expressed in the table nor is it expressed in terms of a percentage.
The sample the student took, despite how many students were interviewed, will have all the percents add up to 100% - as in the case with any study with percent breakdowns. The number of prospective Linguistic students is given (37), and it's know they're a part of the 100% the sample provides. To determine their percent, all the other intended majors percents must be subtracted from the total (100%).
Once this information has been uncovered, this problem becomes a matter of being able to calculate what 37 is 6% of. This can be uncovered through the use of 
Given that fractions of a person cannot be surveyed, the final answer must be rounded to the nearest whole number.
Example Question #3 : How To Find Percentage Equivalent To A Decimal
Which of the following is equivalent to 
To convert a decimal into a percent is fairly straightforward. Begin with your original decimal value:
Then, move your decimal point to the right by two:
Strip off any leading zeroes, add a percent sign, and you are good to go!
Example Question #3 : How To Find Percentage Equivalent To A Decimal
At high elevations, the ability of red blood cells to hold oxygen is decreased. At a particular elevation, the red blood cells' ability to hold oxygen is multiplied by 
To find a percentage from a decimal, multiply the decimal by 
Example Question #2 : How To Find Percentage Equivalent To A Decimal
A chemist mixes a solution out of a bottle which states 
To find a percentage from a decimal, mutiply the decimal by 
Example Question #1 : Percent Of Change
A manager of a pizzeria has five people on his staff. Three are full-time staff, each of whom received a starting salary of $25,000 annually for 40 hours of work per week. Each year they have worked at the pizzeria, their pay increases by 7%. Sally has worked at the pizzeria for one year, Nancy for two years and John for three years. The other two employees are part-time and are paid $8.25 per hour. Irene works 1,000 hours per year and Andrew works 700 hours per year. What is the pizzeria’s cost per year for staff salaries?
$86,025
$94,397.50
$84,275
$96,872.50
$92,525.50
$94,397.50
It is important to remember that the employees who receive an annual increase (Sally, Nancy and John), receive the 7% increase based on the salary from the year before.
If you answered $89,025, you did not account for the 7% increase in salary for Nancy and John.
If you answered $89,525, you did not increase John's salary by 7% for the third year ($26,750 * 7% = $1,872.50 --- $1,872.50 + $26,750 = $28,622.50).
If you answered $91,275, you did not account for the 7% to be applied to John's second year salary; rather, you added the dollar increase ($1750) that he received between his first and second year and added it to his second year salary.
If you answered $93,872.50, you accounted for both part-time employees working 1,000 hours. Therefore, the correct answer is $94,397.50.
Example Question #1 : Percent Of Change
Ben and Sam have a furniture design business. The first year they earn $10,000 in profits. The second year they earn $12,000 in profits. What is the percentage increase in profit between year one and two?
12%
10%
20%
25%
2%
20%
Percentage Increase = (Year Two Profit – Year One Profit) / Year One Profit
= ($12,000 - $10,000) / $10,000 = $2000 / $10,000 = .2 = 20%
Example Question #41 : Percentage
Truck A has a length of 8'3" (8 ft. and 3 inches). Truck B has a length of 14'5".
What is the percentage increase in length going from Truck A to Truck B?
66.53
79.11
35.42
74.74
74.74
Find a common unit—in this case it is inches. The increase is from 99” to 173”. To find the percentage increase we find the difference and then divide by the length of Truck A.
or 74.74%
Example Question #42 : Percentage
Danielle has two jobs. Her retail job pays her $8.50 per hour and she works 20 hours per week in that job. Her office job pays her $12 per hour and she works 15 hours per week in the office. If she starts working an extra 10 hours a week at her office job, what is her percentage increase in total weekly pay? Round to one decimal point.
33.4%
34.3%
25.7%
22.9%
40.0%
34.3%
Pay = Hours worked x Rate per hour
Retail job = 20 x $8.50 = $170.00
Office job = 15 x $12.00 = $180.00
Current weekly pay = $170.00 + $180.00 = $350.00
Additional Office job hours = 10 x $12.00 = $120.00
Percentage Increase = $120 / $350 = .343 (rounded) --> 34.3%
Example Question #1 : Percent Of Change
A university has 
To find the percentage increase, use the following formula:
Increased # of students this year / # of students last year
If there were 
Therefore:
The number of students increased by 
Example Question #5 : Percent Of Change
Thurman is given 
It will decrease over time.
It will increase exponentially over time.
It will first decrease, then increase.
It will increase linearly over time.
It will remain the same over time.
It will decrease over time.
To find out which option is correct, simply follow one complete cycle (that is to say, one day's worth of actions).
We will use 
So, after each cycle, the total amount of money decreases by 
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