ACT Math : Arithmetic
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Example Questions
Example Question #1 : How To Find Proportion
In a school relay race, every 5-man team must sprint 110 yards total. However, Jim’s team is short a person. Thus, Jim must run two sections for his team. How far does Jim have to run?
45.4 yards
110 yards
44 yards
27.5 yards
22 yards
44 yards
We first find out how much each person must run. Thus we take 110/5 to get 22 yards. However, Jim must run twice the amount of a normal competitor, so we multiply by 2 to get 44 yards.
Example Question #1481 : Act Math
A building that is 30 feet tall casts a shadow that is 50 feet long. If another building casts a shadow that is 100 feet long, how tall is the building?
167 feet
6 feet
600 feet
60 feet
1670 feet
60 feet
This problem can be set up as a proportion: 30 feet/x feet = 50 feet/100 feet. To solve, we simply cross multiply: (30 feet * 100 feet) = (50 feet * x feet). Thus, 3000 feet = 50x feet. To solve for x, divide each side by 50. Therefore, x = 60 feet. If you got 167 feet, you may have set up the proportion incorrectly by mixing up the height of the building with the length of the shadow. If you got 6 feet or 600 feet, you may have made a computational error. If you got 1670 feet, you may have set the proportion up incorrectly and made a computational error.
Example Question #41 : Proportion / Ratio / Rate
If a bicyclist can bike 24 miles per hour, how far (in miles) can he travel in 2 minutes, assuming he bikes at a constant speed (answer rounded to the nearest tenth)?
0.5
1.0
0.75
2.0
0.8
0.8
0.8 mile. Using some conversions: ( (24mi/1hr)*(1hr/60min)*2min = 0.8 mile
Example Question #1481 : Act Math
If 10,000 lbs of cement makes 85,000 lbs of concrete, how many pounds of concrete can be made with 3,000 pounds of cement?
12,230
363
30,000
25,500
10,000
25,500
25,500 lbs of concrete. Setting up a ratio with x representing the number of pounds concrete the 3,000 of cement produces, we obtain the relation: (10,000/85,000) = (3,000/x), x = 25,500 pounds of concrete.
Example Question #3 : How To Find Proportion
There are 150 students in a lecture hall class in college. 12% of the students received an A. 20 students received a B. Twice the number of students who earned an A received a C. The remainder of the students received a D. Which grade did the students receive more than any other?
Cannot be determined.
The students who got C's
The students who got D's.
The students who got B's
The students who got A's.
The students who got D's.
First find 12% of 150, so 0.12 * 150 = 18 students received an A.
20 students received a B, and 36 students received a C (double the A's).
To find the number of D-grades, all we have to do is subtract these from the total (since there were no grades of F),
Thus: 150 – 18 – 20 – 36 = 76 students who received a D in the course, which is the most common grade.
Example Question #7 : How To Find Proportion
A brownie recipes calls for a 1:5 ratio of water to brownie mix. If you need 90 cups of brownie mix, how much water do you need?
25 cups
18 cups
36 cups
450 cups
6 cups
18 cups
First set up a proportion, 1/5 = x/90, then solve for x: 5x = 90 → x = 18 cups.
Example Question #1482 : Act Math
If a 12 oz can of lemonade has 75 calories; how many calories are in an 8 oz can of lemonade?
55
65
60
70
50
50
A proportion is a statement of equality between two fractions or two ratios. Set up a proportion between the size of the drink and the calories. To solve a proportion cross multiply and solve the resulting equation.
75/12 = x/8 → 150/24 = 3x/24 → 50/8 = x/8 → x = 50
Example Question #411 : Arithmetic
If there are 75 calories in a 6 oz glass of juice, how many calories will there be in an 8 oz glass?
We set up a proportion:
We cross multiply to get 
Example Question #51 : Proportion / Ratio / Rate
The largest of three numbers is six less than four times the smallest number. The middle number is three more than twice the smallest number. The sum of twice the largest number, three more than three times the middle number, and four times the smallest number is 90. What is the value of the largest number?
10
22
12
14
18
14
Because all the numbers are expressed in terms of the smallest number, let that number be represented by x. Therefore, the largest number can be expressed as 4x-6, and the middle number can be expressed as 2x+3. Plug those numbers into the addition equation and solve for x. Then plug the value for x into the expression representing the largest number.
2(4x-6) + (3+3(2x+3)) + 4(x) = 90 --> 18x = 90 --> x = 5
4(6)-6 = 14
Example Question #416 : Arithmetic
A group of 15 friends is having lunch together. Each person eats at least 2/3 of a pizza. What is the smallest number of whole pizzas needed for lunch?
15
10
5
7
10
The minimum number of whole pizzas needed is 15(2/3) = 10.
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