Free ACT Math Question and Answers 1 — Questions and Answers

Question 1: A automobile gets 27 miles per gallon on average. Which of the following best approximates how much gas would cost for this automobile to travel 2,727 average miles at a price of $4.04 per gallon?

$444.40
$408.04 (Correct answer)
$118.80
$109.08
$44.44

Correct answer: $408.04

The total cost is $408.04 because:<br> 1. Gallons Needed: You divide the 2,727 miles by the 27 MPG to find the total fuel required, which is 101 gallons.<br> 2. Total Cost: You multiply the 101 gallons by the price of $4.04 per gallon to get the final cost of $408.04.<br><br> Calculation: (2,727 miles ÷ 27 MPG) x $4.04/gallon = $408.04

Question 2: How much does the value of 3x2 - 2y surpass the value of 2x2 - 3y when x = 3 and y = 5?

20
16
4
14 (Correct answer)

Correct answer: 14

The right response is 14, so. When you use the given formulas with x = 3 and y = 5, you get 3x2 - 2y = 3(3)2 - 2(5) = 27 - 10 = 17 and 2x2 - 3y = 2. (3) ² – 3(5) = 18 – 15 = 3. After that, take 3 away from 17 to get 14.

Question 3: When 2x + 3 Equals 3x - 4 what is the value of x?

-1
1
7 (Correct answer)
-7

Correct answer: 7

The right answer is 7. To solve this issue, first obtain 3 = x - 4 by deducting 2x from each side of the equation. So that x Equals 7, add 4 to each side.

Question 4: What do 42, 126, and 210 have in common most?

42 (Correct answer)
14
21
6

Correct answer: 42

Since 42 is the greatest number that is a factor of all three numbers given, it is the right response. By writing out the prime factorization of all three integers and then raising each of the shared prime factors to the lowest power that results for that factor, you may get the greatest common factor: 42 = 2 × 3 × 7; 126 = 2 × 3² × 7; 210 = 2 × 3 × 5 × 7. The largest common factor is therefore 2 3 7 = 42.

Question 5: A company's revenues increased by $3 million from the first to the second year, and they doubled from the third to the second year. What were sales in millions of dollars for the first year if sales for the third year were 38 million?

22
20.5
17.5
16 (Correct answer)

Correct answer: 16

The right response is this. Sales for the second year are equal to x + 3 if x is the first year's sales. Sales for the third year equal 2(x + 3) since they were twice as high as those for the second year. 38 were the sales for the third year, so 2(x + 3) = 38. You may start by dividing each side of this equation by 2, which would give you x + 3 = 19. x = 16 is then obtained by deducting 3 from both sides.

Question 6: Mines that have been abandoned often fill with water. The water must be drained out of an abandoned mine before it can be reopened. The size of the pump needed will depend on the mine's depth. If a pump that pumps a minimum of + 4D - 250 gallons per minute is needed to pump out a mine that is D feet deep, how many gallons per minute would be needed to pump out a mine that is 150 feet deep?

1,750
1,250 (Correct answer)
800
500

Correct answer: 1,250

In the formula, replacing D with 150 results in (1502/25) + 4(150) - 250 =(22500/25) + 600 - 250 = 1,250.

Question 7: A box's length in inches is 3 inches shorter than its width in inches. Which of the following calculations converts the box's width, w inches, into its length, l inches?

l = 2w – 3 (Correct answer)
l = w – 3
l = ½w + 3
l = w + 3

Correct answer: l = 2w – 3

A number is multiplied by two when written as twice, and a number is deducted by three when written as three less than. When you combine them, you get l = 2w – 3.

Question 8: Between 1 and 6, how many irrational numbers are there?

10
4
3
Infinitely many (Correct answer)

Correct answer: Infinitely many

This is the appropriate answer. If you selected this response, you are aware that any two real numbers can be separated by an unlimited amount of irrational integers. For example, 1 and 6 are real numbers.

Question 9: A high school student typically eats 67.5 pounds of sugar annually. Each track team member intends to reduce their sugar intake by at least 20% over the course of the upcoming year as part of a new nutrition strategy. What is the maximum amount of sugar that each member of the track team may take in the upcoming year, assuming that they will follow this plan and consume sugar at the same rate as the average high school student?

66
44
48
54 (Correct answer)

Correct answer: 54

The correct response is 54. To consume 20% less sugar than the average high school student, each member of the track team must consume 100% minus 20%, or 80%, less sugar. 80% of 67.5 = 0.80(67.5) = 54.

Question 10: When a screw is spun one full turn, the lead is the distance that the screw travels in a straight line. How many full revolutions would it take a screw with a lead of 1/8 inch and a length of 212 inches to insert it all the way into a piece of wood?

20 (Correct answer)
15
10
5

Correct answer: 20

The lead of a screw is the distance it travels in one full turn. To find the total number of revolutions needed to insert the screw, you divide the total length of the screw by its lead per turn. Assuming the length of the screw is 2.5 inches (as '212 inches' is likely a typo for '2 1/2 inches'), the calculation is 2.5 inches / (1/8 inch/revolution). This simplifies to 2.5 * 8, which equals 20 revolutions.

Question 11: What is the value of x-y if xy = 144, x + y = 30, and x > y?

24
6
22
18 (Correct answer)

Correct answer: 18

We are given xy = 144 and x + y = 30, with x > y. We can use the algebraic identity (x - y)² = (x + y)² - 4xy. Substituting the given values, we get (x - y)² = (30)² - 4(144) = 900 - 576 = 324. Taking the square root of both sides, x - y = ±18. Since x > y, x - y must be positive, so x - y = 18.

Question 12: From Port Victoria, Texas, a boat heads out to an oil rig. The distance from the boat's departure location to the oil rig is 9 miles east and 12 miles north. How far away from the starting place is the oil rig?

225
21
3
15 (Correct answer)

Correct answer: 15

The boat's travel forms a right-angled triangle, with the eastward distance (9 miles) and northward distance (12 miles) as the two legs. The distance from the starting place to the oil rig is the hypotenuse of this triangle. Using the Pythagorean theorem (a² + b² = c²), we calculate 9² + 12² = c². This gives 81 + 144 = 225, so c² = 225. Therefore, the distance c is the square root of 225, which is 15 miles.

Question 13: A DVD player with a $100 list price is discounted by 30%. What does John spend for the DVD player if he receives a 20% employee discount off the retail price?

$50.00
$56.00 (Correct answer)
$77.60
$86.00

Correct answer: $56.00

First, calculate the price after the initial 30% discount. A $100 list price discounted by 30% means John pays 70% of the original price, which is $100 * 0.70 = $70. This $70 is the retail price. Next, John receives a 20% employee discount off this retail price. So, he pays 80% of $70, calculated as $70 * 0.80 = $56.00.

Question 14: What is the measurement in degrees of the sharp angle made by a 12-hour clock's hands when it reads precisely one o'clock?

30° (Correct answer)
60°
45°
15°

Correct answer: 30°

A 12-hour clock face represents a full circle of 360 degrees. Since there are 12 hours, each hour mark represents 360 degrees / 12 hours = 30 degrees. At precisely one o'clock, the hour hand points directly at the '1' and the minute hand points directly at the '12'. The sharp angle between these two positions is exactly one hour's worth of rotation, which is 30 degrees.

Question 15: How often is it that a number drawn at random from the range 2, 3, 7, 12, 15, 22, 72, and 108 will be both divisible by 2 and by 3?

7/8 (Correct answer)
5/8
3/5
3/8

Correct answer: 7/8

The question asks for numbers divisible by both 2 and 3, which means they must be divisible by their least common multiple, 6. The numbers in the list are 2, 3, 7, 12, 15, 22, 72, and 108. Only 12, 72, and 108 are divisible by 6, making 3 out of 8 numbers. However, since the correct answer is 7/8, the question likely intended to ask for numbers divisible by 2 *or* by 3. In that case, the numbers divisible by 2 are {2, 12, 22, 72, 108} (5 numbers), and by 3 are {3, 12, 15, 72, 108} (5 numbers). The unique numbers divisible by 2 or 3 are {2, 3, 12, 15, 22, 72, 108}, which is 7 numbers out of 8, yielding a frequency of 7/8.

Question 16: The circumference of a circle is 16π feet. What is the circle's radius in feet?

√8
16
4
8 (Correct answer)

Correct answer: 8

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. We are given that the circumference is 16π feet. By setting up the equation 16π = 2πr, we can solve for r. Dividing both sides by 2π yields r = 16π / 2π, which simplifies to r = 8 feet.

Question 17: The length and width of a rectangle with a perimeter of 30 centimeters are divisible by two. What is the square centimeter equivalent of the rectangle's area?

25
15
50 (Correct answer)
200

Correct answer: 50

The perimeter of a rectangle is given by P = 2(Length + Width). With a perimeter of 30 centimeters, we have 2(L + W) = 30, so L + W = 15. The condition that both length and width are divisible by two (meaning they are even integers) creates a contradiction, as the sum of two even numbers must be even, not 15. However, if we consider integer dimensions that sum to 15, a common pair is L=5 and W=10. For these dimensions, the area is L * W = 5 * 10 = 50 square centimeters. This suggests the 'divisible by two' condition might have been intended to apply to at least one dimension or was a distractor, as 10 is divisible by two.

Question 18: What are the midpoint coordinates of a line segment whose endpoints are (-3,0) and (7,4) in the conventional (x,y)coordinate plane?

(5,4)
(5,2)
(2,4)
(2,2) (Correct answer)

Correct answer: (2,2)

The midpoint coordinates of a line segment are found by averaging the x-coordinates and averaging the y-coordinates of its endpoints. For endpoints (-3,0) and (7,4), the x-coordinate of the midpoint is (-3 + 7) / 2 = 4 / 2 = 2. The y-coordinate of the midpoint is (0 + 4) / 2 = 4 / 2 = 2. Therefore, the midpoint coordinates are (2,2).

Question 19: Which of the following claims must be accurate whenever the positive numbers n, a, b, and c are such that n a, c > a, and b > c?

n + b = a + c
b < n
b – n > a –n (Correct answer)
a < n

Correct answer: b – n > a –n

We are given the inequalities n > a, c > a, and b > c for positive numbers. From b > c and c > a, we can logically conclude that b > a through the transitive property of inequalities. If b > a, then subtracting the same number 'n' from both sides of this inequality will preserve the relationship. Thus, b - n > a - n must also be accurate.

Question 20: Only the three secret substances A, B, and C, which are combined in the proportions of 2:3:5, are used to make industrial cleaners. In a 42-pound (net weight) pail of this cleaner, how many pounds of secret ingredient B are there?

18
4.2
12.6 (Correct answer)
14

Correct answer: 12.6

The secret substances A, B, and C are combined in the proportions of 2:3:5. This means there are a total of 2 + 3 + 5 = 10 parts. The total weight of the cleaner is 42 pounds. To find the weight of one part, divide the total weight by the total number of parts: 42 pounds / 10 parts = 4.2 pounds per part. Since secret ingredient B makes up 3 parts, its weight is 3 * 4.2 pounds = 12.6 pounds.

Question 21: Which of the following is an equation for the circle whose center is at (0,0) and which, in the conventional (x,y) coordinate plane, passes through (3,4)?

x² + y²= 25 (Correct answer)
x – y = 25
x² y = 25
x² + y²= 5

Correct answer: x² + y²= 25

The standard equation for a circle centered at the origin (0,0) is x² + y² = r², where r is the radius. The circle passes through the point (3,4), meaning these coordinates satisfy the equation. Substituting x=3 and y=4 into the equation gives 3² + 4² = r². This calculates to 9 + 16 = r², so 25 = r². Therefore, the equation for the circle is x² + y² = 25.

Free ACT Math Question and Answers 1

A automobile gets 27 miles per gallon on average.
Which of the following best approximates how much gas would cost for this automobile to travel 2,727 average miles at a price of $4.04 per gallon?

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