ACT Math Mastery Quiz: Challenging Problems to Enhance Your Skills

1) A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles?

275.19

305.93

357.48

If you divide 2,727 miles by 27 miles per gallon you will get the number of gallons: 101. Then, multiply the number of gallons by the cost per gallon: 101(4.04) = 408.04. This gives the cost of gas for this car to travel 2,727 typical miles.

Explanation

If you divide 2,727 miles by 27 miles per gallon you will get the number of gallons: 101. Then, multiply the number of gallons by the cost per gallon: 101(4.04) = 408.04. This gives the cost of gas for this car to travel 2,727 typical miles.

2) When x = 3 and y = 5, by how much does the value of 3x2 − 2y exceed the value of 2x2 − 3y?

11

9

7

When substituting x = 3 and y = 5 into the expressions, 3x2 − 2y = 17 and 2x2 − 3y = 3. Subtracting both values (17 - 3) gives us the correct answer of 14.

Explanation

When substituting x = 3 and y = 5 into the expressions, 3x2 − 2y = 17 and 2x2 − 3y = 3. Subtracting both values (17 - 3) gives us the correct answer of 14.

3) What is the value of x when 2x + 3 = 3x - 4?

12

-1

2

You can solve this problem by first subtracting 2x from each side of the equation to get 3 = x - 4. Then add 4 to each side, so x = 7.

Explanation

You can solve this problem by first subtracting 2x from each side of the equation to get 3 = x - 4. Then add 4 to each side, so x = 7.

4) What is the greatest common factor of 42, 126, and 210?

18

105

56

The greatest common factor is the largest number that is a factor of all three numbers given. By finding the prime factorization of each number and identifying the common prime factors, the greatest common factor is determined to be 42.

Explanation

The greatest common factor is the largest number that is a factor of all three numbers given. By finding the prime factorization of each number and identifying the common prime factors, the greatest common factor is determined to be 42.

5) Sales for a business were 3 million dollars more the second year than the first, and sales for the third year were double the sales for the second year. If sales for the third year were 38 million dollars, what were sales, in millions of dollars, for the first year?

12

25

20

If x = sales for the first year, then x + 3 = sales for the second year. Since sales for the third year were double the sales for the second year, sales for the third year = 2(x + 3). Sales for the third year were 38, so 2(x + 3) = 38. To solve this equation, you could first divide each side by 2 to get x + 3 = 19. Then, by subtracting 3 from both sides, x = 16.

Explanation

If x = sales for the first year, then x + 3 = sales for the second year. Since sales for the third year were double the sales for the second year, sales for the third year = 2(x + 3). Sales for the third year were 38, so 2(x + 3) = 38. To solve this equation, you could first divide each side by 2 to get x + 3 = 19. Then, by subtracting 3 from both sides, x = 16.