ACT Math Practice Test Pool 1

Question 1

A number is divided by four. The result is divided by three, for a final result of two. What was the original number?

Accepted Answer

24

Answer

To find the original number, we can work backward from the final result. The final result of two was obtained after dividing by three, so before that step, the number was 2 multiplied by 3, which is 6. This number 6 was obtained after dividing the original number by four, so the original number must have been 6 multiplied by 4, which is 24.

Question 2

Which of the following is true about the number 0.6666 ?

Accepted Answer

It is a rational number.

Answer

A rational number is defined as any number that can be expressed as a fraction p/q, where p and q are integers and q is not zero. The decimal 0.6666... is a repeating decimal, which is a characteristic of rational numbers. Specifically, 0.6666... is equivalent to the fraction 2/3, thus confirming it is a rational number.

Question 3

The price of a shirt is increased by 20%, and the price of a $40 pair of shoes is decreased by 40%. If the new price of the shirt now equals the new price of the shoes, what was the original price of the shirt?

Accepted Answer

$20

Answer

First, calculate the new price of the shoes: a 40% decrease from $40 is $40 * (1 - 0.40) = $24. Let the original price of the shirt be S. A 20% increase means its new price is S * (1 + 0.20) = 1.2S. Since the new price of the shirt equals the new price of the shoes, we set 1.2S = $24, and solving for S gives S = $24 / 1.2 = $20.

Question 4

Three consecutive integers are such that four times the smallest is three times the largest. What is the largest of these three integers?

Accepted Answer

8

Answer

Let the three consecutive integers be n, n+1, and n+2, where n is the smallest and n+2 is the largest. The problem states that four times the smallest is three times the largest, which translates to the equation 4n = 3(n+2). Solving this equation gives 4n = 3n + 6, so n = 6. Therefore, the smallest integer is 6, and the largest integer is n+2 = 6+2 = 8.

Question 5

Let f(x) = 4x − 3. If f(a) = 9 and f(b) = 5, then what is f(a + b) ?

Accepted Answer

17

Answer

First, use the given information to find the values of 'a' and 'b'. Since f(a) = 9, we have 4a - 3 = 9, which means 4a = 12, so a = 3. Similarly, since f(b) = 5, we have 4b - 3 = 5, which means 4b = 8, so b = 2. Now, calculate a + b = 3 + 2 = 5. Finally, evaluate f(a + b) by finding f(5), which is 4(5) - 3 = 20 - 3 = 17.

ACT Practice Test

ACT Practice Test

ACT Math Practice Test Pool 1