ACT Math Practice Test Pool 1 — Questions and Answers
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?
- 6
- 24 (Correct answer)
- 12
- 18
- 36
Correct answer: 24
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 ?
- It is a rational number.\t (Correct answer)
- It is an irrational number.
- It is correctly gridded as “.66”.
- It is equivalent to 67\/100.
- It was a little devil last night.
Correct answer: It is a rational number.\t
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?
- $16
- $20 (Correct answer)
- $24
- $28
- $32
Correct answer: $20
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?
- 6
- 8 (Correct answer)
- 10
- 12
- 14
Correct answer: 8
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) ?
- 5
- 7
- 14
- 16
- 17 (Correct answer)
Correct answer: 17
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.
Question 6: In a box containing only purple and green marshmallows, 6 marshmallows are purple. If the probability of choos- ing a purple marshmallow from the box is 1\/3 , how many green marshmallows are in the box?
- 2
- 6
- 9
- 12 (Correct answer)
- 18
Correct answer: 12
The probability of choosing a purple marshmallow is given as 1/3, and there are 6 purple marshmallows. Probability is calculated as (favorable outcomes) / (total outcomes). So, 1/3 = 6 / (Total marshmallows). Solving for the total marshmallows gives Total = 3 * 6 = 18. Since there are 18 marshmallows in total and 6 are purple, the number of green marshmallows is 18 - 6 = 12.
Question 7: In a particular card game, the minimum score a player can achieve in a single game is 20, and the maximum score possible in a single game is 52. If a player plays three games and scores a total of 141 points, what is the least number of points that the player could have scored in one of the games?
- 35
- 36
- 38
- 39
- 37 (Correct answer)
Correct answer: 37
To find the least number of points scored in one game, we must assume the scores in the other two games were as high as possible. The maximum score for a single game is 52 points. So, the other two games would have scores of 52 and 52, totaling 104 points. Subtracting this from the total score of 141 points (141 - 104) gives 37 points, which is the minimum possible score for the third game while staying within the allowed range.
Question 8: What is the sum of the four times the largest negative integer and the small- est positive integer?
- -3 (Correct answer)
- -2
- -1
- 0
- 1
Correct answer: -3
The largest negative integer is -1, as any negative integer closer to zero is larger. The smallest positive integer is 1, as any positive integer further from zero is larger. Four times the largest negative integer is 4 * (-1) = -4. Adding the smallest positive integer to this gives -4 + 1 = -3.
Question 9: When a number x is subtracted from 36 and the difference is divided by x, the result is 2. What is the value of x ?
- 2
- 4
- 6
- 12 (Correct answer)
- 18
Correct answer: 12
Translate the word problem into an algebraic equation. 'When a number x is subtracted from 36' means 36 - x. 'The difference is divided by x' means (36 - x) / x. 'The result is 2' means (36 - x) / x = 2. To solve for x, multiply both sides by x to get 36 - x = 2x. Then, add x to both sides to get 36 = 3x, which simplifies to x = 12.
Question 10: Which of the following is NOT a positive multiple of 9 + 3 ?
- 12
- 24
- 48
- 60
- 3 (Correct answer)
Correct answer: 3
First, calculate the value of 9 + 3, which is 12. A positive multiple of 12 is any positive integer that can be divided by 12 without a remainder. Checking the options, 12, 24, 48, and 60 are all positive multiples of 12 (12*1, 12*2, 12*4, 12*5 respectively). However, 3 is not a multiple of 12, as 12 does not divide evenly into 3.
ACT Math Practice Test Pool 1
A number is divided by four.
The result is divided by three, for a final result of two.
What was the original number?