Math Pool Flashcards

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

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.

Which of the following is true about the number 0.6666 ?

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.

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?

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.

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

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.

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

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.

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?

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.

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?

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.

What is the sum of the four times the largest negative integer and the small- est positive integer?

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.

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 ?

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.

Which of the following is NOT a positive multiple of 9 + 3 ?

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.