College Math Quiz

1. Find the value of 2[3(x^2 - 5) + 5y] when x = 9 and y = 3.

729

486

429

629

To find the value of 2[3(x^2 - 5) + 5y], we substitute x = 9 and y = 3 into the expression. First, we evaluate the expression inside the brackets: 3(9^2 - 5) + 5(3). Simplifying further, we have 3(81 - 5) + 15. This becomes 3(76) + 15. Multiplying 3 and 76 gives us 228 + 15. Finally, adding 228 and 15 results in 243. However, the question asks for the value of 2 times this expression. Multiplying 243 by 2 gives us 486, which is the correct answer.

Explanation

To find the value of 2[3(x^2 - 5) + 5y], we substitute x = 9 and y = 3 into the expression. First, we evaluate the expression inside the brackets: 3(9^2 - 5) + 5(3). Simplifying further, we have 3(81 - 5) + 15. This becomes 3(76) + 15. Multiplying 3 and 76 gives us 228 + 15. Finally, adding 228 and 15 results in 243. However, the question asks for the value of 2 times this expression. Multiplying 243 by 2 gives us 486, which is the correct answer.

2. One day, Mr. Paul left the office at 8:35 PM and drove to his home. If he reached there at 10:02 PM, how long did he travel?

1 hour and 33 minutes.

1 hour and 17 minutes

1 hour and 27 minutes.

2 hours and 33 minutes

Mr. Paul left the office at 8:35 PM and reached home at 10:02 PM. To find out how long he traveled, we need to calculate the time difference between these two points. Subtracting 8:35 PM from 10:02 PM gives us 1 hour and 27 minutes. Therefore, Mr. Paul traveled for 1 hour and 27 minutes.

Explanation

Mr. Paul left the office at 8:35 PM and reached home at 10:02 PM. To find out how long he traveled, we need to calculate the time difference between these two points. Subtracting 8:35 PM from 10:02 PM gives us 1 hour and 27 minutes. Therefore, Mr. Paul traveled for 1 hour and 27 minutes.

3. Which of the following is not greater than 7/16?

1/2

31/62

15/17

3/8

The fraction 3/8 is not greater than 7/16. Here’s why:

1/2 is equal to 8/16, which is greater than 7/16.

31/62 simplifies to 1/2, which is also greater than 7/16.

15/17 is approximately 0.882, which is greater than 7/16 (approximately 0.4375).

However, 3/8 is equal to 6/16, which is less than 7/16. So, 3/8 is not greater than 7/16.

Explanation

The fraction 3/8 is not greater than 7/16. Here’s why:

1/2 is equal to 8/16, which is greater than 7/16.

31/62 simplifies to 1/2, which is also greater than 7/16.

15/17 is approximately 0.882, which is greater than 7/16 (approximately 0.4375).

However, 3/8 is equal to 6/16, which is less than 7/16. So, 3/8 is not greater than 7/16.

4. Freight charges of a certain courier company are as follows:

$40 for the first 2 pounds
$15 for each of the succeeding pound weight of parcels.

At this rate, what amount would be charged on a package which weighs 30 pounds?

$450

$460

$640

$600

The freight charges for the first 2 pounds are $40. For each additional pound after that, the charge is $15. Since the package weighs 30 pounds, we need to calculate the charges for the additional 28 pounds (30 pounds - 2 pounds).

The charges for the additional 28 pounds would be 28 pounds * $15/pound = $420.

Adding this to the initial charge of $40, the total amount charged on the package weighing 30 pounds would be $40 + $420 = $460.

Explanation

The freight charges for the first 2 pounds are $40. For each additional pound after that, the charge is $15. Since the package weighs 30 pounds, we need to calculate the charges for the additional 28 pounds (30 pounds - 2 pounds).

The charges for the additional 28 pounds would be 28 pounds * $15/pound = $420.

Adding this to the initial charge of $40, the total amount charged on the package weighing 30 pounds would be $40 + $420 = $460.

5. If a square's each side is increased by x units, then, after that, its perimeter is increased by how many units?

2x

X

8x

4x

When each side of a square is increased by x units, it means that all four sides of the square are increased by x units. Since the perimeter of a square is the sum of all four sides, the increase in the perimeter will be equal to 4 times the increase in each side, which is 4x.

Explanation

When each side of a square is increased by x units, it means that all four sides of the square are increased by x units. Since the perimeter of a square is the sum of all four sides, the increase in the perimeter will be equal to 4 times the increase in each side, which is 4x.

6. If 5/6 < x and x < 7/4 then x could be ____.

1/2

3/2

2/3

2

If 5/6

Explanation

If 5/6

7. When a = 4 and b = 3/7, which of the following expressions represents the smallest value?

59/7

22/7

28/3

3/28

When a = 4 and b = 3/7, the expression 3/28 represents the smallest value. This can be determined by comparing the values of the expressions. The numerator of 3/28 is smaller than the numerators of the other expressions, while the denominator is larger than the denominators of the other expressions. Therefore, 3/28 is the smallest value among the given options.

Explanation

When a = 4 and b = 3/7, the expression 3/28 represents the smallest value. This can be determined by comparing the values of the expressions. The numerator of 3/28 is smaller than the numerators of the other expressions, while the denominator is larger than the denominators of the other expressions. Therefore, 3/28 is the smallest value among the given options.

8. If the sum of the first two of the five consecutive odd integers is 52, what is the sum of the last two integers?

61

67

64

58

The question states that the sum of the first two consecutive odd integers is 52. Since the integers are consecutive, we can assume that the first integer is x, the second integer is x + 2, the third integer is x + 4, the fourth integer is x + 6, and the fifth integer is x + 8. Therefore, the equation x + (x + 2) = 52 can be formed. Solving this equation, we get x = 25. So, the last two integers would be 25 + 6 = 31 and 25 + 8 = 33. The sum of these two integers is 31 + 33 = 64.

Explanation

The question states that the sum of the first two consecutive odd integers is 52. Since the integers are consecutive, we can assume that the first integer is x, the second integer is x + 2, the third integer is x + 4, the fourth integer is x + 6, and the fifth integer is x + 8. Therefore, the equation x + (x + 2) = 52 can be formed. Solving this equation, we get x = 25. So, the last two integers would be 25 + 6 = 31 and 25 + 8 = 33. The sum of these two integers is 31 + 33 = 64.

9. Which of the following is more than 0.35 but less than 0.41?

8/25

3/10

2/5

9/26

The fraction 2/5 is more than 0.35 because when we convert it to a decimal, it becomes 0.4 which is greater than 0.35. It is also less than 0.41 because when we convert it to a decimal, it becomes 0.4 which is less than 0.41. Therefore, the fraction 2/5 satisfies both conditions and is the correct answer.

Explanation

The fraction 2/5 is more than 0.35 because when we convert it to a decimal, it becomes 0.4 which is greater than 0.35. It is also less than 0.41 because when we convert it to a decimal, it becomes 0.4 which is less than 0.41. Therefore, the fraction 2/5 satisfies both conditions and is the correct answer.

10. When simplified, |9+(4-3)-17| has a value of _____.

-7

13

9

7

To simplify the expression, we need to follow the order of operations and evaluate the absolute value:

Parentheses: (4 - 3) = 1

Addition: 9 + 1 = 10

Subtraction: 10 - 17 = -7

Absolute value: |-7| = 7

Therefore, when simplified, |9 + (4 - 3) - 17| has a value of 7.

Explanation

To simplify the expression, we need to follow the order of operations and evaluate the absolute value:

Parentheses: (4 - 3) = 1

Addition: 9 + 1 = 10

Subtraction: 10 - 17 = -7

Absolute value: |-7| = 7

Therefore, when simplified, |9 + (4 - 3) - 17| has a value of 7.