PSAT Math Practice Test

1) What is the sum of all the positive integer factors of 12 ?

The sum of all the positive integer factors of 12 can be found by listing out the factors and adding them up. The factors of 12 are 1, 2, 3, 4, 6, and 12. Adding them together gives a sum of 28.

Explanation

The sum of all the positive integer factors of 12 can be found by listing out the factors and adding them up. The factors of 12 are 1, 2, 3, 4, 6, and 12. Adding them together gives a sum of 28.

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2) (3 x 10⁴) + (2 x 10²) + (4 x 10) =

The given expression is a sum of three terms, each involving a multiplication operation. The first term is 3 multiplied by 104, which equals 312. The second term is 2 multiplied by 10 squared, which equals 200. The third term is 4 multiplied by 10, which equals 40. Adding these three terms together gives a total of 312 + 200 + 40 = 552. However, the correct answer is given as 30240, which suggests that there may be an error in the given question or answer.

Explanation

The given expression is a sum of three terms, each involving a multiplication operation. The first term is 3 multiplied by 104, which equals 312. The second term is 2 multiplied by 10 squared, which equals 200. The third term is 4 multiplied by 10, which equals 40. Adding these three terms together gives a total of 312 + 200 + 40 = 552. However, the correct answer is given as 30240, which suggests that there may be an error in the given question or answer.

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3) The number 0.127 is how much greater than 1/8 ?

1/2

1/5

1/50

1/500

1/250

The number 0.127 is greater than 1/8 by a very small amount. To find out how much greater, we can subtract 1/8 from 0.127. This gives us 0.127 - 1/8 = 0.127 - 0.125 = 0.002. Therefore, 0.127 is 0.002 greater than 1/8. In fraction form, 0.002 is equal to 1/500.

Explanation

The number 0.127 is greater than 1/8 by a very small amount. To find out how much greater, we can subtract 1/8 from 0.127. This gives us 0.127 - 1/8 = 0.127 - 0.125 = 0.002. Therefore, 0.127 is 0.002 greater than 1/8. In fraction form, 0.002 is equal to 1/500.

4)

A² + b² + 1

A + b

A - b

Ab

It cannot be simplified further

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Explanation

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5)

Which of the following could be a value of x, in the diagram above?

10

20

40

50

All of the above

In the diagram above, there is no specific information provided about the value of x. Therefore, any of the given options - 10, 20, 40, or 50 - could potentially be a valid value for x.

Explanation

In the diagram above, there is no specific information provided about the value of x. Therefore, any of the given options - 10, 20, 40, or 50 - could potentially be a valid value for x.

6) 3x + y = 19 , and x + 3y = 1.
Find the value of 2x + 2y

28

18

11

10

5

To find the value of 2x + 2y, we can multiply the first equation by 2 and the second equation by 2, which gives us 6x + 2y = 38 and 2x + 6y = 2. By adding these two equations together, we eliminate the variable x and obtain 8y = 40. Dividing both sides by 8, we find that y = 5. Substituting this value back into the second equation, we get x + 3(5) = 1, which simplifies to x + 15 = 1. Subtracting 15 from both sides, we find that x = -14. Finally, substituting these values into 2x + 2y, we get 2(-14) + 2(5) = -28 + 10 = -18 + 10 = -8 + 10 = 2 + 10 = 12.

Explanation

To find the value of 2x + 2y, we can multiply the first equation by 2 and the second equation by 2, which gives us 6x + 2y = 38 and 2x + 6y = 2. By adding these two equations together, we eliminate the variable x and obtain 8y = 40. Dividing both sides by 8, we find that y = 5. Substituting this value back into the second equation, we get x + 3(5) = 1, which simplifies to x + 15 = 1. Subtracting 15 from both sides, we find that x = -14. Finally, substituting these values into 2x + 2y, we get 2(-14) + 2(5) = -28 + 10 = -18 + 10 = -8 + 10 = 2 + 10 = 12.

7) Courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $1.55 ?

1155

1145

1040

950

259

The charge for the first 250 grams is 65 cents, and for each additional 100 grams or part thereof, it is 10 cents. To find the weight of the package, we need to subtract the fixed charge of 65 cents from the total charge of $1.55. The remaining amount, $0.90, represents the charge for the additional weight. Since each additional 100 grams or part thereof costs 10 cents, we can divide $0.90 by 10 cents to find the number of additional 100 grams. This gives us 9. Multiplying 9 by 100 grams gives us an additional weight of 900 grams. Adding this to the initial 250 grams, we get a total weight of 1150 grams. Therefore, the weight of the package is 1155 grams.

Explanation

The charge for the first 250 grams is 65 cents, and for each additional 100 grams or part thereof, it is 10 cents. To find the weight of the package, we need to subtract the fixed charge of 65 cents from the total charge of $1.55. The remaining amount, $0.90, represents the charge for the additional weight. Since each additional 100 grams or part thereof costs 10 cents, we can divide $0.90 by 10 cents to find the number of additional 100 grams. This gives us 9. Multiplying 9 by 100 grams gives us an additional weight of 900 grams. Adding this to the initial 250 grams, we get a total weight of 1150 grams. Therefore, the weight of the package is 1155 grams.

8) The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent. The two reductions together are equal to a single reduction of..

45%

40%

35%

32..5%

30%

When the price of the cycle is reduced by 25%, it means that the new price is 75% of the original price. Then, when the new price is reduced by a further 20%, it means that the final price is 80% of the reduced price. To find the overall reduction, we need to multiply 75% by 80%, which equals 60%. Therefore, the two reductions together are equal to a single reduction of 40%.

Explanation

When the price of the cycle is reduced by 25%, it means that the new price is 75% of the original price. Then, when the new price is reduced by a further 20%, it means that the final price is 80% of the reduced price. To find the overall reduction, we need to multiply 75% by 80%, which equals 60%. Therefore, the two reductions together are equal to a single reduction of 40%.

9) Helpers are needed to prepare for the fete. Each helper can make either 2 large cakes per hour, or 35 small cakes per hour. The kitchen is available for 3 hours and 20 large cakes and 700 small cakes are needed. How many helpers are required?

10

15

20

25

30

To find the number of helpers required, we need to calculate the total number of cakes each helper can make in 3 hours. One helper can make 2 large cakes per hour, so in 3 hours, they can make 2 * 3 = 6 large cakes. Similarly, one helper can make 35 small cakes per hour, so in 3 hours, they can make 35 * 3 = 105 small cakes.

To fulfill the requirement of 20 large cakes, we need 20 / 6 = 3.33 helpers. Since we cannot have a fraction of a helper, we round up to the nearest whole number, which is 4.

To fulfill the requirement of 700 small cakes, we need 700 / 105 = 6.67 helpers. Again, rounding up to the nearest whole number, we get 7.

Therefore, the total number of helpers required is 4 + 7 = 11.

Explanation

To find the number of helpers required, we need to calculate the total number of cakes each helper can make in 3 hours. One helper can make 2 large cakes per hour, so in 3 hours, they can make 2 * 3 = 6 large cakes. Similarly, one helper can make 35 small cakes per hour, so in 3 hours, they can make 35 * 3 = 105 small cakes.

To fulfill the requirement of 20 large cakes, we need 20 / 6 = 3.33 helpers. Since we cannot have a fraction of a helper, we round up to the nearest whole number, which is 4.

To fulfill the requirement of 700 small cakes, we need 700 / 105 = 6.67 helpers. Again, rounding up to the nearest whole number, we get 7.

Therefore, the total number of helpers required is 4 + 7 = 11.