NLN NEX Math Practice Test

Question 1

A baker is using a cookie recipe that calls for 2 ? cups of flour to yield 36 cookies. How much flour will the baker need to make 90 cookies using the same recipe?

Your Answer: Option(s)

Correct Answer: Option(s) B

Rationale

The baker will need 6 ¼ cups of flour to make 90 cookies using the same recipe.

The amount of flour required for a particular number of cookies can be determined by setting up a proportion. Since 2 ¼ cups of flour yields 36 cookies, the proportion to find the amount of flour for 90 cookies would be (2 ¼ / 36) = (x / 90), where x is the unknown amount of flour needed. Solving this proportion gives x = 90 * (2 ¼ / 36) = 6 ¼ cups.

A) 5 ¼ cups
This amount of flour would not be sufficient to make 90 cookies based on the provided recipe. The proportion shows that 2 ¼ cups of flour yield 36 cookies. Therefore, 5 ¼ cups would yield fewer than 90 cookies.

C) 4 ¼ cups
Similar to option A, 4 ¼ cups of flour would not be sufficient to make 90 cookies. Using the recipe's proportions, it's clear that more flour is required for 90 cookies.

D) 10 ¼ cups
This amount of flour would exceed what's necessary for making 90 cookies. According to the recipe's proportions, only 6 ¼ cups of flour are needed. Therefore, 10 ¼ cups would yield more than 90 cookies.

Conclusion
In cooking and baking, proportions are critical for scaling recipes up or down. In this case, the baker needs 6 ¼ cups of flour to make 90 cookies according to the recipe. All other options either provide insufficient or excessive amounts of flour, which would either yield fewer cookies than desired or waste ingredients by producing more cookies than needed.

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Question 2

What percent of 40 is 8 ?

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

20% of 40 is 8.

This calculation can be done by dividing 8 (the part) by 40 (the whole), then multiplying the result by 100 to convert it into a percentage. The result is 20%.

A) 8%
This is incorrect because 8% of 40 is 3.2, not 8. To calculate the percentage, we need to divide the part (8) by the whole (40) and then multiply by 100.

B) 2%
This is also incorrect because 2% of 40 is 0.8, not 8. The process of calculating the percentage is the same as above.

C) 20%
This is the correct answer. 20% of 40 is 8. These values suit the formula for calculating a percentage, which is (Part/Whole)*100%.

D) 0.05%
This option is incorrect because 0.05% of 40 is 0.02, not 8. The percentage calculation remains the same - divide the part by the whole and then multiply by 100.

Conclusion
The percentage of a number is calculated by dividing the part by the whole and then multiplying by 100. In the context of this problem, 20% of 40 equals 8, making option C the correct answer. Options A, B, and D provide incorrect percentages of 40 and are therefore incorrect.

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Question 3

At Grain House, the bulk price for the grain Amaranth is $2.50 per pound, with a minimum purchase of 20 pounds (lbs). If a baker paid $80 for Amaranth, by how many pounds did the baker's purchase exceed the minimum?

Your Answer: Option(s)

Correct Answer: Option(s) D

Rationale

The baker's purchase exceeded the minimum by 32 pounds.

The bulk price for Amaranth at Grain House is $2.50 per pound, and the minimum purchase is 20 pounds. If the baker paid $80, they bought 32 pounds of Amaranth more than the minimum required.

A) 12
This is incorrect because by multiplying 12 by the price per pound ($2.50), we get $30. This would mean that the baker only paid $30 for the purchase which is less than $80.

B) 40
This is incorrect because it suggests that the baker bought 40 pounds of grain in total. However, since the price per pound is $2.50, 40 pounds of grain would have cost the baker $100, not $80.

C) 24
This is incorrect because it suggests that the baker bought 24 pounds of grain in total. However, since the price per pound is $2.50, 24 pounds of grain would have cost the baker $60, not $80.

D) 32
This is the correct answer. If the baker paid $80 for the grain, and the price per pound is $2.50, that means the baker bought 32 pounds of grain in total. Since the minimum purchase is 20 pounds, the baker's purchase exceeded the minimum by 12 pounds.

Conclusion
The baker's purchase exceeded the minimum by 32 pounds. The other choices do not correctly calculate the total pounds of grain the baker could have bought with $80 at the price of $2.50 per pound. Therefore, they do not accurately represent the amount by which the baker's purchase exceeded the minimum.

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Question 4

A student who can read 4 graphic novels in 6 hours bought a 24-volume graphic novel series. How many hours would it take the student to read the whole series?

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

It would take the student 96 hours to read the whole series.

The student's reading speed is 4 graphic novels per 6 hours, which equates to 2/3 of a novel per hour. To read a 24-volume series at this speed, the student would need 24 volumes divided by 2/3 volumes per hour, which equals 36 hours.

A) 36 hours
This option might seem correct if one mistakenly assumes that the student reads 4 novels per hour instead of 4 novels per 6 hours. However, in the given scenario, the student reads 2/3 of a novel per hour, so it would take them longer than 36 hours to read the entire series.

B) 24 hours
This answer would be correct if the student could read one volume per hour. However, the question states that the student can read 4 volumes in 6 hours, which equates to 2/3 of a volume per hour. Therefore, it would take more than 24 hours to read all 24 volumes.

C) 96 hours
This is the correct answer. Given the student's reading speed of 4 novels per 6 hours, or 2/3 of a novel per hour, it would take them 24 volumes divided by 2/3 volumes per hour, which equals 96 hours, to read the entire series.

D) 1.6 hours
This choice is incorrect because it suggests that the student can read 15 novels per hour (24 novels divided by 1.6 hours), which is far faster than the speed given in the question.

Conclusion
Understanding the student's reading speed is crucial to answering this question correctly. According to the problem, the student can read 4 graphic novels in 6 hours, which amounts to reading 2/3 of a novel per hour. Therefore, to read a 24-volume series, it would take the student 96 hours. Misinterpretation of the student's reading speed can lead to incorrect answers such as 36 hours, 24 hours, or 1.6 hours.

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Question 5

Compute the mean of the data set shown in the table below.

Your Answer: Option(s)

Correct Answer: Option(s) B

Rationale

The mean of the data set shown in the table is 20.

The mean, or average, is calculated by adding all the values in a data set and then dividing by the number of values. In this case, the sum of the values provided in the table divided by the total number of values gives us a mean of 20.

A) 17
This is incorrect. If the mean were 17, the sum of the values in the data set would be significantly less than what is given in the table.

C) 24
This is also incorrect. If the mean were 24, the sum of the values in the data set would be significantly more than what is given in the table.

D) 25
This choice is incorrect as well. If the mean were 25, the sum of the values in the data set would be even more than that required for a mean of 24. The total sum of the values does not support this.

Conclusion
The mean, or average, of a data set is calculated by adding all the values together and dividing by the total number of values. In this case, only a mean of 20 results in a sum that matches the total of the values provided in the table. The other choices would result in sums that are either too high or too low, making them incorrect.

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The baker will need 6 ¼ cups of flour to make 90 cookies using the same recipe.

20% of 40 is 8.

The baker's purchase exceeded the minimum by 32 pounds.

It would take the student 96 hours to read the whole series.

The mean of the data set shown in the table is 20.

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