Praxis 5733 Core Academic Math Answers

Question 1

Last week a bookstore ordered a total of 92 books. The number of science fiction books, historical novels, and dictionaries ordered are shown in the pictograph above. How many books are needed to represent the number of biographies ordered?

Your Answer: Option(s)

Correct Answer: Option(s) A

Rationale

Six books are needed to represent the number of biographies ordered.

The total number of books ordered was 92, and after accounting for the known quantities of science fiction books, historical novels, and dictionaries as represented in the pictograph, it is determined that 6 biographies were ordered to complete the total.

A) 6
This choice correctly reflects the number of biographies ordered. Since the total number of books is 92 and the quantities of other categories have been summed, subtracting these from 92 yields 6, indicating that 6 biographies were ordered.

B) 7
Choosing 7 implies that there were more biographies ordered than calculated. Given that the sum of the other categories already accounts for a specific number of books, selecting 7 would exceed the total of 92 when combined with the other categories.

C) 17
This choice suggests an even higher number of biographies than 6 or 7. As previously stated, the calculations based on the pictograph clearly indicate that the total must remain at 92 when all categories are considered, making 17 an incorrect representation.

D) 23
Selecting 23 would again lead to an inconsistency in the total calculation. The cumulative total of the other book categories already leaves insufficient room to accommodate 23 biographies without exceeding the overall order of 92 books.

E) 75
This choice presents an unrealistically high number of biographies. Such a number would overshadow the combined total of other categories, invalidating the total order of 92 books and demonstrating a misunderstanding of the pictograph's data.

Conclusion
The correct number of biographies ordered is 6, derived from subtracting the known quantities of other book types from the total of 92. Each incorrect option either exceeds or misrepresents the total, highlighting the importance of accurate data interpretation in such problems.

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Question 2

The numbers shown above are the weights, in pounds, of 9 pumpkins sold yesterday at a farm market. What is the median weight of the 9 pumpkins sold yesterday?

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

The median weight of the 9 pumpkins sold yesterday is 4.65 pounds.

To find the median, we first need to arrange the weights in ascending order. With 9 weights, the median will be the fifth number in this ordered list, which is 4.65 pounds.

A) 4.2
The value 4.2 is less than the fifth number in the ordered list of weights. It is likely one of the lower values in the dataset, but it does not represent the median, which is defined as the middle value of a sorted list.

B) 4.5
While 4.5 is a possible weight of one of the pumpkins, it falls below the median position in the ordered list. The median must be the central value, and since 4.5 is not the fifth number, it cannot be the correct answer.

D) 4.75
The weight of 4.75 is higher than the median weight of 4.65. In an ordered list, it occupies a position beyond the median, indicating that it is not the middle value in the dataset.

E) 4.8
4.8 is also above the median weight and would be one of the larger weights in the dataset. As such, it cannot be the median, which must be the value that separates the lower half from the upper half of the ordered weights.

Conclusion
The median weight serves as a central tendency measure, effectively representing the middle value in an ordered set of data. In this case, the median weight of the 9 pumpkins is 4.65 pounds, as it is the fifth weight in the arranged list. All other choices either fall below or above this central value, confirming that they do not meet the criteria for being the median.

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Question 3

A travel agency has booked 231 passengers for a bus trip. Each bus has seats for 30 passengers, and each passenger must sit in one seat. What is the least number of buses needed for the trip, and how many seats will be empty?

Your Answer: Option(s)

Correct Answer: Option(s) D

Rationale

8 buses with 21 empty seats.

To accommodate 231 passengers, the travel agency requires a minimum of 8 buses, as 8 x 30 equals 240 seats, leaving 21 seats unoccupied. This calculation ensures that all passengers have a seat while minimizing the number of buses used.

A) 10 buses with 31 empty seats
Using 10 buses would provide 300 total seats (10 x 30), which is more than necessary for 231 passengers. While this option does ensure all passengers are seated, it is not the least number of buses required, as 8 buses suffice.

B) 9 buses with 21 empty seats
Nine buses would yield 270 seats (9 x 30), indeed accommodating all 231 passengers with 39 empty seats. However, this exceeds the requirement of 8 buses, making it an inefficient choice.

C) 8 buses with 31 empty seats
While 8 buses provide enough seats for the passengers, the calculation shows that 8 x 30 equals 240 seats, leaving only 21 empty. This option incorrectly states the number of empty seats.

D) 8 buses with 21 empty seats
This is the correct choice. With 8 buses, there are 240 seats available, allowing for 231 passengers to be seated, resulting in 21 empty seats.

E) 8 buses with 9 empty seats
This option incorrectly underestimates the number of empty seats. Eight buses yield 240 seats, and with 231 passengers, there are actually 21 seats left unoccupied, not 9.

Conclusion
The most efficient way to transport 231 passengers is by using 8 buses, which provides 240 seats and results in 21 empty seats. All other options either overestimate the number of buses needed or miscalculate the number of empty seats, highlighting the importance of accurate calculations in logistical planning.

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Question 4

The two rectangles above are similar, where x > 18. What is the value of x?

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

x = 27.

In similar rectangles, the ratios of corresponding sides are equal. By setting up a proportion based on the given dimensions of the rectangles, we can solve for the value of x.

A) 21
If x were 21, the ratio of the sides would not be consistent with the proportions required for similarity. This choice results in a ratio that does not match the established ratio of the corresponding sides of the rectangles.

B) 24
Choosing 24 for x would also yield a ratio inconsistent with the similarity condition of the rectangles. The calculations would show that the dimensions do not maintain the proportion necessary for similarity, thus making this option invalid.

C) 27
With x equal to 27, the ratios of the sides align perfectly, confirming that the rectangles are similar. This value satisfies the proportional relationship established by the dimensions of the rectangles, making it the correct answer.

D) 33
If x were 33, the resulting ratio would exceed the proportional relationship required for similarity. This choice leads to an inconsistent ratio, disqualifying it as a valid solution for the problem.

E) 54
Selecting 54 for x would result in a ratio that significantly diverges from the expected proportions of the rectangles. This discrepancy renders the option invalid as it does not satisfy the conditions of similarity.

Conclusion
The value of x must be 27 to maintain the proportional relationship between the sides of the similar rectangles. Other options fail to satisfy the requirements for similarity, as they do not yield consistent ratios. Thus, understanding the properties of similar shapes is crucial for determining correct values in geometric problems.

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Question 5

Jordan has budgeted $100 for the repair of his computer. The repair service charges a service fee of $35 for each repair job plus $20 per hour of labor. Which of the following represents the greatest possible number of hours of labor that the repair service can charge at that rate without exceeding Jordan's budget?

Your Answer: Option(s)

Correct Answer: Option(s) A

Rationale

(100 - 35) / 20

To determine the greatest possible number of hours of labor Jordan can afford, we first subtract the fixed service fee of $35 from his total budget of $100, leaving him with $65 for labor. Dividing this amount by the hourly rate of $20 gives us the maximum hours of labor.

A) (100 - 35) / 20
This expression correctly calculates the number of hours of labor Jordan can afford after accounting for the service fee. Subtracting the service fee of $35 from the $100 budget results in $65, which when divided by the hourly rate of $20 gives 3.25 hours, the maximum hours available for labor without exceeding the budget.

B) (100 - 20) / 35
This option incorrectly subtracts the hourly rate of $20 from the total budget. It does not consider the service fee, leading to an inaccurate representation of the budget allocation for labor. The result will not provide the correct maximum hours of labor.

C) 20 * (100 - 35)
This choice incorrectly multiplies the hourly rate by the remaining budget after the service fee. Instead of calculating the number of hours, it erroneously computes a dollar amount, which does not answer the question about the greatest number of labor hours.

D) (100 - 35) / (20 - 35)
This expression contains an incorrect denominator of (20 - 35), which results in a negative value and makes the calculation invalid. The negative value does not represent any feasible number of hours Jordan can afford for labor.

E) 100 - 20 * 35
This choice incorrectly computes the budget by multiplying the hourly rate by the service fee. The operation does not account for the service fee correctly and results in a miscalculation of available funds for labor, leading to an illogical number.

Conclusion
The best representation of the greatest possible number of labor hours Jordan can afford is given by the expression (100 - 35) / 20. This calculation accurately considers the service fee, allowing for a correct determination of his remaining budget for labor, thereby ensuring that he does not exceed his total budget of $100.

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Six books are needed to represent the number of biographies ordered.

The median weight of the 9 pumpkins sold yesterday is 4.65 pounds.

8 buses with 21 empty seats.

x = 27.

(100 - 35) / 20

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