Praxis 5003 Study Guide

Question 1

Each can of Brand A paint will cover 200 square feet. A building has two walls to be painted. One is a rectangle with length 30 feet and width 16.5 feet, and the other is a triangle with height 12 feet and base 16 feet. What is the least number of cans of Brand A paint that are needed to paint the two walls in their entirety?

Your Answer: Option(s)

Correct Answer: Option(s) B

Rationale

Three cans of Brand A paint are needed to cover the two walls.

To determine the total paint required, we first calculate the area of both walls and then divide by the coverage of one can of paint. The rectangular wall has an area of 495 square feet, and the triangular wall has an area of 96 square feet, leading to a combined area of 591 square feet. Dividing this by the 200 square feet coverage per can gives us approximately 2.95, which rounds up to 3 cans.

A) 2
Choosing 2 cans would only cover 400 square feet (2 x 200), which is insufficient for the total area of 591 square feet. This option underestimates the paint required, failing to account for the areas of both the rectangular and triangular walls.

B) 3
This option is correct, as it accurately reflects the amount of paint needed. With a total area of 591 square feet and each can covering 200 square feet, 3 cans will cover 600 square feet, providing enough paint to cover both walls entirely.

C) 4
While 4 cans would cover 800 square feet (4 x 200), which is more than enough, it is not the least number of cans required. This option represents an overestimation of the paint needed, leading to unnecessary expenditure.

D) 5
Similar to option C, 5 cans would cover 1000 square feet (5 x 200), greatly exceeding the area needed. This choice is excessive and economically inefficient, as it far surpasses the actual paint requirement for the job.

Conclusion
To paint both walls of the building, a total area of 591 square feet must be covered. Three cans of Brand A paint will adequately cover this area, as each can covers 200 square feet. Options A, C, and D either underestimate or overestimate the required amount, making B the only viable choice for the least number of cans needed.

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Question 2

Which of the following statements is true about the number 90?

Your Answer: Option(s)

Correct Answer: Option(s) B

Rationale

It has 6 and 15 as factors.

The number 90 can be evenly divided by both 6 and 15, confirming that they are indeed factors of 90. This means that when 90 is divided by either of these numbers, the result is a whole number, demonstrating their integral relationship to 90.

A) It has 10 as a multiple
While 90 is indeed a multiple of 10 (as 90 can be expressed as 10 times 9), this statement is misleading because it implies that 10 is a factor of 90, which it is not. A factor must divide a number evenly, and 10 does not meet this criterion since 90 divided by 10 results in 9, not a whole number.

C) It has four distinct prime factors
The prime factorization of 90 is 2 × 3 × 3 × 5, which consists of three distinct prime factors (2, 3, and 5). Therefore, stating that it has four distinct prime factors is incorrect, as there are only three unique primes that multiply to give 90.

D) It is divisible by 9 but not by 18
Although 90 is divisible by 9 (90 divided by 9 equals 10), it is also divisible by 18 since 90 divided by 18 equals 5. This makes the statement false, as 90 meets the criteria for divisibility by both 9 and 18.

Conclusion
Among the provided options, only the statement that 90 has 6 and 15 as factors is accurate. This reveals a fundamental property of the number, highlighting its divisibility. The other choices either misinterpret the relationships between factors and multiples or incorrectly state the number of distinct prime factors, thereby verifying B as the only true statement regarding the number 90.

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Question 3

Which of the following is a decomposition of the number 1260?

Your Answer: Option(s)

Correct Answer: Option(s) D

Rationale

1 thousand, 2 hundreds, and 60 tens

This option correctly breaks down the number 1260 into its respective place values, showing that it consists of 1 thousand, 2 hundreds, and 60 tens.

A) 12 hundreds and 6 tens
This option represents a total of 1200 (12 hundreds) plus 60 (6 tens), which sums to 1260. However, it inaccurately represents the number as it does not use a thousand place value; instead, it should illustrate a breakdown that includes thousands.

B) 11 hundreds and 60 tens
This choice adds up to 1100 (11 hundreds) plus 600 (60 tens), equating to 1700. This significantly overshoots the value of 1260 and fails to accurately reflect the decomposition of the number.

C) 1 thousand and 26 hundreds
This option totals 1000 (1 thousand) plus 2600 (26 hundreds), which equals 3600. This is incorrect as it exceeds the value of 1260 and does not properly represent the breakdown of the number.

D) 1 thousand, 2 hundreds, and 60 tens
This option gives the precise breakdown of 1260, with 1 thousand (1000), 2 hundreds (200), and 60 tens (600), correctly summing to 1260.

Conclusion
Understanding the decomposition of numbers into their respective place values is essential for mathematical clarity. In this case, option D accurately represents the number 1260 as consisting of 1 thousand, 2 hundreds, and 60 tens, making it the only correct choice among the options provided. The other choices either misrepresent the thousand place or yield incorrect totals, highlighting the importance of precise numerical breakdowns.

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Question 4

A high school schedules 288 students to take a math class during first period. If there are 12 math teachers, what is the student-to-teacher ratio for the math classes during first period?

Your Answer: Option(s)

Correct Answer: Option(s) B

Rationale

The student-to-teacher ratio for the math classes during first period is 24 to 1.

To find the student-to-teacher ratio, divide the total number of students by the total number of teachers. With 288 students and 12 teachers, the ratio is calculated as 288 ÷ 12 = 24.

A) 12 to 1
This ratio implies that for every teacher, there are only 12 students. However, when calculating the correct ratio of 288 students to 12 teachers, this is incorrect since it would suggest a much lower total number of students.

B) 24 to 1
This is the correct ratio. It accurately represents that there are 24 students for every teacher, resulting from the division of 288 students by 12 teachers, providing a clear understanding of the distribution of students among the teachers.

C) 36 to 1
This option suggests that there are 36 students for each teacher. However, this would imply a total of 432 students (36 x 12), which exceeds the actual number of 288 students scheduled for the class.

D) 48 to 1
Choosing this ratio indicates a scenario where there are 48 students per teacher. This would suggest a total of 576 students (48 x 12), a number that is significantly higher than the 288 students enrolled in the class.

Conclusion
The correct student-to-teacher ratio for the math classes during the first period is 24 to 1, derived from dividing the total number of students, 288, by the number of teachers, 12. This calculation ensures an accurate reflection of the classroom environment, illustrating how many students are supported by each teacher. Other options incorrectly represent either fewer or greater student counts, demonstrating a misunderstanding of the ratio calculation.

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Question 5

Based on the preceding computation, what is the value of 1085 / 12?

Your Answer: Option(s)

Correct Answer: Option(s) D

Rationale

90.5

The division of 1085 by 12 results in 90.5, confirming that this is the correct answer. This calculation yields a quotient of 90 with a remainder that translates into a decimal, leading to the final result of 90.5.

A) 90
This choice represents the integer part of the division but fails to account for the remainder. When dividing 1085 by 12, the full answer includes the decimal portion, which reflects the complete quotient. Thus, while 90 is part of the answer, it is not the complete result.

B) 90{5/1085}
This option incorrectly suggests a fraction that does not arise from the division of 1085 by 12. The format "90{5/1085}" implies a very different number than the intended result, which should represent the decimal from the actual division. Therefore, this choice is not relevant to the question.

C) 90{5/12}
This choice misrepresents the result by suggesting a fraction that does not correspond to the division performed. The expression "90{5/12}" mistakenly indicates that 5 is over 12 instead of being part of the decimal derived from the division of 1085 by 12. This choice does not accurately reflect the computation.

D) 90.5
This choice accurately represents the result of dividing 1085 by 12. The decimal indicates the remainder from the division, providing a precise value that combines both the integer quotient and the fractional part derived from the calculation.

Conclusion
When dividing 1085 by 12, the correct result is 90.5, which captures both the integer and decimal components of the quotient. Other choices either provide incomplete information or misrepresent the result, emphasizing the importance of recognizing both parts of a division outcome in numerical computations.

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Three cans of Brand A paint are needed to cover the two walls.

It has 6 and 15 as factors.

1 thousand, 2 hundreds, and 60 tens

The student-to-teacher ratio for the math classes during first period is 24 to 1.

90.5

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