5003 Praxis Math Answers

Question 1

Students at a local middle school are selling candy bars for a fund-raiser. The candy bars come packaged in cases of 60 bars, and the school makes a $0.75 profit from each candy bar sold. How many cases of candy bars need to be sold for the school to make a profit of $900?

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

20 cases of candy bars need to be sold for the school to make a profit of $900.

To determine the number of cases required to achieve a $900 profit, we first calculate the total profit from selling one case of candy bars. Each case contains 60 bars, and the school earns $0.75 per bar, leading to a profit of $45 per case. Dividing the target profit of $900 by $45 gives us 20 cases.

A) 8
If 8 cases are sold, the total profit would amount to 8 cases × $45 per case = $360. This amount is significantly lower than the required profit of $900, indicating that more cases must be sold to reach the target.

B) 12
Selling 12 cases yields a profit of 12 cases × $45 per case = $540. Although this profit is higher than selling 8 cases, it still falls short of the $900 goal, showing that further sales are necessary.

C) 20
As previously calculated, selling 20 cases results in a profit of 20 cases × $45 per case = $900. This matches the desired profit exactly, making it the correct answer.

D) 40
If 40 cases are sold, the profit calculates to 40 cases × $45 per case = $1,800. While this exceeds the target profit of $900, it is not the minimum number of cases required to achieve the goal, indicating an overestimation.

Conclusion
To achieve a profit of $900, the school must sell exactly 20 cases of candy bars, as this quantity precisely yields the necessary profit based on the earnings per case. Other choices either fall short of this target or exceed it without necessity, reinforcing that careful calculations based on profit per item are crucial in fundraising scenarios.

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Question 2

Each of the digits 3. 5. 7, and 8 is written on its own card. The four cards are given to a student, and then the student is asked to use the cards to form the largest three-digit number that is greater than 300 and less than 700. In the number formed, what digit will be in the tens place?

Your Answer: Option(s)

Correct Answer: Option(s) D

Rationale

The digit in the tens place will be 8.

To form the largest three-digit number greater than 300 and less than 700 using the digits 3, 5, 7, and 8, the optimal arrangement places 8 in the tens place. This configuration leads to the maximum possible value while adhering to the constraints of the number range.

A) 3
If 3 were in the tens place, the largest three-digit number that could be formed would be 378, which is less than what can be achieved with 8 in the tens place. Consequently, using 3 in the tens place will not yield the largest possible number.

B) 5
Placing 5 in the tens place would result in the largest number being 578. While this is a valid option, it is still less than the number that can be formed with 8 in the tens place, which is 873. Therefore, 5 does not maximize the value of the three-digit number.

C) 7
Using 7 in the tens place allows for the formation of the number 578, which again is less than what is possible with 8 in that position. The digit 7 does not provide the highest three-digit number within the specified range when compared to using 8.

D) 8
By placing 8 in the tens place, the largest three-digit number formed is 578, which meets the criteria of being greater than 300 and less than 700. This arrangement utilizes the highest digit available in the tens position, optimizing the overall number.

Conclusion
In conclusion, to create the largest three-digit number between 300 and 700 using the digits 3, 5, 7, and 8, positioning the digit 8 in the tens place is essential. This maximizes the value of the number formed, resulting in 578, while ensuring compliance with the specified range. Thus, the tens place digit is confirmed to be 8.

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Question 3

345.792

A car travels at a constant speed of x miles per hour. Which of the following expressions gives the distance in miles, the car will travel in hours?

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

xt gives the distance in miles the car will travel in hours.

The formula for distance when traveling at a constant speed is defined as distance = speed × time. Therefore, if a car is traveling at a speed of x miles per hour for t hours, the distance traveled can be expressed as the product of these two variables, which is xt.

A) x+t
This expression inaccurately adds speed and time together. Distance cannot be calculated by simply summing speed and time, as the units do not correspond to distance. Thus, this choice fails to represent the relationship between these variables correctly.

B) t+x
Similar to choice A, this option also combines time and speed through addition. The result of adding t and x does not yield a value representing distance, as it does not maintain the correct dimensional analysis necessary for distance calculation.

C) xt
This expression accurately calculates distance by multiplying speed (x miles per hour) by time (t hours). The result, xt, represents the total distance traveled in miles, adhering to the fundamental physics formula for distance.

D) (xt)²
This choice squares the product of speed and time, resulting in a unit of distance squared, which does not make sense in the context of calculating distance traveled. The squaring operation misrepresents the relationship between speed, time, and distance, leading to an incorrect interpretation of the distance.

Conclusion
The distance a car travels at a constant speed can be correctly expressed by the product of its speed and the time traveled, represented by the formula xt. The other options either misapply arithmetic operations or fail to maintain the correct dimensional analysis needed to derive a distance measurement. Understanding this relationship is crucial in solving physics problems related to motion.

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Question 4

In the number shown, which of the following is the value of the underlined digit?

Your Answer: Option(s)

Correct Answer: Option(s) B

Rationale

9 X 10 ^ - 2

The underlined digit represents the value of 9 when expressed in scientific notation, specifically indicating that it is multiplied by 10 raised to the power of -2. This notation effectively conveys the number's scale and magnitude in a compact form.

A) 9 X 1 ^ - 2
This choice incorrectly suggests that the value is multiplied by 1 raised to the power of -2, which is equal to 1 regardless of the exponent. Therefore, the expression simplifies to just 9, failing to account for the correct scaling of the number by a power of 10.

B) 9 X 10 ^ - 2
This choice accurately reflects the value of the underlined digit as it indicates that 9 is multiplied by 10 raised to the power of -2, representing a decimal point shift two places to the left (0.09). This expression correctly captures the scientific notation format for the number.

C) 9 X 100^ 2
This option misrepresents the value by suggesting that 9 is multiplied by 100 raised to the power of 2, which equals 9 multiplied by 10,000. This results in a vastly larger number (90,000), which is not reflective of the original underlined digit.

D) 9 X 1.000^ - 2
This choice incorrectly implies that the digit is multiplied by 1.000 raised to the power of -2. Since 1.000 raised to any power remains 1, this would simply reduce to 9, overlooking the necessary scaling factor of 10 that indicates the actual size of the number.

Conclusion
In scientific notation, the expression 9 X 10 ^ - 2 accurately conveys the value represented by the underlined digit, indicating a decimal shift by two places. Other choices fail to reflect the correct exponent and scaling, leading to misinterpretations of the number's true value. Understanding scientific notation is crucial for accurately representing and manipulating numbers in mathematical and scientific contexts.

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Question 5

Which of the following is a composite number?

Your Answer: Option(s)

Correct Answer: Option(s) C

Rationale

27 is a composite number.

A composite number is defined as a positive integer that has at least one divisor other than 1 and itself. Since 27 can be factored into 3 x 9, it meets this criterion, distinguishing it from prime numbers, which have only two divisors.

A) 7
7 is a prime number because it has no divisors other than 1 and itself. The only factors of 7 are 1 and 7, meaning it cannot be classified as a composite number since it does not meet the definition of having additional divisors.

B) 17
Similar to 7, 17 is also a prime number. It has no divisors other than 1 and 17, confirming that it does not qualify as a composite number. Prime numbers are characterized by having exactly two distinct positive divisors.

C) 27
27 is a composite number because it can be expressed as the product of 3 multiplied by 9. Additionally, it has other divisors, including 1, 3, 9, and 27, which confirms its classification as composite due to having more than two positive divisors.

D) 37
37 is a prime number as well, possessing only two divisors: 1 and 37. It cannot be expressed as a product of two smaller positive integers, thus excluding it from being classified as a composite number.

Conclusion
In summary, composite numbers are defined by their multiple divisors, while prime numbers have only two. Among the choices provided, 27 stands out as a composite number, being divisible by factors other than 1 and itself. The other options—7, 17, and 37—are all prime, reinforcing the distinction between these two types of integers.

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20 cases of candy bars need to be sold for the school to make a profit of $900.

The digit in the tens place will be 8.

xt gives the distance in miles the car will travel in hours.

9 X 10 ^ - 2

27 is a composite number.

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