5003 Elementary Education Mathematics Subtest Version 2 Questions

Explanation

<h2>To make a profit of $900, the school needs to sell 20 cases of candy bars.</h2> To determine how many cases must be sold to achieve a $900 profit, we first calculate the total profit per case. Since each case contains 60 bars and the profit per bar is $0.75, the profit per case is 60 x $0.75 = $45. Dividing the desired profit of $900 by the profit per case gives us 900 / 45 = 20 cases. <b>A) 8</b> Selling 8 cases would yield a profit of 8 x $45 = $360, which is significantly less than the required $900. Therefore, this option does not meet the profit goal. <b>B) 12</b> If the school sells 12 cases, the profit would be 12 x $45 = $540. While this is an improvement over option A, it still falls short of the $900 needed. <b>C) 20</b> This option is correct as explained earlier. Selling 20 cases results in a profit of 20 x $45 = $900, precisely meeting the fundraising target. <b>D) 40</b> Selling 40 cases would result in a profit of 40 x $45 = $1,800. While this exceeds the $900 target, it is not the required amount and would indicate selling more than necessary. <b>Conclusion</b> To achieve a profit of $900, the school must sell 20 cases of candy bars. Each case contributes $45 to the profit, so calculating the number of cases needed directly leads to the answer. Options A, B, and D do not meet the required profit target, confirming that 20 cases is the optimal solution for the school's fundraising goal.

Explanation

<h2>The digit in the tens place will be 8.</h2> To form the largest three-digit number between 300 and 700 using the digits 3, 5, 7, and 8, we must start with the largest possible hundreds digit that still meets the criteria. In this case, 5 or 7 can be used as the hundreds digit, but to maximize the number, we choose 5 for the hundreds place, followed by 8 in the tens place, making the number 582. <b>A) 3</b> If 3 is placed in the tens position, the largest possible number we can create is 375, which is significantly smaller than 582. Thus, this choice does not maximize the three-digit number. <b>B) 5</b> Using 5 in the tens place would lead to forming the number 578 if we select 7 for the hundreds place. However, this number is smaller than 582, which is formed by placing 8 in the tens position. Therefore, this option does not yield the largest number. <b>C) 7</b> If we place 7 in the tens position, the largest number we can form would be 587, which is again smaller than 582. Thus, this choice does not yield the largest valid three-digit number under the given constraints. <b>D) 8</b> Choosing 8 for the tens place, with 5 in the hundreds place and 2 in the units place, gives us the number 582. This is the largest number that can be formed using the digits provided, while also satisfying the condition of being greater than 300 and less than 700. <b>Conclusion</b> To maximize the three-digit number within the specified range using the digits 3, 5, 7, and 8, the optimal choice for the tens place is 8. By strategically selecting 5 for the hundreds place and 2 for the units, the largest valid number 582 is achieved, confirming that 8 is indeed the digit in the tens place.

Explanation

<h2>xt gives the distance in miles the car will travel in hours.</h2> The formula for distance when traveling at a constant speed is derived from the relationship between speed, time, and distance, which states that distance equals speed multiplied by time. Therefore, if the car travels at a speed of x miles per hour for t hours, the distance traveled is expressed as xt. <b>A) x+t</b> This expression represents the sum of speed and time, which does not correspond to any physical quantity related to distance. The calculation for distance requires multiplication, not addition, of speed and time. <b>B) t+x</b> Similar to option A, this expression is simply the addition of time and speed. It fails to represent the actual distance traveled since it does not use the correct formula of multiplying speed by time. <b>C) xt</b> This is the correct expression, as it accurately reflects the formula for calculating distance. By multiplying the speed (x miles per hour) by the time (t hours), we derive the total distance traveled by the car in miles. <b>D) (xt)²</b> This expression squares the product of speed and time, which is not relevant for calculating distance. Squaring the result would yield a unit of distance squared, which does not apply to this scenario and misrepresents the relationship between speed, time, and distance. <b>Conclusion</b> Distance traveled by a vehicle can be calculated using the straightforward formula distance = speed × time. In this case, the expression xt correctly represents the distance a car traveling at x miles per hour will cover in t hours. The other options fail to adhere to this fundamental principle, highlighting the importance of using the correct mathematical operations to derive meaningful physical quantities.

Explanation

<h2>9 × 10 ^ - 2 represents the value of the underlined digit in the number 345.792.</h2> The underlined digit in the given number is the second digit after the decimal point, which is 9. In decimal notation, this digit is in the hundredths place, corresponding to a value of 0.09, which can be expressed as 9 × 10 ^ - 2. <b>A) 9 × 1 ^ - 2</b> This expression evaluates to 9, as any number raised to the power of zero is 1. Therefore, it does not represent the value of the underlined digit in the number 345.792. <b>B) 9 × 10 ^ - 2</b> This is the correct choice, as it accurately represents the value of the underlined digit '9' in the hundredths place. It equals 0.09, which correctly corresponds to the position of the digit in the decimal number. <b>C) 9 × 100 ^ 2</b> This expression equals 9 × 10,000, which is 90,000. This is far greater than the value of the underlined digit and therefore does not represent its value. <b>D) 9 × 1.000 ^ - 2</b> This expression simplifies to 9 × 1, which equals 9. While it is a numerical value, it does not correspond to the underlined digit in the context of its decimal placement. <b>Conclusion</b> The value of the underlined digit '9' in the number 345.792 is best represented by the expression 9 × 10 ^ - 2, which indicates its position in the hundredths place as 0.09. All other options either misrepresent the value or yield results that do not align with the context of the number. Understanding the significance of decimal placement is crucial in accurately identifying values in numerical expressions.

Explanation

<h2>27 is a composite number.</h2> A composite number is defined as a natural number greater than one that has more than two distinct positive divisors. In this case, 27 can be divided by 1, 3, 9, and 27, making it a composite number, while the other options are prime numbers. <b>A) 7</b> 7 is a prime number because it has exactly two distinct positive divisors: 1 and 7 itself. It cannot be divided evenly by any other numbers, which disqualifies it from being a composite number. <b>B) 17</b> 17 is also a prime number with only two distinct positive divisors: 1 and 17. Like 7, it cannot be factored into smaller natural numbers, confirming it is not composite. <b>C) 27</b> 27 is a composite number as it has more than two factors: 1, 3, 9, and 27. This means it can be expressed as a product of smaller integers (3 × 3 × 3), thereby fitting the definition of a composite number. <b>D) 37</b> 37 is a prime number as well, having only two positive divisors, 1 and 37. It cannot be factored into smaller natural numbers, thus it does not meet the criteria for being a composite number. <b>Conclusion</b> Composite numbers are characterized by having more than two distinct positive divisors. Among the choices provided, only 27 satisfies this condition, with its factors including 1, 3, 9, and 27. The other options, 7, 17, and 37, are all prime numbers and therefore do not qualify as composite. Understanding these classifications is essential in number theory and its applications.