5003 Elementary Education Mathematics Subtest Version 4 Questions

Explanation

<h2>Three cans of Brand A paint are needed to cover the walls.</h2> To determine the total coverage required, we first calculate the area of both walls and then divide by the coverage per can of paint. The areas of the rectangle and triangle combine to necessitate three cans of paint, given the coverage of 200 square feet per can. <b>A) 2</b> Choosing two cans would provide a total coverage of 400 square feet. However, the total area of the walls exceeds this coverage, so two cans are insufficient for complete coverage. <b>B) 3</b> This choice accurately reflects the total area calculation. The rectangle's area is 495 square feet (30 ft × 16.5 ft), and the triangle's area is 96 square feet (0.5 × 16 ft × 12 ft), giving a combined area of 591 square feet. Dividing this by the 200 square feet covered by each can shows that three cans are necessary to fully cover the walls. <b>C) 4</b> While four cans would provide 800 square feet of coverage, which exceeds the required area, it is unnecessary. The calculation confirms that only three cans are needed, making this choice excessive and incorrect. <b>D) 5</b> Five cans would cover 1000 square feet, which is significantly more than what is needed. This choice is not only excessive but also misrepresents the actual requirement based on the area to be painted. <b>Conclusion</b> To fully paint the two walls, calculating the areas and dividing by the coverage provided by each can leads to the conclusion that three cans of Brand A paint are necessary. Options A, C, and D do not accurately reflect the area calculations and thus do not serve as valid solutions. The choice of three cans is the most efficient and accurate for this painting task.

Explanation

<h2>It has 6 and 15 as factors.</h2> 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 number, the result is a whole number without any remainder. <b>A) It has 10 as a multiple</b> While 10 is a multiple of 90, this statement is misleading as it implies the reverse. Instead, 90 is a multiple of 10, meaning that 10 can be evenly multiplied to produce 90, rather than the other way around. <b>C) It has four distinct prime factors</b> The prime factorization of 90 is 2 × 3 × 3 × 5, which includes only three distinct prime factors: 2, 3, and 5. Therefore, this statement is false, as it overstates the count of distinct prime factors. <b>D) It is divisible by 9 but not by 18</b> This statement is incorrect because 90 is divisible by both 9 and 18. When 90 is divided by 9, the result is 10, and when divided by 18, the result is 5, confirming that 90 is divisible by both numbers. <b>Conclusion</b> In summary, the valid statement regarding the number 90 is that it has 6 and 15 as factors, clearly demonstrating its divisibility by these numbers. The other choices either misinterpret the relationships of multiples and factors or inaccurately assess the number of distinct prime factors, reinforcing that understanding the fundamentals of factors and multiples is essential in number theory.

Explanation

<h2>1 thousand, 2 hundreds, and 60 tens is a decomposition of the number 1260.</h2> This decomposition breaks down 1260 into its constituent place values, clearly illustrating the contributions of each position (thousands, hundreds, and tens) to the overall number. <b>A) 12 hundreds and 6 tens</b> This choice represents a total of 1200 (12 hundreds) plus 60 (6 tens), which sums to 1260. However, it does not accurately depict the breakdown into thousands, hundreds, and tens as required by the decomposition format. <b>B) 11 hundreds and 60 tens</b> Calculating this option gives 1100 (11 hundreds) plus 600 (60 tens), resulting in a total of 1700. This exceeds the target number of 1260 and fails to correctly decompose it into the required components. <b>C) 1 thousand and 26 hundreds</b> This choice translates to 1000 (1 thousand) plus 2600 (26 hundreds), which totals 3600. Again, this exceeds the target number and does not reflect a valid decomposition of 1260. <b>D) 1 thousand, 2 hundreds, and 60 tens</b> This option accurately breaks down the number 1260 into its respective components: 1000 (1 thousand) + 200 (2 hundreds) + 60 (60 tens), which equals 1260. This decomposition correctly represents the number in terms of its place values. <b>Conclusion</b> The valid decomposition of the number 1260 is best represented by the breakdown of 1 thousand, 2 hundreds, and 60 tens. Other options either misrepresent the number or exceed the total, emphasizing the importance of accurate place value representation in numerical decomposition.

Explanation

<h2>The student-to-teacher ratio for the math classes during first period is 24 to 1.</h2> To find the student-to-teacher ratio, divide the total number of students by the total number of teachers. In this case, 288 students divided by 12 teachers yields a ratio of 24 students for every teacher. <b>A) 12 to 1</b> This option suggests that there are 12 students for each teacher. However, when dividing the total number of students (288) by the number of teachers (12), the calculation shows that each teacher actually oversees 24 students, not 12. This option represents a significant underestimation of the actual ratio. <b>B) 24 to 1</b> This is the correct choice, as it accurately reflects the calculation of 288 students divided by 12 teachers. This results in a student-to-teacher ratio of 24 students per teacher, which is appropriate for a classroom setting. <b>C) 36 to 1</b> Choosing 36 to 1 implies that each teacher would be responsible for 36 students. However, calculating 288 students divided by 36 yields only 8 teachers, which is fewer than the 12 teachers available. This indicates a misunderstanding of the total student population assigned to each teacher. <b>D) 48 to 1</b> This option suggests an even higher ratio of 48 students per teacher. Performing the division of 288 students by 48 would indicate only 6 teachers are needed, which again does not align with the 12 teachers present. This choice misrepresents the actual distribution of students among teachers. <b>Conclusion</b> The student-to-teacher ratio in this scenario is determined by dividing the total number of students by the number of teachers, resulting in a ratio of 24 to 1. This means each teacher is responsible for 24 students during first period, allowing for a balanced instructional environment. The other options incorrectly represent the relationship between the number of students and teachers, leading to misleading ratios.

Explanation

<h2>1085 divided by 12 equals 90.5.</h2> The calculation of 1085 divided by 12 yields exactly 90.5. This result is derived from performing the division operation, which accurately reflects the quotient of these two numbers. <b>A) 90</b> This choice represents an integer value that is the approximate result of the division but fails to account for the decimal remainder. Since 1085 divided by 12 does not result in a whole number, this answer is incorrect. <b>B) 90{5/1085}</b> This option mistakenly suggests a fraction that implies a very small addition to 90, which does not correctly represent the actual decimal result of the division. The notation used here is confusing and does not properly express the outcome of the division, making it incorrect. <b>C) 90{5/12}</b> While this choice correctly indicates a fraction, it misrepresents the division result. The term "90{5/12}" suggests that the remainder is expressed in terms of 12 rather than accurately reflecting the decimal representation of the quotient from the division of 1085 by 12. Thus, this choice is also incorrect. <b>D) 90.5</b> This is the correct answer as it accurately reflects the result of dividing 1085 by 12. The calculation confirms that 90.5 is the exact quotient, including both the integer part and the decimal fraction. <b>Conclusion</b> The division of 1085 by 12 results in 90.5, which is the only choice that correctly captures the complete value of the quotient. The other options either provide inaccurate approximations or misrepresent the mathematical computation involved. Understanding the correct result is critical for accurate calculations in various mathematical and real-world applications.