Sienna has four times as many DVDs as Teri. Robert has half as many DVDs as Teri. If Robert has 32 DVDs, how many DVDs does Sienna have?
- A. 4
- B. 16
- C. 64
- D. 256
Correct Answer & Rationale
Correct Answer: D
To determine how many DVDs Sienna has, start with Robert's count. Since Robert has 32 DVDs and he has half as many as Teri, Teri must have 64 DVDs (32 x 2). Sienna has four times as many DVDs as Teri, so she has 256 DVDs (64 x 4). Option A (4) is incorrect because it underestimates the number of DVDs based on Teri's count. Option B (16) is also incorrect, as it does not align with the calculations derived from Robert's DVDs. Option C (64) mistakenly represents Teri's count rather than Sienna's. Thus, the only valid option reflecting Sienna's total is 256.
To determine how many DVDs Sienna has, start with Robert's count. Since Robert has 32 DVDs and he has half as many as Teri, Teri must have 64 DVDs (32 x 2). Sienna has four times as many DVDs as Teri, so she has 256 DVDs (64 x 4). Option A (4) is incorrect because it underestimates the number of DVDs based on Teri's count. Option B (16) is also incorrect, as it does not align with the calculations derived from Robert's DVDs. Option C (64) mistakenly represents Teri's count rather than Sienna's. Thus, the only valid option reflecting Sienna's total is 256.
Other Related Questions
Which of the following inequalities is true?
- A. 0.7 < 0.1 < 0.11 < 0.101
- B. 0.1 < 0.7 < 0.101 < 0.11
- C. 0.1 < 0.7 < 0.11 < 0.101
- D. 0.1 < 0.101 < 0.11 < 0.7
Correct Answer & Rationale
Correct Answer: D
Option D accurately represents the correct order of the numbers. When comparing the values, 0.1 is the smallest, followed by 0.101, then 0.11, and finally 0.7, which is the largest. Option A is incorrect as it mistakenly places 0.7 as less than both 0.1 and 0.11, which is not true. Option B incorrectly suggests that 0.101 is less than 0.11, which is also inaccurate. Option C places 0.11 before 0.101, misrepresenting their actual values. Thus, D is the only option that correctly orders the numbers from smallest to largest.
Option D accurately represents the correct order of the numbers. When comparing the values, 0.1 is the smallest, followed by 0.101, then 0.11, and finally 0.7, which is the largest. Option A is incorrect as it mistakenly places 0.7 as less than both 0.1 and 0.11, which is not true. Option B incorrectly suggests that 0.101 is less than 0.11, which is also inaccurate. Option C places 0.11 before 0.101, misrepresenting their actual values. Thus, D is the only option that correctly orders the numbers from smallest to largest.
7.50 ÷ 0.125 =
- A. 60
- B. 6
- C. 0.6
- D. 1/6
Correct Answer & Rationale
Correct Answer: A
To solve 7.50 ÷ 0.125, it's helpful to convert the division into a more manageable form. Dividing by 0.125 is the same as multiplying by 8 (since 1 ÷ 0.125 = 8). Therefore, 7.50 × 8 equals 60, confirming option A as the right choice. Option B (6) is incorrect; it underestimates the quotient significantly. Option C (0.6) is also wrong, as it suggests a much smaller result than what is obtained. Lastly, option D (1/6) misrepresents the division entirely, implying a fractional outcome that does not align with the calculations.
To solve 7.50 ÷ 0.125, it's helpful to convert the division into a more manageable form. Dividing by 0.125 is the same as multiplying by 8 (since 1 ÷ 0.125 = 8). Therefore, 7.50 × 8 equals 60, confirming option A as the right choice. Option B (6) is incorrect; it underestimates the quotient significantly. Option C (0.6) is also wrong, as it suggests a much smaller result than what is obtained. Lastly, option D (1/6) misrepresents the division entirely, implying a fractional outcome that does not align with the calculations.
2,3/8 + 5,5/6 =
- A. 7,5/24
- B. 7,4/7
- C. 8,5/24
- D. 8,4/7
Correct Answer & Rationale
Correct Answer: C
To solve 2,3/8 + 5,5/6, first convert the mixed numbers into improper fractions. For 2,3/8, this becomes (2 * 8 + 3)/8 = 19/8. For 5,5/6, it is (5 * 6 + 5)/6 = 35/6. Next, find a common denominator, which is 24. Convert the fractions: 19/8 becomes 57/24, and 35/6 becomes 140/24. Adding these gives 197/24, which converts back to a mixed number as 8,5/24. Options A and B do not match this result. Option D, while close, inaccurately represents the fraction.
To solve 2,3/8 + 5,5/6, first convert the mixed numbers into improper fractions. For 2,3/8, this becomes (2 * 8 + 3)/8 = 19/8. For 5,5/6, it is (5 * 6 + 5)/6 = 35/6. Next, find a common denominator, which is 24. Convert the fractions: 19/8 becomes 57/24, and 35/6 becomes 140/24. Adding these gives 197/24, which converts back to a mixed number as 8,5/24. Options A and B do not match this result. Option D, while close, inaccurately represents the fraction.
6 + 5,1/3 ÷ (6 - 5,1/3) =
- A. 1,1/3
- B. 5,1/3
- C. 16
- D. 17
Correct Answer & Rationale
Correct Answer: C
To solve the equation, first evaluate the expression in the parentheses: \(6 - 5\frac{1}{3}\) equals \(6 - \frac{16}{3} = \frac{18}{3} - \frac{16}{3} = \frac{2}{3}\). Next, compute \(5\frac{1}{3}\) as \(\frac{16}{3}\). The equation now reads \(6 + \frac{16}{3} \div \frac{2}{3}\). Dividing \(\frac{16}{3}\) by \(\frac{2}{3}\) gives \(8\). Adding this to \(6\) results in \(14\), leading to the final answer of \(16\). Option A (1\(\frac{1}{3}\)) is incorrect due to miscalculating the operations. Option B (5\(\frac{1}{3}\)) fails to account for the division correctly. Option D (17) mistakenly adds an extra unit instead of properly evaluating the expression.
To solve the equation, first evaluate the expression in the parentheses: \(6 - 5\frac{1}{3}\) equals \(6 - \frac{16}{3} = \frac{18}{3} - \frac{16}{3} = \frac{2}{3}\). Next, compute \(5\frac{1}{3}\) as \(\frac{16}{3}\). The equation now reads \(6 + \frac{16}{3} \div \frac{2}{3}\). Dividing \(\frac{16}{3}\) by \(\frac{2}{3}\) gives \(8\). Adding this to \(6\) results in \(14\), leading to the final answer of \(16\). Option A (1\(\frac{1}{3}\)) is incorrect due to miscalculating the operations. Option B (5\(\frac{1}{3}\)) fails to account for the division correctly. Option D (17) mistakenly adds an extra unit instead of properly evaluating the expression.