The fraction x/24 is equal to 0.75. What is the value of x?
- A. 3
- B. 6
- C. 9
- D. 18
Correct Answer & Rationale
Correct Answer: D
To find the value of x in the equation x/24 = 0.75, we start by converting 0.75 to a fraction, which is 75/100 or 3/4. Setting the two fractions equal gives us x/24 = 3/4. Cross-multiplying leads to 4x = 72. Dividing both sides by 4 results in x = 18. Option A (3) is too low; substituting it back yields 3/24 = 0.125. Option B (6) also falls short, as 6/24 = 0.25. Option C (9) gives 9/24 = 0.375, still incorrect. Only option D (18) satisfies the original equation, confirming its validity.
To find the value of x in the equation x/24 = 0.75, we start by converting 0.75 to a fraction, which is 75/100 or 3/4. Setting the two fractions equal gives us x/24 = 3/4. Cross-multiplying leads to 4x = 72. Dividing both sides by 4 results in x = 18. Option A (3) is too low; substituting it back yields 3/24 = 0.125. Option B (6) also falls short, as 6/24 = 0.25. Option C (9) gives 9/24 = 0.375, still incorrect. Only option D (18) satisfies the original equation, confirming its validity.
Other Related Questions
60 ÷ 3/3 =
- A. 20
- B. 21
- C. 23
- D. 24
Correct Answer & Rationale
Correct Answer: A
To solve 60 ÷ 3/3, first simplify the expression. Dividing by a fraction involves multiplying by its reciprocal. Therefore, 3/3 equals 1, and dividing by 1 does not change the value. Thus, the equation simplifies to 60 ÷ 1, which equals 60. Now, let's analyze the options: A: 20 is incorrect as it does not represent the result of the division. B: 21 is also incorrect, being too low compared to the actual value. C: 23 is incorrect for the same reason, as it underestimates the result. D: 24 is incorrect and does not reflect the correct division outcome. The only accurate interpretation leads to the conclusion that 60 divided by 1 remains 60.
To solve 60 ÷ 3/3, first simplify the expression. Dividing by a fraction involves multiplying by its reciprocal. Therefore, 3/3 equals 1, and dividing by 1 does not change the value. Thus, the equation simplifies to 60 ÷ 1, which equals 60. Now, let's analyze the options: A: 20 is incorrect as it does not represent the result of the division. B: 21 is also incorrect, being too low compared to the actual value. C: 23 is incorrect for the same reason, as it underestimates the result. D: 24 is incorrect and does not reflect the correct division outcome. The only accurate interpretation leads to the conclusion that 60 divided by 1 remains 60.
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.
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.
A record store sold 100 copies of a CD in January. In February, the store's sales of the CD increased by 10 percent over the January sales. In March, the store sold 20 percent more copies of the CD than it sold in February. How many copies of the CD did the store sell in March?
- A. 120
- B. 122
- C. 130
- D. 132
Correct Answer & Rationale
Correct Answer: D
To find the number of CDs sold in March, start with January's sales of 100 copies. February's sales increased by 10%, resulting in 100 + (10% of 100) = 110 copies sold. In March, the store sold 20% more than February's sales: 110 + (20% of 110) = 110 + 22 = 132 copies. Option A (120) incorrectly assumes a lower percentage increase in February. Option B (122) miscalculates the increase in March. Option C (130) underestimates the sales for March by not applying the correct percentage increase. Thus, the accurate calculation leads to 132 copies sold in March.
To find the number of CDs sold in March, start with January's sales of 100 copies. February's sales increased by 10%, resulting in 100 + (10% of 100) = 110 copies sold. In March, the store sold 20% more than February's sales: 110 + (20% of 110) = 110 + 22 = 132 copies. Option A (120) incorrectly assumes a lower percentage increase in February. Option B (122) miscalculates the increase in March. Option C (130) underestimates the sales for March by not applying the correct percentage increase. Thus, the accurate calculation leads to 132 copies sold in March.