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.
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.
3 × (1/2 + 1/3) =
- A. 2,1/2
- B. 2,5/6
- C. 3,1/6
- D. 3,5/6
Correct Answer & Rationale
Correct Answer: A
To solve 3 × (1/2 + 1/3), first find a common denominator for the fractions 1/2 and 1/3, which is 6. This gives us (3/6 + 2/6) = 5/6. Multiplying by 3 results in 3 × (5/6) = 15/6, which simplifies to 2 1/2 (Option A). Option B (2 5/6) incorrectly adds an extra fraction. Option C (3 1/6) miscalculates the multiplication. Option D (3 5/6) also misinterprets the original problem, leading to an incorrect total. Thus, only Option A accurately represents the solution.
To solve 3 × (1/2 + 1/3), first find a common denominator for the fractions 1/2 and 1/3, which is 6. This gives us (3/6 + 2/6) = 5/6. Multiplying by 3 results in 3 × (5/6) = 15/6, which simplifies to 2 1/2 (Option A). Option B (2 5/6) incorrectly adds an extra fraction. Option C (3 1/6) miscalculates the multiplication. Option D (3 5/6) also misinterprets the original problem, leading to an incorrect total. Thus, only Option A accurately represents the solution.
1 is 3 percent of what number?
- A. 1/3
- B. 3
- C. 30
- D. 33,1/3
Correct Answer & Rationale
Correct Answer: D
To find the number of which 1 is 3 percent, we set up the equation: 1 = 0.03 * x. Solving for x gives x = 1 / 0.03, which equals 33.33 (or 33 1/3). Option A (1/3) is incorrect as it represents a much smaller value, specifically 0.33. Option B (3) misinterprets the percentage, suggesting that 1 is 33.33% of 3, which is not accurate. Option C (30) also fails, as 3% of 30 is 0.9, not 1. Thus, only option D correctly identifies the number as 33 1/3.
To find the number of which 1 is 3 percent, we set up the equation: 1 = 0.03 * x. Solving for x gives x = 1 / 0.03, which equals 33.33 (or 33 1/3). Option A (1/3) is incorrect as it represents a much smaller value, specifically 0.33. Option B (3) misinterprets the percentage, suggesting that 1 is 33.33% of 3, which is not accurate. Option C (30) also fails, as 3% of 30 is 0.9, not 1. Thus, only option D correctly identifies the number as 33 1/3.