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.
Other Related Questions
165 is what percent of 150?
- A. 95%
- B. 110%
- C. 111%
- D. 115%
Correct Answer & Rationale
Correct Answer: B
To find what percent 165 is of 150, divide 165 by 150 and then multiply by 100. This calculation yields 110%, indicating that 165 is 110% of 150. Option A (95%) underestimates the value, as it suggests 165 is less than 150. Option C (111%) slightly overestimates the percentage, as it does not accurately reflect the calculation. Option D (115%) also exaggerates the value, implying that 165 exceeds 150 by a larger margin than it actually does. Therefore, 110% is the precise representation of 165 in relation to 150.
To find what percent 165 is of 150, divide 165 by 150 and then multiply by 100. This calculation yields 110%, indicating that 165 is 110% of 150. Option A (95%) underestimates the value, as it suggests 165 is less than 150. Option C (111%) slightly overestimates the percentage, as it does not accurately reflect the calculation. Option D (115%) also exaggerates the value, implying that 165 exceeds 150 by a larger margin than it actually does. Therefore, 110% is the precise representation of 165 in relation to 150.
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.
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.
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.