6[4 + 2(1 - 3)] =
- B. 20
- C. 24
- D. 48
Correct Answer & Rationale
Correct Answer: A
To solve the expression 6[4 + 2(1 - 3)], begin by simplifying inside the brackets. The calculation within the parentheses, 1 - 3, equals -2. Next, multiply by 2 to get -4. Now, the expression inside the brackets is 4 - 4, which simplifies to 0. Finally, multiplying 6 by 0 results in 0. Option B (20), C (24), and D (48) arise from miscalculations, such as incorrectly handling the order of operations or not simplifying the expression fully. None of these options account for the zero outcome from the calculations.
To solve the expression 6[4 + 2(1 - 3)], begin by simplifying inside the brackets. The calculation within the parentheses, 1 - 3, equals -2. Next, multiply by 2 to get -4. Now, the expression inside the brackets is 4 - 4, which simplifies to 0. Finally, multiplying 6 by 0 results in 0. Option B (20), C (24), and D (48) arise from miscalculations, such as incorrectly handling the order of operations or not simplifying the expression fully. None of these options account for the zero outcome from the calculations.
Other Related Questions
The large square above has area 1 and is divided into 25 squares of equal area. Which of the following represents the area of the shaded region?
- A. 0.8
- B. 0.16
- C. 0.24
- D. 0.32
Correct Answer & Rationale
Correct Answer: D
In a large square with an area of 1, each of the 25 smaller squares has an area of \( \frac{1}{25} = 0.04 \). To find the area of the shaded region, count the number of shaded squares. If there are 8 shaded squares, then the area of the shaded region is \( 8 \times 0.04 = 0.32 \). Option A (0.8) is incorrect as it exceeds the total area of the large square. Option B (0.16) represents 4 shaded squares, which is not consistent with the given information. Option C (0.24) suggests 6 shaded squares, which also does not match. Thus, the area of the shaded region is accurately represented by option D, 0.32.
In a large square with an area of 1, each of the 25 smaller squares has an area of \( \frac{1}{25} = 0.04 \). To find the area of the shaded region, count the number of shaded squares. If there are 8 shaded squares, then the area of the shaded region is \( 8 \times 0.04 = 0.32 \). Option A (0.8) is incorrect as it exceeds the total area of the large square. Option B (0.16) represents 4 shaded squares, which is not consistent with the given information. Option C (0.24) suggests 6 shaded squares, which also does not match. Thus, the area of the shaded region is accurately represented by option D, 0.32.
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.
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.
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.