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
John worked at a bookstore for two weeks. The second week he earned 20 percent more than he did the first week. If he earned $300 the second week, how much did he earn the first week?
- A. 240
- B. 250
- C. 280
- D. 380
Correct Answer & Rationale
Correct Answer: B
To determine John’s earnings for the first week, we know that his second week earnings were 20% more than the first week. If he earned $300 in the second week, we can calculate his first week earnings by setting up the equation: Let x be the first week’s earnings. Then, x + 0.2x = 300. This simplifies to 1.2x = 300. Dividing both sides by 1.2 gives x = 250. Option A ($240) is too low, as it would not result in a $300 second week. Option C ($280) would imply a second week earning of $336, which exceeds $300. Option D ($380) is also incorrect as it suggests a second week earning of $456. Thus, $250 is the only viable answer.
To determine John’s earnings for the first week, we know that his second week earnings were 20% more than the first week. If he earned $300 in the second week, we can calculate his first week earnings by setting up the equation: Let x be the first week’s earnings. Then, x + 0.2x = 300. This simplifies to 1.2x = 300. Dividing both sides by 1.2 gives x = 250. Option A ($240) is too low, as it would not result in a $300 second week. Option C ($280) would imply a second week earning of $336, which exceeds $300. Option D ($380) is also incorrect as it suggests a second week earning of $456. Thus, $250 is the only viable answer.
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.
Alexia, Bob, and Comelia recorded the number of pages of books they read last month. Alexia read 135 pages, Bob read 26 pages less than Alexia, and Comelia read 3 and one-half times more pages than Alexia and Bob combined. Which of the following represents the total number of pages that Alexia, Bob, and Comelia read last month?
- A. 3.5(135 + 26)
- B. 3.5[2(135) - 26]
- C. 4.5[2(135) - 26]
- D. 4.5[2(135) + 26]
Correct Answer & Rationale
Correct Answer: C
To determine the total number of pages read, first calculate Bob's pages: he read 135 - 26 = 109 pages. The combined pages of Alexia and Bob is 135 + 109 = 244 pages. Comelia read 3.5 times this total, resulting in 3.5 × 244. Option A incorrectly uses 135 + 26, which does not account for Bob's actual pages read. Option B mistakenly uses a subtraction instead of addition for the combined total. Option D incorrectly adds Bob's pages instead of using the correct combined total for Comelia's calculation. Thus, C accurately represents the total with 3.5(244), leading to the correct final total.
To determine the total number of pages read, first calculate Bob's pages: he read 135 - 26 = 109 pages. The combined pages of Alexia and Bob is 135 + 109 = 244 pages. Comelia read 3.5 times this total, resulting in 3.5 × 244. Option A incorrectly uses 135 + 26, which does not account for Bob's actual pages read. Option B mistakenly uses a subtraction instead of addition for the combined total. Option D incorrectly adds Bob's pages instead of using the correct combined total for Comelia's calculation. Thus, C accurately represents the total with 3.5(244), leading to the correct final total.
3/8 expressed as a percent is
- A. 3.75%
- B. 37.50%
- C. 38%
- D. 38,1/3%
Correct Answer & Rationale
Correct Answer: B
To convert a fraction to a percent, multiply by 100. For 3/8, the calculation is (3 ÷ 8) × 100, which equals 37.5%. This aligns with option B: 37.50%. Option A (3.75%) results from miscalculating the fraction, likely confusing the decimal representation. Option C (38%) rounds up incorrectly, as it does not accurately reflect the precise conversion. Option D (38, 1/3%) misrepresents the fraction by suggesting a value that exceeds the actual percentage, further indicating a misunderstanding of the conversion process. Thus, option B is the only accurate representation of 3/8 as a percent.
To convert a fraction to a percent, multiply by 100. For 3/8, the calculation is (3 ÷ 8) × 100, which equals 37.5%. This aligns with option B: 37.50%. Option A (3.75%) results from miscalculating the fraction, likely confusing the decimal representation. Option C (38%) rounds up incorrectly, as it does not accurately reflect the precise conversion. Option D (38, 1/3%) misrepresents the fraction by suggesting a value that exceeds the actual percentage, further indicating a misunderstanding of the conversion process. Thus, option B is the only accurate representation of 3/8 as a percent.