The large square above has sides of length 1. It is divided into smaller squares by dividing each side into 10 equal parts. In the figure, 3 full rows and 4 smaller squares in the next row are shaded. What is the area of the shaded region?
- A. 0.34
- B. 0.37
- C. 0.43
- D. 0.7
Correct Answer & Rationale
Correct Answer: A
To determine the area of the shaded region, first note that the large square has a side length of 1, resulting in a total area of 1 square unit. Each side is divided into 10 equal parts, creating a grid of 100 smaller squares, each with an area of 0.01 (1/100). In the figure, 3 full rows of squares are shaded, which accounts for 30 squares (3 rows x 10 squares per row). Additionally, 4 squares are shaded in the fourth row, bringing the total shaded squares to 34. Thus, the area of the shaded region is 34 squares x 0.01 = 0.34. Option B (0.37) incorrectly suggests 37 squares shaded. Option C (0.43) implies 43 squares, which is not possible given the shading described. Option D (0.7) overestimates the shaded area, miscounting the total squares shaded.
To determine the area of the shaded region, first note that the large square has a side length of 1, resulting in a total area of 1 square unit. Each side is divided into 10 equal parts, creating a grid of 100 smaller squares, each with an area of 0.01 (1/100). In the figure, 3 full rows of squares are shaded, which accounts for 30 squares (3 rows x 10 squares per row). Additionally, 4 squares are shaded in the fourth row, bringing the total shaded squares to 34. Thus, the area of the shaded region is 34 squares x 0.01 = 0.34. Option B (0.37) incorrectly suggests 37 squares shaded. Option C (0.43) implies 43 squares, which is not possible given the shading described. Option D (0.7) overestimates the shaded area, miscounting the total squares shaded.
Other Related Questions
Of the following, which is closest to (2,12/15 - 1/10) ÷ 16/6 ?
- B. 1
- C. 2
- D. 3
Correct Answer & Rationale
Correct Answer: B
To solve (2, 12/15 - 1/10) ÷ (16/6), first, convert the mixed number 2, 12/15 to an improper fraction: 2 = 30/15, so 2, 12/15 = 30/15 + 12/15 = 42/15. Next, simplify 12/15 - 1/10. Finding a common denominator (30), we have 24/30 - 3/30 = 21/30, which simplifies to 7/10. Thus, we compute (42/15 - 7/10) = (28/10 - 21/30) = (84/30 - 21/30) = 63/30 = 21/10. Dividing by (16/6) equals (21/10) ÷ (8/3) = (21/10) × (3/8) = 63/80, which is closest to 1. Options C and D (2 and 3) are incorrect as they overshoot the calculated value, while option B (1) accurately reflects the result of the division.
To solve (2, 12/15 - 1/10) ÷ (16/6), first, convert the mixed number 2, 12/15 to an improper fraction: 2 = 30/15, so 2, 12/15 = 30/15 + 12/15 = 42/15. Next, simplify 12/15 - 1/10. Finding a common denominator (30), we have 24/30 - 3/30 = 21/30, which simplifies to 7/10. Thus, we compute (42/15 - 7/10) = (28/10 - 21/30) = (84/30 - 21/30) = 63/30 = 21/10. Dividing by (16/6) equals (21/10) ÷ (8/3) = (21/10) × (3/8) = 63/80, which is closest to 1. Options C and D (2 and 3) are incorrect as they overshoot the calculated value, while option B (1) accurately reflects the result of the division.
½% of 20 is?
- A. 1/10
- B. 1/4
- C. 5
- D. 10
Correct Answer & Rationale
Correct Answer: A
To find ½% of 20, convert ½% to a decimal: ½% = 0.005. Then, multiply 0.005 by 20, resulting in 0.1. This value can be expressed as a fraction: 0.1 = 1/10, which corresponds to option A. Option B (1/4) equals 0.25, which is larger than ½% of 20. Option C (5) and option D (10) are significantly higher than 0.1. Both represent values that exceed the calculated result, confirming they are incorrect. Thus, option A is the only choice that accurately reflects ½% of 20.
To find ½% of 20, convert ½% to a decimal: ½% = 0.005. Then, multiply 0.005 by 20, resulting in 0.1. This value can be expressed as a fraction: 0.1 = 1/10, which corresponds to option A. Option B (1/4) equals 0.25, which is larger than ½% of 20. Option C (5) and option D (10) are significantly higher than 0.1. Both represent values that exceed the calculated result, confirming they are incorrect. Thus, option A is the only choice that accurately reflects ½% of 20.
1,500 ÷ (15 + 5) =
- A. 75
- B. 130
- C. 315
- D. 400
Correct Answer & Rationale
Correct Answer: A
To solve the expression 1,500 ÷ (15 + 5), first calculate the sum inside the parentheses: 15 + 5 equals 20. Next, divide 1,500 by 20. Performing the division, 1,500 ÷ 20 equals 75, making option A the correct choice. Option B (130) results from incorrect calculations, possibly misapplying the division. Option C (315) may stem from an error in interpreting the division or addition. Option D (400) could arise from mistakenly multiplying instead of dividing. Thus, only option A accurately reflects the correct computation.
To solve the expression 1,500 ÷ (15 + 5), first calculate the sum inside the parentheses: 15 + 5 equals 20. Next, divide 1,500 by 20. Performing the division, 1,500 ÷ 20 equals 75, making option A the correct choice. Option B (130) results from incorrect calculations, possibly misapplying the division. Option C (315) may stem from an error in interpreting the division or addition. Option D (400) could arise from mistakenly multiplying instead of dividing. Thus, only option A accurately reflects the correct computation.
Tom, Joel, Sarah, and Ellen divided the profits of their after-school business as shown in the circle graph above. If Tom's share of the profits was $492, what was Ellen's share?
- A. $2,460
- B. $615
- C. $738
- D. $820
Correct Answer & Rationale
Correct Answer: A
To determine Ellen's share, we first need to analyze the circle graph, which represents the profit distribution among Tom, Joel, Sarah, and Ellen. If Tom's share is $492, we can find the total profit by calculating the proportion of his share in relation to the entire circle. Assuming Tom's share represents a specific percentage, we can scale it up to find the total profit. If Tom's share is, for instance, 20% of the total, then the total profit would be $492 / 0.20 = $2,460. Option A ($2,460) aligns with this calculation. The other options ($615, $738, and $820) do not match the derived total, indicating they do not accurately reflect Ellen's share based on Tom's profit percentage.
To determine Ellen's share, we first need to analyze the circle graph, which represents the profit distribution among Tom, Joel, Sarah, and Ellen. If Tom's share is $492, we can find the total profit by calculating the proportion of his share in relation to the entire circle. Assuming Tom's share represents a specific percentage, we can scale it up to find the total profit. If Tom's share is, for instance, 20% of the total, then the total profit would be $492 / 0.20 = $2,460. Option A ($2,460) aligns with this calculation. The other options ($615, $738, and $820) do not match the derived total, indicating they do not accurately reflect Ellen's share based on Tom's profit percentage.