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
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.
What is 0.3 percent of 90?
- A. 0.027
- B. 0.27
- C. 0.3
- D. 2.7
Correct Answer & Rationale
Correct Answer: B
To find 0.3 percent of 90, convert the percentage to a decimal by dividing by 100, resulting in 0.003. Then, multiply 0.003 by 90, yielding 0.27. Option A (0.027) is too small, as it miscalculates the multiplication. Option C (0.3) represents the percentage itself, not the calculated value of 0.3 percent of 90. Option D (2.7) is ten times larger than the correct answer, indicating a misunderstanding of the percent calculation. Thus, B (0.27) accurately represents 0.3 percent of 90.
To find 0.3 percent of 90, convert the percentage to a decimal by dividing by 100, resulting in 0.003. Then, multiply 0.003 by 90, yielding 0.27. Option A (0.027) is too small, as it miscalculates the multiplication. Option C (0.3) represents the percentage itself, not the calculated value of 0.3 percent of 90. Option D (2.7) is ten times larger than the correct answer, indicating a misunderstanding of the percent calculation. Thus, B (0.27) accurately represents 0.3 percent of 90.
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%) is incorrect as it underestimates the relationship between the two numbers. Option C (111%) slightly overestimates the value, while Option D (115%) significantly exaggerates it. Each of these options fails to accurately represent the proportion of 165 to 150, reinforcing that 110% is the precise measure of this relationship.
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%) is incorrect as it underestimates the relationship between the two numbers. Option C (111%) slightly overestimates the value, while Option D (115%) significantly exaggerates it. Each of these options fails to accurately represent the proportion of 165 to 150, reinforcing that 110% is the precise measure of this relationship.
4/9 (3/16 - 1/12) =
- A. 5/108
- B. 5/48
- C. 2/9
- D. 20/48
Correct Answer & Rationale
Correct Answer: A
To solve \( \frac{4}{9} \left( \frac{3}{16} - \frac{1}{12} \right) \), first calculate \( \frac{3}{16} - \frac{1}{12} \). Finding a common denominator (48), we convert the fractions: \( \frac{3}{16} = \frac{9}{48} \) and \( \frac{1}{12} = \frac{4}{48} \). Thus, \( \frac{9}{48} - \frac{4}{48} = \frac{5}{48} \). Next, multiply \( \frac{4}{9} \) by \( \frac{5}{48} \): \[ \frac{4 \times 5}{9 \times 48} = \frac{20}{432} = \frac{5}{108} \] Option B (5/48) is incorrect as it misrepresents the multiplication step. Option C (2/9) ignores the subtraction and multiplication entirely. Option D (20/48) fails to simplify the fraction correctly.
To solve \( \frac{4}{9} \left( \frac{3}{16} - \frac{1}{12} \right) \), first calculate \( \frac{3}{16} - \frac{1}{12} \). Finding a common denominator (48), we convert the fractions: \( \frac{3}{16} = \frac{9}{48} \) and \( \frac{1}{12} = \frac{4}{48} \). Thus, \( \frac{9}{48} - \frac{4}{48} = \frac{5}{48} \). Next, multiply \( \frac{4}{9} \) by \( \frac{5}{48} \): \[ \frac{4 \times 5}{9 \times 48} = \frac{20}{432} = \frac{5}{108} \] Option B (5/48) is incorrect as it misrepresents the multiplication step. Option C (2/9) ignores the subtraction and multiplication entirely. Option D (20/48) fails to simplify the fraction correctly.