Which of the following numbers is closest to 1?
- A. 4/5
- B. 5/4
- C. 5/6
- D. 6/5
Correct Answer & Rationale
Correct Answer: C
To determine which number is closest to 1, we can convert each option to decimal form: A: 4/5 = 0.8, which is 0.2 away from 1. B: 5/4 = 1.25, which is 0.25 away from 1. C: 5/6 ≈ 0.833, which is approximately 0.167 away from 1. D: 6/5 = 1.2, which is 0.2 away from 1. Among these, 5/6 is the closest to 1, as it has the smallest difference from 1 compared to the other options. The other fractions either exceed or fall short of 1 by a larger margin.
To determine which number is closest to 1, we can convert each option to decimal form: A: 4/5 = 0.8, which is 0.2 away from 1. B: 5/4 = 1.25, which is 0.25 away from 1. C: 5/6 ≈ 0.833, which is approximately 0.167 away from 1. D: 6/5 = 1.2, which is 0.2 away from 1. Among these, 5/6 is the closest to 1, as it has the smallest difference from 1 compared to the other options. The other fractions either exceed or fall short of 1 by a larger margin.
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%) 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.
Harriet took 48 minutes to ride her bike the distance from her house to the town library. If she rode at a constant rate, what fraction of the total distance did she ride in the first 12 minutes?
- A. 1/4
- B. 1/3
- C. 1/2
- D. 3/4
Correct Answer & Rationale
Correct Answer: A
To determine the fraction of the total distance Harriet rode in the first 12 minutes, we start by recognizing that she took 48 minutes for the entire trip. Riding at a constant rate means that her distance covered is proportional to the time spent riding. In 12 minutes, which is one-fourth of the total 48 minutes, she would have covered one-fourth of the total distance. Thus, the fraction of the total distance she rode in the first 12 minutes is 1/4. Options B (1/3), C (1/2), and D (3/4) misrepresent the proportion of time to total time. Each suggests a greater fraction than what corresponds to 12 minutes relative to 48 minutes, leading to incorrect conclusions about the distance covered.
To determine the fraction of the total distance Harriet rode in the first 12 minutes, we start by recognizing that she took 48 minutes for the entire trip. Riding at a constant rate means that her distance covered is proportional to the time spent riding. In 12 minutes, which is one-fourth of the total 48 minutes, she would have covered one-fourth of the total distance. Thus, the fraction of the total distance she rode in the first 12 minutes is 1/4. Options B (1/3), C (1/2), and D (3/4) misrepresent the proportion of time to total time. Each suggests a greater fraction than what corresponds to 12 minutes relative to 48 minutes, leading to incorrect conclusions about the distance covered.
Alexia bought a book that is 252 pages long. She read the book in 3 days. The first day, she read 1/2 of the book's pages, the second day, she read 1/3 of the book's pages, and the third day she read all the remaining pages. How many pages did Alexia read the third day?
- A. 3200%
- B. 3600%
- C. 4000%
- D. 4200%
Correct Answer & Rationale
Correct Answer: D
To determine how many pages Alexia read on the third day, we first calculate the pages read on the first two days. On the first day, she read half of 252 pages, which is 126 pages. On the second day, she read one-third, totaling 84 pages. Adding these gives 210 pages read over the first two days. Thus, the remaining pages for the third day are 252 - 210 = 42 pages. Options A, B, and C do not relate to the total pages read, as they present percentages rather than the actual number of pages. The correct choice reflects the accurate calculation of pages read on the final day.
To determine how many pages Alexia read on the third day, we first calculate the pages read on the first two days. On the first day, she read half of 252 pages, which is 126 pages. On the second day, she read one-third, totaling 84 pages. Adding these gives 210 pages read over the first two days. Thus, the remaining pages for the third day are 252 - 210 = 42 pages. Options A, B, and C do not relate to the total pages read, as they present percentages rather than the actual number of pages. The correct choice reflects the accurate calculation of pages read on the final day.
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.