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.
Other Related Questions
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.
50.50 ÷ 0.25
- A. 202
- B. 2.2
- C. 2.02
- D. 0.22
Correct Answer & Rationale
Correct Answer: A
To solve 50.50 ÷ 0.25, converting the division into a simpler form is helpful. Dividing both numbers by 0.25 effectively transforms the problem into 50.50 ÷ 0.25 = 50.50 × 4, which equals 202. Option B (2.2) is incorrect as it misrepresents the scale of the division, resulting from a misunderstanding of decimal placement. Option C (2.02) also miscalculates the division, likely stemming from incorrect multiplication or division steps. Option D (0.22) is far too low, indicating a significant error in understanding the relationship between the dividend and divisor.
To solve 50.50 ÷ 0.25, converting the division into a simpler form is helpful. Dividing both numbers by 0.25 effectively transforms the problem into 50.50 ÷ 0.25 = 50.50 × 4, which equals 202. Option B (2.2) is incorrect as it misrepresents the scale of the division, resulting from a misunderstanding of decimal placement. Option C (2.02) also miscalculates the division, likely stemming from incorrect multiplication or division steps. Option D (0.22) is far too low, indicating a significant error in understanding the relationship between the dividend and divisor.
Kayla has a stack of photographs that is 20 centimeters high. If each photograph is 0.04 cm thick, how many photos are there in the stack?
- A. 8
- B. 50
- C. 80
- D. 500
Correct Answer & Rationale
Correct Answer: D
To determine the number of photographs in the stack, divide the total height of the stack by the thickness of each photograph. The stack is 20 cm high and each photograph is 0.04 cm thick. Calculating this gives: 20 cm ÷ 0.04 cm = 500 photographs. Option A (8) is incorrect as it underestimates the total by not accounting for the thickness appropriately. Option B (50) also miscalculates the total, suggesting a much smaller number of photographs. Option C (80) is an overestimation, failing to consider the correct division of height by thickness. Only option D (500) accurately reflects the calculation, confirming the total number of photographs in the stack.
To determine the number of photographs in the stack, divide the total height of the stack by the thickness of each photograph. The stack is 20 cm high and each photograph is 0.04 cm thick. Calculating this gives: 20 cm ÷ 0.04 cm = 500 photographs. Option A (8) is incorrect as it underestimates the total by not accounting for the thickness appropriately. Option B (50) also miscalculates the total, suggesting a much smaller number of photographs. Option C (80) is an overestimation, failing to consider the correct division of height by thickness. Only option D (500) accurately reflects the calculation, confirming the total number of photographs in the stack.
Multiplying a certain nonzero number by 0.01 gives the same result as dividing the number by
- A. 100
- B. 10
- C. 1/10
- D. 1/100
Correct Answer & Rationale
Correct Answer: A
When a nonzero number is multiplied by 0.01, it is equivalent to dividing that number by 100. This is because multiplying by 0.01 (or 1/100) reduces the value of the number to one-hundredth of its original amount. Option B (10) is incorrect as dividing by 10 would yield a larger result than multiplying by 0.01. Option C (1/10) is also wrong because dividing by 1/10 actually increases the number, contrary to the operation of multiplying by 0.01. Option D (1/100) might seem close, but it represents the multiplication factor rather than the division needed. Thus, dividing by 100 accurately reflects the operation of multiplying by 0.01.
When a nonzero number is multiplied by 0.01, it is equivalent to dividing that number by 100. This is because multiplying by 0.01 (or 1/100) reduces the value of the number to one-hundredth of its original amount. Option B (10) is incorrect as dividing by 10 would yield a larger result than multiplying by 0.01. Option C (1/10) is also wrong because dividing by 1/10 actually increases the number, contrary to the operation of multiplying by 0.01. Option D (1/100) might seem close, but it represents the multiplication factor rather than the division needed. Thus, dividing by 100 accurately reflects the operation of multiplying by 0.01.