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
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.
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.
Linda has borrowed 8 more books than Susan from the school library. Richard has borrowed half as many books as Linda has. If Richard has borrowed 17 books from the library, how many books has Susan borrowed?
- A. 25
- B. 26
- C. 34
- D. 42
Correct Answer & Rationale
Correct Answer: B
To determine how many books Susan has borrowed, start with Richard's 17 books. Since Richard has borrowed half as many books as Linda, Linda must have borrowed 34 books (17 x 2). Given that Linda has borrowed 8 more books than Susan, we can set up the equation: Linda's books = Susan's books + 8. Therefore, if Linda has 34 books, we find Susan's total by subtracting 8: 34 - 8 = 26. Option A (25) is incorrect as it underestimates Susan's total. Option C (34) mistakenly suggests Susan borrowed the same amount as Linda. Option D (42) overestimates Susan's total by not accounting for the difference of 8 books. Thus, the only valid option is 26.
To determine how many books Susan has borrowed, start with Richard's 17 books. Since Richard has borrowed half as many books as Linda, Linda must have borrowed 34 books (17 x 2). Given that Linda has borrowed 8 more books than Susan, we can set up the equation: Linda's books = Susan's books + 8. Therefore, if Linda has 34 books, we find Susan's total by subtracting 8: 34 - 8 = 26. Option A (25) is incorrect as it underestimates Susan's total. Option C (34) mistakenly suggests Susan borrowed the same amount as Linda. Option D (42) overestimates Susan's total by not accounting for the difference of 8 books. Thus, the only valid option is 26.
Which of the four labeled points on the number line above has coordinate-?
- A. A
- B. B
- C. C
- D. D
Correct Answer & Rationale
Correct Answer: B
Point B is positioned at the coordinate -2 on the number line, making it the accurate choice. Point A is located at -1, which is not the specified coordinate. Point C is at 0, representing the origin, and thus does not match the target coordinate. Point D is found at 1, clearly outside the negative range required. Each of these points is distinctly marked, confirming that only Point B aligns with the coordinate of -2. This clarity in placement reinforces the understanding of negative values on a number line.
Point B is positioned at the coordinate -2 on the number line, making it the accurate choice. Point A is located at -1, which is not the specified coordinate. Point C is at 0, representing the origin, and thus does not match the target coordinate. Point D is found at 1, clearly outside the negative range required. Each of these points is distinctly marked, confirming that only Point B aligns with the coordinate of -2. This clarity in placement reinforces the understanding of negative values on a number line.