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.
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.
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.
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.