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.
Other Related Questions
At the Crest Coffee Shop, the cost of a plain bagel was $0.75 last year. This year the cost of a plain bagel is $0.90. By what percent did the cost of a plain bagel increase from last year to this year?
- A. 10%
- B. 15%
- C. 17%
- D. 20%
Correct Answer & Rationale
Correct Answer: D
To determine the percent increase in the cost of a plain bagel, the formula used is: \[ \text{Percent Increase} = \left( \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \right) \times 100 \] Substituting the given values: \[ \text{Percent Increase} = \left( \frac{0.90 - 0.75}{0.75} \right) \times 100 = \left( \frac{0.15}{0.75} \right) \times 100 = 20\% \] Option A (10%) underestimates the increase, while B (15%) and C (17%) also fail to reflect the correct calculation. Therefore, the accurate calculation confirms a 20% increase in cost.
To determine the percent increase in the cost of a plain bagel, the formula used is: \[ \text{Percent Increase} = \left( \frac{\text{New Price} - \text{Old Price}}{\text{Old Price}} \right) \times 100 \] Substituting the given values: \[ \text{Percent Increase} = \left( \frac{0.90 - 0.75}{0.75} \right) \times 100 = \left( \frac{0.15}{0.75} \right) \times 100 = 20\% \] Option A (10%) underestimates the increase, while B (15%) and C (17%) also fail to reflect the correct calculation. Therefore, the accurate calculation confirms a 20% increase in cost.
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.
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.
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.