To reach a height of 2 feet, 2 feet wide stairs are to be made. A height of 0.5 feet is to be kept between one step and the next. The depth of each step is 0.5 feet. If the dimensions of a brick are 0.5 x 0.5 x 0.5 feet, then the number of bricks required for the stairs is?

1. A

   48

2. B

   40

3. C

   36

4. D

   44

Appeared in: UPUMS Nsg officer-2023

Explanation

• The total height (2 ft) and step height (0.5 ft) mean there are 4 steps in total.
• The structure can be visualized as 4 vertical columns, each 4 bricks wide and 1 brick deep.
• The heights of these columns are 1, 2, 3, and 4 bricks, respectively, from the front to the back.
• The number of bricks for each column is (1×4×1), (2×4×1), (3×4×1), and (4×4×1).
• Summing these values gives the total: 4 + 8 + 12 + 16 = 40 bricks.

Why Other Options Were Wrong

• Option A: 48 is incorrect. This might result from incorrectly calculating the bricks for each step, for example, by multiplying the bricks for the top step (16) by the number of steps minus one (16 x 3 = 48), which is a flawed method.
• Option C: 36 is incorrect. This value could be obtained by forgetting to include the bricks for the first (lowest) step in the total sum (8 + 12 + 16 = 36).
• Option D: 44 is incorrect. This is likely the result of a simple arithmetic error during the summation of the bricks for each step (e.g., 4 + 8 + 12 + 20).

Related Visual

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Solid Geometry and Mensuration as background academic context rather than a clinical decision trigger.
• This question tests general aptitude, specifically quantitative reasoning and problem-solving skills.
• While not directly clinical, these skills are essential for nurses for tasks like medication dosage calculations, interpreting data from medical devices, and managing resources.
• What if the depth of each step was 1 foot? The number of bricks per column would double (as each column is now 2 bricks deep). The total would be (1×4×2) + (2×4×2) + (3×4×2) + (4×4×2) = 8 + 16 + 24 + 32 = 80 bricks.

How to Approach the Question

• First, carefully read the problem and list all the given dimensions: total height, step height, step depth, stair width, and brick size.
• Break the problem down into smaller, manageable parts. Calculate the total number of steps required.
• Visualize the 3D structure of the staircase. A helpful method is to think of it as either horizontal layers or vertical columns.
• Calculate the number of bricks needed for each part (e.g., each vertical column). Remember that the height of each successive column increases.
• Sum the number of bricks from all the parts to get the final total.
• Double-check your arithmetic to avoid simple calculation errors.

Concept Tested & Keywords

• Concept Tested: Solid Geometry and Mensuration
• Stem keywords: stairs, height, width, depth, bricks, dimensions
• Lead-in keywords: number of bricks required

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Q4gSSYwwyCap12dqnZeubU

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