**UCAT** **Question Analysis - Quantitative Reasoning Question 22**

An architect has drawn up plans for an apartment using a scale of 1:200.

**Although the plans only show the surface area at floor level, we know that, in the dining room, there is:**

**• One French window (1.50 m wide and 2 m high) on the side opposite to the lounge • One door (60 cm x 2 m) between the hall and the dining room • One door (90 cm x 2 m) between the lounge and the dining room**

**The walls are 2.65 m high.**

**Metre to feet conversion rate: 1 m = 3.27 ft**

**Q22.1 What is the surface area of the apartment?**

a. 69.68 ft^2

b. 181.99 ft^2

c. 208.14 ft^2

d. 481.72 ft^2

e. 680.61 ft^2

**Q22.2 What is the surface area occupied by the hall on the architect's plans on paper?**

a. 1.86 cm^2

b. 2.84 cm^2

c. 3.60 cm^2

d. 3.72 cm^2

e. 7.44 cm^2

**Q22.3 The bedroom has a surface area of 8.76 m2. What is the length of the longer portion of wall separating the bedroom and the bath-room?**

a. 1.20 m

b. 1.25 m

c. 1.30 m

d.1.45 m

e. 1 50m

**Q22.4 The landlord wishes to paper over the walls of the dining room. What is the surface covered by the wallpaper?**

a. 13.80 m^2

b. 24.80 m^2

c. 25.48 m^2

d. 30.57 m^2

e. 36.57 m^2

**Q22.5 What is the total length of the outside walls of the apartment?**

a. 26.2 m

b. 29.3 m

c. 32.4 m

d. 35.4 m

e. 35.7 m

**Q22.6 The landlord is contemplating laying down a wooden floor in the lounge. Wooden floors come in planks of 1 m length and 10 cm width. The planks are laid one after the other in a row; the last plank of a row can be cut easily to fit the dimensions of the room. The part which was cut out can then be used to start the next row. There are no gaps between planks. Planks are sold in packs of 25, with one pack costing £27.53. How much will the owner need to spend to buy the required number of packs?**

a. £119.48

b. £137.65

c. £143.46

d. £164.78

e. £166.34

**Answer and Explanation**

**Q22.1 - d: 481.72 ft^2**

Instead of converting all dimensions into feet, it is quicker to make the cal-culation in metres and to convert the result into ft2using the conversion rate 1 m2 = (3.27)2 ft2, i.e. 10.6929 ft2. The total surface area is equal to: (3.2 + 1.2 + 1.8 + 3.3) x 3.6 + (3.5 x 3.1) = 45.05 m2. 45.05 x 10.6929 = 481.72 ft2.

**Q22.2 - a: 1.86 cm^2**

On a scale of 1:200, each dimension must be divided by 200. The hall's surface on paper is therefore: (3.20 + 1.20 + 1.80) / 200 x (1.20 / 200) = 0.000186 m2

Given that 1 m2 = 100 dm2 = 10,000 cm2, this is equal to: 0.000186 x 10,000 = 1.86 cm2•

**Q22.3 - e: 1.50 m**

The combined surface area of the rectangle made up of the bedroom and the bathroom is (3.20 + 1.20) x (3.60 - 1.20) = 10.56 m2. The surface of the bathroom alone is therefore: 10.56 - 8.76 = 1.80 m2. The length of the longer wall is therefore equal to 1.80 / 1.20 (the length of the shorter wall) = 1.50 m.

**Q22.4 - d: 30.57 m^2**

The total surface of the walls, ignoring any of the openings, is calculated as the total length of the walls multiplied by the height of the walls (2.65 m): (3.60 + 3.30) x 2 x 2.65 = 36.57 m2.

The surface area occupied by the openings is: (1.5 x 2) + (0.6 x 2) + (0.9 x 2) = 6 m2.

The area occupied by the wallpaper is therefore 36.57 - 6 = 30.57 m2.

**Q22.5 - c: 32.4m**

Top wall: 3.20 + 1.20 + 1.80 + 3.30 = 9.5 m Right wall: 3.6 + 3.1 = 6.7 m

Bottom wall (L shaped): Horizontal walls add up to 9.5 m (i.e. same as top wall) + 3.1 m for the lounge's left wall = 12.6 m

Left wall: 3.6 m

Total: 32.4 m The astute candidate will have spotted that in fact this is the same as twice the length of the top wall + twice the length of the right wall.

**Q22.6 - b: £137.65**

There are two ways to think about this problem, both of which lead to the same calculation.

Method 1 (using surface area) The surface area occupied by the wooden floor should equal that of the room. The room's surface area is 3.5 x 3.1 = 10.85 m2. One plank covers 1 x 0.10 = 0.10 m2. Therefore we need 10.85 / 0.10 = 108.50 planks, i.e. we need to buy 5 packs (one not fully used). The cost is 5 x 27.53 = £137.65.

Method 2 (using length' The lounge's length is 3.5 m, therefore one row of planks will consist of 3.5 planks. The lounge's width is 3.1 m. Since each plank has a width of 10 cm, we can fit 10 planks in one metre and there in 3.1 m we can fit 31 planks. The total number of planks required is therefore 3.5 x 31 = 108.5, i.e. 5 packs (one not fully used). The cost is 5 x 27.53 = £137.65.

Drafted by Juno(UCAT Prep)