On the scale drawing of a certain house plan

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On the scale drawing of a certain house plan,if 1 centimeter represents x meters,what is the value of x?

(1) A rectangular room that has a floor area of 12 square meters is represented by a region of area 48 square centimeters.
(2) The 15-meter length of the house is represented by a segment 30 centimeters long.

OA:D

Source:OG 2017

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by crackverbal » Mon Oct 10, 2016 12:56 pm
Hi NandishSS,

Keep in mind that this is a value DS where we need to find the value of x, given that 1 centimeter = x meters.

Statement 1 : A rectangular room that has a floor area of 12 square meters is represented by a region of area 48 square centimeters

The area of a square is given by a^2 (if we consider each side to be of length 'a').
Actual area of the room is 12 square meters -----> a^2 = 12 ------> a = 2(root3) meters
Area of the scale drawing is 48 square centimeters -----> a^2 = 48 -----> a = 4(root3) centimeters

Since 4(root3)centimeters = 2(root3)meters, 1 centimeter = 2(root3)/4(root3) = 1/2 meter.Sufficient.

Statement 2 : The 15-meter length of the house is represented by a segment 30 centimeters long.

Given 30 centimeters = 15 meters, 1 centimeter = 15/30 = 1/2 meter. Sufficient.

Hope this helps!

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by fiza gupta » Thu Oct 13, 2016 5:53 am
1cm = x meter
squaring both sides
1 = x2

(1) 48cm^2=12m^2
cm^2=(1/4)m^2
1cm = 1/2 m

(2) 30cm = 15 m
1cm = 1/2m

both are sufficient
so d
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NandishSS wrote:
Sun Oct 09, 2016 9:54 am
On the scale drawing of a certain house plan,if 1 centimeter represents x meters,what is the value of x?

(1) A rectangular room that has a floor area of 12 square meters is represented by a region of area 48 square centimeters.
(2) The 15-meter length of the house is represented by a segment 30 centimeters long.

OA:D

Source:OG 2017
Solution:

Question Stem Analysis:

We need to determine the value of x, which is the number of meters represented by 1 centimeter on a floor plan.

Statement One Alone:

Since 12 sq. m equals 48 sq. cm on the floor plan, 1 sq. m equals 4 sq. cm, and hence 1 m equals 2 cm. In other words, 1 cm represents ½ m; that is, x = ½. Statement one alone is sufficient.

Statement Two Alone:

Since 15 m equals 30 cm on the floor plan, 1 m equals 2 cm. Again, we can see that 1 cm represents ½ m. Statement two alone is sufficient.

Answer: D

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