On the scale drawing of a certain house plan if 1 centimeter represent

This question was so easy I spent 2 minutes trying to figure out if there was a trick

1 cm is represented by x m. This is a ratio of \(\frac{1 cm}{x m}\)

Statement 1: You have a rectangle with an area of 48 \(cm^2\) that represents a rectangle with area 12 \(m^2\). That means \(\frac{48}{12} = \frac{1}{x}\). This is sufficient.

Statement 2: You have a line that is 30 cm long that represents 15 m. That means \(\frac{30}{15} = \frac{1}{x}\). This is sufficient.

Both sufficient, answer is D.

(1) talks about the area, hence squaring.

We are given that 1 centimeter represents x meters. Therefore, the area of 1*1 = 1 square centimeters represents the area of x*x = x^2 square meters.
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Answer is D : Both are individually sufficient

Based on question, 1 cm is scale of x m, so 1 sq.cm is scale of \(x^2\) sq.m

(1) A rectangular room that has a floor area of 12 square meters is represented by a region of area 48 square centimeters.
Based on this and using the statement from the question, we can equate as, if 1 sq.cm : \(x^2\) sq.m :: 48 sq.cm : 12 sq.m.
No need to solve, but we know x can be solved, so Select A and D

(2) The 15-meter length of the house is represented by a segment 30 centimeters long.
This is straight forward to derive x, so select D.

Answer is therefore D

let L and B are the length and breadth of rectangle area = Lx B = 12 sq m

1 cm = x mtr ; 1mtr =1/x cm

on map area L/x * B/ x = 48 ; LxB=12 given

x = .5

Hence A alone also sufficient

How is Statment 1 sufficient here? I'm just not following. I understand statement 2. Why are people squaring things at all in statement 1? x^2??

gmatbusters niks18 Abhishek009 amanvermagmat



Can anyone help me to simplify the statements and help me know if in approach used by
joondez , when we take two proportions we must have same units on LHS and RHS. In this approach,
we have units of area on LHS and length on RHS. Also how user has assumed 48\(cm^2\) as area of rectangle?
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hi adkikani

you are partly correct here. the calculation for statement 1 as per joondez approach is incorrect, hence you will get two different values of \(x\) from statement 1 & 2 and they are 1/4 & 1/2 respectively which is not possible in GMAT. GMAT DS statements gives the same value for any particular variable.

Statement 1 should be solved as \(\frac{48}{12}=\frac{1}{x^2}\)

Do note that a Ratio per-say does not have any unit., you can have a scenario where ratio of area equals ratio of length but that is not the case here.

If you read the stem carefully you will realize that x is simply a multiple that when multiplied by length on map results in actual length,

so in effect we have Actual length/breadth \(= x*\)Length/breadth on Map

Statement 1 mentions that the floor whose actual area is \(12m^2\) is represented by area of \(48cm^2\) on map which implies that area of floor as per map is 48.

Hence Actual area\(=x^2*\)Area on Map

1cm = x meters

x=?

(1) 12m^2 = 48cm^2
1cm^2 = x meters^2

substitute x meters^2
= 12x meters^2 = 48cm^2
x meters ^2 = 48/12
x= 2
sufficient

(2) 15 meters of the house is represented by a line 30cm long
15m= 30 cm length

since x meters = 1 cm we can substitute
15x = 30cm


sufficient

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.

1 cm = x meters
\(xm^2\) = \(cm^2\)
\(12xm^2\) = \(48 cm^2\)
\(xm^2\) = \(\frac{48 cm^2}{12}\)
\(xm^2\) = \(4\)
\(x\) = \(2\)

SUFFICIENT.

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

\(\frac{30}{15} = 2\)

SUFFICIENT.
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(1) 1 square centimeter = x square meters

48 square centimeters = 12 square meters

1 square centimeter \(= \frac{12}{48}=\frac{1}{2}\) square meters; Sufficient.

(2) 30 centimeters=15-meter

1 centimeter \(= \frac{15}{30}=\frac{1}{2}\) meter; Sufficient.

The answer is D

Hi Bunuel

Is the rule for statement 1 that since the lengths are in ratio 1:x, therefore the areas are in ratio (1^2):(x^2)? I read this for similar triangles, but I believe this rule holds for all polygons

Yes, it works for all 2-D figures.


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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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Hi Bunuel

Sorry for the silly question, but Can I interpret the statement 1 to be 12m^2 = 48cm^2 ? are square meters and meters square one and the same?

Thank you..!!

Yes, square meters and meters squared refer to the same unit of measurement for area.

1 square centimeters is represented by x^2 square meters (from the stem).

48 square centimeters is represented by 12 square meters (from statement 1).
From the above, 1 square centimeters is represented by 12/48 square meters. Hence, x^2 = 12/48 = 1/4, which gives x = 1/2.

Hope it helps.
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