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The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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12
61 00:00

Difficulty:   95% (hard)

Question Stats: 36% (02:21) correct 64% (03:02) wrong based on 349 sessions

### HideShow timer Statistics  The figure above shows the inside dimensions, in feet, of a certain room. An architect made a scale model of the room that had a floor and four walls, but not a ceiling. What was the scale of the model, in inches per foot, if the inside of the model had a total surface area of 2,304 square inches?

A. 0.25
B. 0.75
C. 1.8
D. 2
E. 4

Attachment: 2017-07-16_1619.png [ 28.7 KiB | Viewed 24412 times ]

Originally posted by devbond on 02 Apr 2016, 12:21.
Last edited by Bunuel on 16 Jul 2017, 05:22, edited 1 time in total.
Edited the question.
Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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29
22
devbond wrote:
Attachment:
Screen Shot 1938-01-14 at 00.41.44.png

A. 0.25
B. 0.75
C. 1.8
D. 2
E. 4

Since the model does not have roof, lets find the surface area without roof of ACTUAL room
16 *10 +2*8*10 + 2*8*16 = 576 sq feet

576 sq feet is represented by 2304 square inches..
so 1 sq feet is represented by 2304/576 = 4 square inches..

The answer has to be in inches per feet..
SO if 1 sq feet is represented by 4 square inches..
1 feet will be reprsented by 2 inches

Answer is in inches per feet = 2 inches /1 feet = 2 inches per feet

D
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Re: The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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9
6
Chiragjordan wrote:
hey
How did you write this =>
"SO if 1 sq feet is represented by 4 square inches..
1 feet will be reprsented by 2 inches"

I guess Gmat will give us the conversion rate ?

You don't need the conversion rate.

You know that $$576 feet^2 = 2304 inches^2$$
Then $$1 feet^2= 4 inches^2$$

And as the questions ask what was the scale (in inches per foot) we should get rid of the ^2.

Therefore: $$\sqrt{1 feet^2} = \sqrt{4 inches^2}$$

1 feet = 2 inches
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GRE 1: Q169 V154 Re: The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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1
Quick Question..
Can somebody tell me what does scale refer to here ?
bit confusing
thanks
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Re: The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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Scale means- how many times bigger or smaller was the model as compared to the original.
Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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1
1
Chiragjordan wrote:
Quick Question..
Can somebody tell me what does scale refer to here ?
bit confusing
thanks

Hi,

Scale is basically the ratio of sides..
Mostly used in MAPs/Sketches
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GRE 1: Q169 V154 Re: The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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1
chetan2u wrote:
devbond wrote:
Attachment:
Screen Shot 1938-01-14 at 00.41.44.png

A. 0.25
B. 0.75
C. 1.8
D. 2
E. 4

Since the model does not have roof, lets find the surface area without roof of ACTUAL room
16 *10 +2*8*10 + 2*8*16 = 576 sq feet

576 sq feet is represented by 2304 square inches..
so 1 sq feet is represented by 2304/576 = 4 square inches..

The answer has to be in inches per feet..
SO if 1 sq feet is represented by 4 square inches..
1 feet will be reprsented by 2 inches

Answer is in inches per feet = 2 inches /1 feet = 2 inches per feet

D

hey
How did you write this =>
"SO if 1 sq feet is represented by 4 square inches..
1 feet will be reprsented by 2 inches"

I guess Gmat will give us the conversion rate ?
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Re: The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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stonecold wrote:
chetan2u wrote:
devbond wrote:
Attachment:
Screen Shot 1938-01-14 at 00.41.44.png

A. 0.25
B. 0.75
C. 1.8
D. 2
E. 4

Since the model does not have roof, lets find the surface area without roof of ACTUAL room
16 *10 +2*8*10 + 2*8*16 = 576 sq feet

576 sq feet is represented by 2304 square inches..
so 1 sq feet is represented by 2304/576 = 4 square inches..

The answer has to be in inches per feet..
SO if 1 sq feet is represented by 4 square inches..
1 feet will be reprsented by 2 inches

Answer is in inches per feet = 2 inches /1 feet = 2 inches per feet

D

hey
How did you write this =>
"SO if 1 sq feet is represented by 4 square inches..
1 feet will be reprsented by 2 inches"

I guess Gmat will give us the conversion rate ?

NO.

the above relation was :

feet^2 =4 inch^2 or value = 4 (inch^2/feet^2)

you need to find

feet =inch or answer = sqrt 4 (inch^2/feet^2) =2 inch/feet
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Re: The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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1
$$Surface\; area:\; the\; area\; of\; all\; surfaces\; inside\; the\; model\;$$

$$\left( remember\; we\; are\; told\; that\; measure\; is\; in\; in^{2},\; so\; it\; can\; only\; be\; a\; sum\; of\; in^{2 \right)$$

$$So\; let$$'$$s\; say\; that\; the\; scale\; is\; represented\; by\; n,\;$$

$$meaning\; that\; if\; the\; real\; deal\; is\; 2*small\; face\; +\; 2*big\; face\; +\; base\; =\; 2*\left( 8*10 \right)+2*\left( 16*8 \right)+10*16$$

$$then\; the\; model\; will\; be\; 2*\left( 8n*10n \right)+2*\left( 16n*8n \right)+10n*16n,\;$$

$$since\; we\; are\; given\; the\; area\; of\; the\; model,\;$$
$$we\; know\; that\; 2*\left( 8n*10n \right)+2*\left( 16n*8n \right)+10n*16n=2304,\; 160n^{2}\; +\; 256n^{2}+160n^{2}=2304,\; 576n^{2}=2304,$$

$$and\; since\; 576\; =\; 625-49\; =\; \left( 25-7 \right)\left( 25+7 \right)\; and\; 2304=\; 2500-196\; =\; \left( 50-14 \right)\left( 50+14 \right),\; n^{2}=\; \frac{\left( 36\cdot 64 \right)}{\left( 18\cdot 32 \right)}\; =\; 4,\;$$

$$n=2$$

$$Answer\; D$$
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Re: The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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2
So the dimension of the original room is: 576 ft2. (Surface area - ceiling)
The dimension of the model : 2304 in2.

Scale ratio: 2304 in2/576 ft2 = 4 inc2/ft2 => 2 in/ft (ans)
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GMAT 1: 650 Q49 V29 Re: The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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Architect wants to make a model room, so model room dimensions need to be reduced, SO each side needs to be in the same ratio.

let's say on the scale - 1 feet = x inch ( example 10 feet long wall needs to be shown as a model- so we can have a scale of each 1 inch equivalent to= 10 feet, in the same way other dimensions need to be reduced.)

let's say
01 feet = x inch on the scale , NOW WE NEED TO FIND THIS X
SO 01 inch = 1/x feet

so area 01 square inch= (1/x)*(1/x) square feet = 1/x^2
we have given the model box area = 2304 square inch
so actual area in square feet= 2304 *1/x^2 square feet ------ equation 01

we already have the dimensions of the actual building in feet, let's calculate the are of it -

2*8*10 ( 02 side wall with 8 and 10 feet side) + 2*8*16 + 10*16 ( only the floor, no roof) --------------- equation 2

equation 2= equation1

8 ( 20 +32+20 ) = 2304/x^2

or x^2 = 2304/8*72

x^2= 4
so x=2

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Re: The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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1
I cannot see the full picture. Please fix the error for this post, thanks.
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Re: The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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chesstitans wrote:
I cannot see the full picture. Please fix the error for this post, thanks.

_______________
Fixed it.
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Re: The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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good one on scales - the meaning was not clear to me also thanks for the question. i knew the formula for this question... but the application went wrong on my side.. great question any ways,,, thanks
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Re: The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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IMO, this question is pretty straight forward since we are looking for in/ft. And that is exactly what the question provided. We already have the scaled surface area in (in sq), i.e 2304 . We just needed to find the original area in feet from the diagram. This is 2(8*10) + 2(16*8) + 16*10 = 576 (ft sq)
Scale = 2304 in sq/ 576 ft sq = 4 (in/ft) sq. Take the square root to get 2 in/ft.
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Re: The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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1
I've found these conversion problems particularly confusing, especially because there isn't a well-defined process for handling conversions (at least that I've seen).

Here's a process I've found useful for navigating conversions

Create a conversion ratio:

$$1m : 100cm$$

Raise both sides to the power of the operation (for volume operations, the power is three, for surface are operations, the power is 2, for regular ratios, the power is 1)

$$(1m)^3:(100cm)^3 \rightarrow 1m^3:1,000,000cm^3$$

So something with a volume of $$15m^3$$ is equivalently $$15,000,000cm^3$$ in volume

This process can be reversed also. Say, for example, you know the ratio of area for two squares is $$1in^2:16in^2$$. This represents a squared amount, so the ratio of these two square's sides is the square root of the ratio of area:

$$\sqrt{1in^2}:\sqrt{16in^2} \rightarrow 1in:4in$$

This process is fairly intuitive with base-10 metric conversions, but works the same with questions like this one.

Two $$8x10$$ walls:

$$2*8*10 = 160ft^2$$

Two $$8x16$$ walls:

$$2*8*16=256ft^2$$

One $$10x16$$ wall:

$$10*16=160ft^2$$

So there are $$160+256+160=576ft^2$$ of surface area for the actual room, and $$2304in^2$$ for the model

$$576ft^2:2304in^2 \rightarrow 1ft^2:4in^2$$

This is a surface area (second dimension) problem with a ratio comparing already squared units, so to find the ratio of the un-squared units (first dimension), take the square root of the ratio:

$$\sqrt{1ft^2}:\sqrt{4in^2} \rightarrow 1ft:2in$$

So for every two inches in the model there is one foot in real life.

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Re: The figure above shows the inside dimensions in feet of a certain room  [#permalink]

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chetan2u if they asked instead for the scale of the house to the model in inches per foot then we would have to convert (*12 twice?) the 576 ft ^2 right? But since they ask for inches/per for which is already the units we have there is no need? I misunderstood the question and got mixed up in trying to convert... Re: The figure above shows the inside dimensions in feet of a certain room   [#permalink] 05 Jun 2019, 10:42
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