On a scale drawing, a rectangle 1 inch by 1 1/3 inches represents the

Question

On a scale drawing, a rectangle 1 inch by \(1\frac{1}{3}\) inches represents the floor of a room and the indicated scale is 1 inch equals 15 feet. How many square tiles 6 inches on a side will be needed to cover this floor? (1 foot = 12 inches)

A. 40
B. 70
C. 120
D. 700
E. 1,200

PS40602.01
OG2020 NEW QUESTION

A. 40
B. 70
C. 120
D. 700
E. 1,200

PS40602.01
OG2020 NEW QUESTION

https://gmatclub.com/forum/download/file.php?id=72729

EgmatQuantExpert · Accepted Answer

Solution

Given:  
 • Dimensions of the rectangular floor = 1 inch by 1  \frac{1}{3}  inches
 o 1 inch = 15 feet
o 1 feet = 12 inches

To find:  
 • The number of square tiles 6 inches on a side will be needed to cover this floor.

Approach and Working:  
 • Dimensions of the rectangle in feet= 1* 15 feet by  \frac{4}{3}  * 15 feet = 15 feet by 20 Feet
• Dimensions of the rectangle in inches = 15* 20 inches by 20 * 12 inch = 180 inches by 240 inches

Area of the floor = 180* 240

• Total number of square tiles of side length 6 inches need to cover this floor =  \frac{180 * 240}{6 * 6} 
 o = 1200 
• Hence, the correct answer is option E.

Correct Answer: E

Chethan92 · Answer

1 inch = 15ft
4/3 inch = 20ft

15*12 = 180 inches
20*12 = 240 inches

Total number of tiles = 180/6*240/6 = 30*40 = 1200 tiles

E is the answer.

ZoltanBP · Answer

The dimensions of the floor:
 1 \ in'=15 \ ft=15\cdot 12 \ in 
 \frac{4}{3} \ in'=\frac{4}{3}\cdot 15=20 \ ft=20\cdot 12 \ in

Since, in inches, each dimension of the floor is a multiple of the side length of a square tile, the number of tiles needed is the ratio of the floor area to the area of a square tile.

\frac{15\cdot 12\cdot 20 \cdot 12}{6\cdot 6}=30\cdot 40=1200

Answer: E

nigina93 · Answer

1 inch = 15 feet
4/3 inch = 20 feet.
Convert to inches now => 15*12=180; 20*12=240. So, we are getting 180 by 240 or 30(180/6)*40(240/6)=1200 (E)

ScottTargetTestPrep · Answer

If the scale of the drawing is 1 inch = 15 feet, then the room has dimensions of 15 ft by 20 ft. Therefore, the area of the room is 15 x 20 = 300 sq. ft. Since each tile is 1/2 x 1/2 = 1/4 sq. ft, we need 300/(1/4) = 300 x 4 = 1,200 tiles to cover the floor of the room.

Answer: E

dcummins · Answer

Convert the drawing from inches to feet and you end up with a rectangle that is 20ft by 15ft
each tile is 6 inches or 1/2 ft

20ft/ 1/2ft per tile = 40 tiles 
15ft / 1/2ft per tile = 30 tiles
40*30 = 1200

GMAThunterr · Answer

I really donot understand how the borh statement can be true :

o 1 inch = 15 feet
o 1 feet = 12 inches

According to statement 1 , we can say that:
12 inches =300feet which is not aligned with the statement 2.
So basically we have two scales so we have two measurements.
Can somebody please explain :

Posted from my mobile device

GMATinsight · Answer

GMAThunterr 
o 1 inch = 15 feet -  This is the scale conversion i,.e. 1 inch on scale = 15 feet actually 
o 1 feet = 12 inches -  This is the real conversion of foot into inches.

MHIKER · Answer

Please help to figure out my problem:
What I did is:
1 inch = 15 feet
4/3 inch = 20 feet 
so, the area of the floor is 15 x 20 = 300

area of the tiles is 6^2 = 36 square inch, which is 36/12 = 3 feet
Hence the required number of tiles is = 300/3 = 100

So, I can't convert square inch into feet, right? As 12 inches = 1 foot, not 12 square inches, is that?

ScottTargetTestPrep · Answer

Exactly. You must convert "square inches" into "square feet".

DaenerysTargaryen · Answer

I think the confusion on this one may be accidentally conflating 1 foot (12 inches) with the measurement of 1 square foot. 1 square foot is 144 square inches.

The solutions others have provided are the fastest ways to solve it, but to think about it differently:

Convert the Scale Drawing of the Floor to Full Scale 
1 inch at scale = 15 feet.
4/3 inch at scale = 20 feet.

Calculate the Area of the Floor 
15 feet * 20 feet = 300 square feet. 
300 feet * 144  (1 square foot in square inches)  = 43,200 square inches.

Calculate the Area of One Tile  
6 inches * 6 inches = 36 square inches.

Calculate Total Tiles to Cover the Entire Floor 
43,200 square inches / 36 square inches = 1,200 tiles to cover the floor.

This is a long way to solve the problem that would not be optimal for the test, but maybe it will help make sense of it for those who are still getting 100 tiles (incorrectly calculating it as I first did: 15*20=300, 300*12=3600/(6*6)=100). Also, I'm not great at math...  AndrewN  or  ScottTargetTestPrep , can you validate the rationale I've laid out?

AndrewN · Answer

Yes,  DaenerysTargaryen , you have it just right. (If you are wondering how I solved the problem, I converted the tile dimensions to feet instead. Why? Because I am lazy, and I would rather work with smaller numbers.) I like to say that as long as you end up with the correct answer within a reasonable amount of time, there is no wrong way to solve a question. Well done on this one.

- Andrew

GMATinsight · Answer

Answer: Option E

Video solution by  GMATinsight

https://www.youtube.com/watch?v=mXvrABOph2Q

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=TAGYO1ndJKw

Hoozan · Answer

Similar Question: https://gmatclub.com/forum/on-a-scale-d ... l#p2266243 https://gmatclub.com/forum/on-an-aerial ... ml#p776791

yannichc · Answer

can we also do 15*20/(1/2*1/2)= 30*40 =1200?

Bunuel · Answer

Yes. You are dividing the area of the room which is 15*20 = 300 square feet, by the area of one tile, which is 1/2*1/2 = 1/4 square feet, to get the number of tiles.

aashusuman1 · Answer

1inch * 4/3 inch * 15 * 15 ( For foot conversion) = 15ft* 20 ft
15ft*20ft*144 ( for inch conversion) as tile area is given in sqr inch.

(15*20*144)/36

1200.

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