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# If 72% of rectangular floor is covered by a rectangular rug that is 9

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
If 72% of rectangular floor is covered by a rectangular rug that is 9  [#permalink]

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30 Aug 2018, 04:13
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Difficulty:

35% (medium)

Question Stats:

71% (01:18) correct 29% (01:17) wrong based on 78 sessions

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If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?

A. 28
B. 56
C. 80
D. 200
E. 560

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Joined: 02 Aug 2009
Posts: 7334
If 72% of rectangular floor is covered by a rectangular rug that is 9  [#permalink]

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30 Aug 2018, 04:45
2
Bunuel wrote:
If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?

A. 28
B. 56
C. 80
D. 200
E. 560

Hi ..
72% of total =9*16
Don't multiply, may save time while dividing..

So $$\frac{72}{100}*total=9*16.......total =9*16*\frac{100}{72}$$
Divide both by 9 first..
$$total = 16*\frac{100}{8}$$
Now divide by 8
$$total=2*100=200$$

Therefore uncovered area = 200-9*16=56

B
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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If 72% of rectangular floor is covered by a rectangular rug that is 9  [#permalink]

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Updated on: 30 Aug 2018, 05:05
Bunuel wrote:
If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?

A. 28
B. 56
C. 80
D. 200
E. 560

Let the total area be x

we are given 0.72(x)=16*9
=>x=200

Area of uncovered floor is 28% of x = 56

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Originally posted by gmat1393 on 30 Aug 2018, 04:51.
Last edited by gmat1393 on 30 Aug 2018, 05:05, edited 1 time in total.
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Posts: 241
If 72% of rectangular floor is covered by a rectangular rug that is 9  [#permalink]

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30 Aug 2018, 04:56
Isn't the area of uncovered floor 28 percemt of 200?

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Joined: 08 Oct 2015
Posts: 241
Re: If 72% of rectangular floor is covered by a rectangular rug that is 9  [#permalink]

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30 Aug 2018, 04:57
chetan2u wrote:
Bunuel wrote:
If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?

A. 28
B. 56
C. 80
D. 200
E. 560

Hi ..
72% of total =9*16
Don't multiply, may save time while dividing..

So $$\frac{72}{100}*total=9*16.......total =9*16*\frac{100}{72}$$
Divide both by 9 first..
$$total = 16*\frac{100}{8}$$
Now divide by 8
$$total=2*100=200$$

D

Shouldn't the ans be 0.28 x 200?as it asks for uncovered area

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Joined: 06 Nov 2016
Posts: 62
Location: Viet Nam
GPA: 3.54
Re: If 72% of rectangular floor is covered by a rectangular rug that is 9  [#permalink]

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30 Aug 2018, 05:04
1
chetan2u wrote:
Bunuel wrote:
If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?

A. 28
B. 56
C. 80
D. 200
E. 560

Hi ..
72% of total =9*16
Don't multiply, may save time while dividing..

So $$\frac{72}{100}*total=9*16.......total =9*16*\frac{100}{72}$$
Divide both by 9 first..
$$total = 16*\frac{100}{8}$$
Now divide by 8
$$total=2*100=200$$

D

Hi chetan2u
Here is my approach.
% of floor___Area
72 ----------> 9*16
28 ----------> $$\frac{(9*16)*28}{72}$$
--> Area of uncovered floor = $$\frac{(9*16)*28}{72}=\frac{(9*16)*28}{9*8}=2*28=56$$ -> Answer B.
According to your solution, shouldn't 200 be the area of total floor, not the area of uncovered floor ?
Please correct me if I am wrong.
Thank you.
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Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: If 72% of rectangular floor is covered by a rectangular rug that is 9  [#permalink]

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30 Aug 2018, 05:07
1
Izzyjolly wrote:
chetan2u wrote:
Bunuel wrote:
If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?

A. 28
B. 56
C. 80
D. 200
E. 560

Hi ..
72% of total =9*16
Don't multiply, may save time while dividing..

So $$\frac{72}{100}*total=9*16.......total =9*16*\frac{100}{72}$$
Divide both by 9 first..
$$total = 16*\frac{100}{8}$$
Now divide by 8
$$total=2*100=200$$

D

Hi chetan2u
Here is my approach.
% of floor___Area
72 ----------> 9*16
28 ----------> $$\frac{(9*16)*28}{72}$$
--> Area of uncovered floor = $$\frac{(9*16)*28}{72}=\frac{(9*16)*28}{9*8}=2*28=56$$ -> Answer B.
According to your solution, shouldn't 200 be the area of total floor, not the area of uncovered floor ?
Please correct me if I am wrong.
Thank you.

You are absolutely correct ..
I have answered for the total area, but it has to be for uncovered..
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Posts: 93
Re: If 72% of rectangular floor is covered by a rectangular rug that is 9  [#permalink]

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30 Aug 2018, 05:13
Bunuel wrote:
If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?

A. 28
B. 56
C. 80
D. 200
E. 560

Here 72% = 16*9 = 144
Therefore, uncovered floor = 28%
Now, since 72% = 144
Therefore, 28% = (144/72)*28 = 56

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Posts: 1162
Concentration: Accounting, Finance
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If 72% of rectangular floor is covered by a rectangular rug that is 9  [#permalink]

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30 Aug 2018, 05:31
Bunuel wrote:
If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?

A. 28
B. 56
C. 80
D. 200
E. 560

Note: we are looking for the are of the Uncovered Floor. Covered is 72% . So uncovered area is 28%.

covered floor = 16*9 = 144.

72% represents 144

1% represents 144/72

28% represents 144*28 / 72

= 56.

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Re: If 72% of rectangular floor is covered by a rectangular rug that is 9  [#permalink]

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30 Aug 2018, 06:15
Bunuel wrote:
If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?

A. 28
B. 56
C. 80
D. 200
E. 560

$$\frac{16*9}{72}*28$$

= 56, Answer must be (B)

PS : Skippe steps in between , anyone requirng explainations please feel free to revert.
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Re: If 72% of rectangular floor is covered by a rectangular rug that is 9  [#permalink]

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04 Sep 2018, 03:38
Bunuel wrote:
If 72% of rectangular floor is covered by a rectangular rug that is 9 feet by 16 feet, what is the area, in square feet, of the uncovered floor?

A. 28
B. 56
C. 80
D. 200
E. 560

Letting n = the area of the floor, we can create the following equation:

(9 x 16) = 0.72n

144 = 0.72n

200 = n

So the area of the uncovered floor is 200 - 144 = 56 square feet.

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Re: If 72% of rectangular floor is covered by a rectangular rug that is 9   [#permalink] 04 Sep 2018, 03:38
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