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Math Expert V
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If 60 percent of a rectangular floor is covered by a rectang  [#permalink]

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If 60 percent of a rectangular floor is covered by a rectangular rug that is 9 feet by 12 feet, what is the area, in square feet, of the floor?

(A) 65
(B) 108
(C) 180
(D) 270
(E) 300

Problem Solving
Question: 15
Category: Geometry; Arithmetic Area; Percents
Page: 63
Difficulty: 550

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Re: If 60 percent of a rectangular floor is covered by a rectang  [#permalink]

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SOLUTION

If 60 percent of a rectangular floor is covered by a rectangular rug that is 9 feet by 12 feet, what is the area, in square feet, of the floor?

(A) 65
(B) 108
(C) 180
(D) 270
(E) 300

The area of the rug is 9*12 = 108 square feet.

So, we have that {area of the floor}*0.6 = 108 --> {area of the floor} = 180 square feet.

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GMAT 1: 590 Q45 V27 Re: If 60 percent of a rectangular floor is covered by a rectang  [#permalink]

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Firstly, let us find the area of the rectangular rug: 9 * 12 = 108 sq.ft;
If 60% of floor = area of the rectangular rug,
(0.6 * x) = 108, where x is the area of the floor;
x = (108 * 100)/60
x = 180.

Ans is (C).
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Re: If 60 percent of a rectangular floor is covered by a rectang  [#permalink]

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If 60 percent of a rectangular floor is covered by a rectangular rug that is 9 feet by 12 feet, what is the area, in square feet, of the floor?

(A) 65
(B) 108
(C) 180
(D) 270
(E) 300

Rug Area = 12 * 9

Floor Area * (60/100) = Rug Area

Or, Floor Area =2 12 * 9 * 10/ 6 = 2 * 9 * 10 = 180

Alternative Solution

It is given:
Rug Area = 12 * 9
Floor area / Rug Area = 3/5 (Since, 60% = 3/5)

Let any one side of the rug be multiplied by 5/3 to calculate floor area.
Or, One side of Floor = 9 * 5/3 = 15

So, Floor area = 12 * 15 = 180

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Re: If 60 percent of a rectangular floor is covered by a rectang  [#permalink]

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12 *9 = 108;

108 --------------> 60%
??? --------------> 40%

therefore 40% ------ > 72.
108+72= 180 ;
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GMAT 1: 780 Q51 V46 Re: If 60 percent of a rectangular floor is covered by a rectang  [#permalink]

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15 second approach:

108 is more than half but less than all of the floor. We need something between 108 and 216. Answer C.
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Re: If 60 percent of a rectangular floor is covered by a rectang  [#permalink]

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Bunuel wrote:

If 60 percent of a rectangular floor is covered by a rectangular rug that is 9 feet by 12 feet, what is the area, in square feet, of the floor?

(A) 65
(B) 108
(C) 180
(D) 270
(E) 300

60% area = 9*12 = 108 sq. feet
Hence 100% area = (108/60) * 100 [By unitary method]

Hence total area = 180 sq. feet.

Correct Option: C
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Re: If 60 percent of a rectangular floor is covered by a rectang  [#permalink]

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Area = length x breath
Area of rug = 12 x 9 = 108
108 = $$\frac{60}{100}$$ x Area of rectangular floor
180
C
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Re: If 60 percent of a rectangular floor is covered by a rectang  [#permalink]

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Bunuel wrote:

If 60 percent of a rectangular floor is covered by a rectangular rug that is 9 feet by 12 feet, what is the area, in square feet, of the floor?

(A) 65
(B) 108
(C) 180
(D) 270
(E) 300

We are given that 60 percent of a rectangular floor is covered by a 9-foot by 12-foot rug. Thus, the area of the rug is 9 x 12 = 108 square feet. To determine the area of the floor, we can create the following equation in which the total area of the floor is n:

0.6n = 108

6n = 1,080

n = 1,080/6 = 180 square feet

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Re: If 60 percent of a rectangular floor is covered by a rectang  [#permalink]

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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If 60 percent of a rectangular floor is covered by a rectangular rug that is 9 feet by 12 feet, what is the area, in square feet, of the floor?

(A) 65
(B) 108
(C) 180
(D) 270
(E) 300

Problem Solving
Question: 15
Category: Geometry; Arithmetic Area; Percents
Page: 63
Difficulty: 550

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

This problem requires you to 1) copy the information down correctly and 2) use the appropriate ratio.

Here we know that 9*12 = 3/5x. Instead of multiplying 9*12, we should leave it as-is so we can then bring over 3/5 and divide 9 by 3.

9*12 * 5/3 = x

3*12*5 = x

60*3 = x

x = 180.
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GMAT 1: 730 Q50 V38 Re: If 60 percent of a rectangular floor is covered by a rectangular rug  [#permalink]

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If 60 percent of a rectangular floor is covered by a rectangular rug that is 9 feet by 12 feet, what is the area, in square feet, of the floor?

60 % of rectangular floor area = area of rug 9feet by 12 feet
=> (60/100)* rectangular floor area = 9* 12
=> Rectangular floor area = (100/60) * (9*12) = 180

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Re: If 60 percent of a rectangular floor is covered by a rectangular rug  [#permalink]

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Let the area of the the whole floor be x

Therefore,

0.6*x = 9*12
0.6*x = 108

x = 180

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Joined: 22 May 2016
Posts: 3578
If 60 percent of a rectangular floor is covered by a rectangular rug  [#permalink]

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Bunuel wrote:
If 60 percent of a rectangular floor is covered by a rectangular rug that is 9 feet by 12 feet, what is the area, in square feet, of the floor?

(A) 65
(B) 108
(C) 180
(D) 270
(E) 300

Area of rug = LW = (9 * 12) = 108 ft$$^2$$

Area of rug is 60 percent of the floor F's area

$$108 = .6F$$

$$\frac{108}{.6} = \frac{108}{\frac{6}{10}}= F$$

$$108 *\frac{10}{6} = 180 = F$$

Area of floor = 180 ft$$^2$$

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Posts: 4018
Re: If 60 percent of a rectangular floor is covered by a rectangular rug  [#permalink]

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Top Contributor
Bunuel wrote:
If 60 percent of a rectangular floor is covered by a rectangular rug that is 9 feet by 12 feet, what is the area, in square feet, of the floor?

(A) 65
(B) 108
(C) 180
(D) 270
(E) 300

Area of rectangular RUG = (base)(height) = (9)(12) =108
This RUG covers 60% of the FLOOR
In other words, 108 = 60% of the area of the FLOOR
Or we can write: 108 = 0.6(area of FLOOR)

So, 108 /0.6 = area of FLOOR
Evaluate to get: 180 = area of FLOOR

Cheers,
Brent
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Re: If 60 percent of a rectangular floor is covered by a rectangular rug  [#permalink]

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PRO TIP :D

Once we know that So, 108 /0.6 = area of FLOOR, we can apply some number sense to avoid dividing 0.6 into 108

Notice that 108 /0.5 = 216
Since 0.6 is a bit bigger than 0.5, we know that 108 /0.6 will be a little bit less than 216
Check the answer choices...only answer choice C is a bit less than 216

ASIDE: This shortcut works, because the answer choices are nicely spread apart.

For more on this strategy, watch the following math tips video

Cheers,
Brent
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Re: If 60 percent of a rectangular floor is covered by a rectangular rug  [#permalink]

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Bunuel wrote:
If 60 percent of a rectangular floor is covered by a rectangular rug that is 9 feet by 12 feet, what is the area, in square feet, of the floor?

(A) 65
(B) 108
(C) 180
(D) 270
(E) 300

To avoid multiple calculations, just translate the question into:

$$\frac{60}{100}$$ * $$F$$ = 9 * 12.........we can simplify the equation in one step

F =180

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Re: If 60 percent of a rectangular floor is covered by a rectangular rug  [#permalink]

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Bunuel wrote:
If 60 percent of a rectangular floor is covered by a rectangular rug that is 9 feet by 12 feet, what is the area, in square feet, of the floor?

(A) 65
(B) 108
(C) 180
(D) 270
(E) 300

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

(9 x 12) = 0.6n

108 = 0.6n

180 = n

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If 60 percent of a rectangular floor is covered by a rectang  [#permalink]

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Hi All,

With this question, we can use the answer choices 'against' the prompt and TEST THE ANSWERS. To start, we know that the area of the rug is...

(9 ft)(12 ft) = 108 ft^2

We're told that this value represents 60% of the area of the rug. Since we're asked to find the area of the rug, 108 is 60% of one of the answer choices.

Since 60% of 200 = 120, we're clearly looking for an answer that is LESS than200 (but not that much less).

Let's TEST Answer C: 180

(.6)(180) = 108

This is an exact match for what we were told, so this must be the answer.

GMAT assassins aren't born, they're made,
Rich
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Re: If 60 percent of a rectangular floor is covered by a rectang  [#permalink]

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dheeraj24 wrote:
12 *9 = 108;

108 --------------> 60%
??? --------------> 40%

therefore 40% ------ > 72.
108+72= 180 ;

how did u get 72

Posted from my mobile device

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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If 60 percent of a rectangular floor is covered by a rectang  [#permalink]

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Hi crescendoboy,

You can use a ratio to determine the value of 40%. Since 60% = 108.....

40%/60% = X/108
4/6 = X/108
2/3 = X/108
3X = 216
X = 72

GMAT assassins aren't born, they're made,
Rich
_________________ Re: If 60 percent of a rectangular floor is covered by a rectang   [#permalink] 18 Mar 2018, 17:35

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