GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 21 Jan 2019, 03:51

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

January 21, 2019

January 21, 2019

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.
• ### The winners of the GMAT game show

January 22, 2019

January 22, 2019

10:00 PM PST

11:00 PM PST

In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one.

# The length of a rectangular floor is twice its width. The

Author Message
TAGS:

### Hide Tags

Intern
Joined: 28 May 2013
Posts: 2
Location: United States
Concentration: Marketing, Healthcare
Schools: Duke '17 (WA$) WE: Military Officer (Military & Defense) The length of a rectangular floor is twice its width. The [#permalink] ### Show Tags Updated on: 03 Nov 2013, 10:51 15 20 00:00 Difficulty: 15% (low) Question Stats: 83% (02:15) correct 17% (02:56) wrong based on 690 sessions ### HideShow timer Statistics The length of a rectangular floor is twice its width. The floor is partially covered by a rectangular carpet whose length is the same as the lenfth of the floor and whose width is two feet less than the width of the floor. If the area of the carpet is 160 sq. feet, what is the length, in feet, of the floor? A. 8 B. 16 C. 20 D. 24 E. 32 Got this wrong on a practice test and think I've come up with the correct answer, but cant check it since the damn software erased my test; throwing it up here on the forum, hoping someone on here can confirm or disprove what I came up with on the second shot... Originally posted by Jem2905 on 02 Nov 2013, 13:09. Last edited by Bunuel on 03 Nov 2013, 10:51, edited 1 time in total. Edited the question and added the OA ##### Most Helpful Expert Reply MBA Section Director Affiliations: GMAT Club Joined: 21 Feb 2012 Posts: 6001 City: Pune The length of a rectangular floor is twice its width. The [#permalink] ### Show Tags 02 Nov 2013, 15:02 4 6 Jem2905 wrote: The length of a rectangular floor is twice its width. The floor is partially covered by a rectangular carpet whose length is the same as the lenfth of the floor and whose width is two feet less than the width of the floor. If the area of the carpet is 160 sq. feet, what is the length, in feet, of the floor? a) 8 b) 16 c) 20 d) 24 e) 32 Should be C Dimensions of Rectangular floor Width = w Length = 2w Dimensions of Carpet Width = w-2 Length = 2w Area = 160 sq.ft. Area = 160 = 2w(w-2) ---------> $$160 = 2w^2 - 4w$$ ---------> $$2w^2 - 4w - 160 = 0$$ ---------> $$w^2 - 2w - 80 = 0$$ --------> $$(w-10)(w+8)=0$$ So, w=10 Hence L=20 _________________ ##### Most Helpful Community Reply Intern Joined: 23 Nov 2016 Posts: 10 Re: The length of a rectangular floor is twice its width. The [#permalink] ### Show Tags 15 Mar 2018, 08:30 6 Jem2905 wrote: The length of a rectangular floor is twice its width. The floor is partially covered by a rectangular carpet whose length is the same as the lenfth of the floor and whose width is two feet less than the width of the floor. If the area of the carpet is 160 sq. feet, what is the length, in feet, of the floor? A. 8 B. 16 C. 20 D. 24 E. 32 Got this wrong on a practice test and think I've come up with the correct answer, but cant check it since the damn software erased my test; throwing it up here on the forum, hoping someone on here can confirm or disprove what I came up with on the second shot... There is a simpler solution- Let Table area = l*2l --- (where l=width and 2l=length) ---- (1) Therefore Cloth area = (l-2)*2l ------(2) So all we need is the value of 2l . From the given information in (2) , we get (l-2)*2l = 160 Simplifying we get (l-2)*l =80 From the above eq. we can easily workout (l-2)*l = 8*10 This give l=10 . Now all we need is 2l= 20 . Hence answer = C ##### General Discussion Intern Joined: 17 Dec 2014 Posts: 11 Re: The length of a rectangular floor is twice its width. The [#permalink] ### Show Tags 19 Jan 2015, 13:51 Ah nice this is much quicker than my method. I did it like this: L=2w area = L*w area is here 160 = L*w but because the carpet is 2 feet less w = w-2 160= w-2 * 2w this can be: 1 * 160 or 2 * 80 or 4 * 40 or 5 * 32 or 8 * 20 or 10 * 16 Now you see that 8 * 20 is the only option. But it takes much more time.. Intern Joined: 17 Dec 2014 Posts: 11 Re: The length of a rectangular floor is twice its width. The [#permalink] ### Show Tags 19 Jan 2015, 13:53 Ah nice this is much quicker than my method. I did it like this: L=2w area = L*w area is here 160 = L*w but because the carpet is 2 feet less w = w-2 160= w-2 * 2w this can be: 1 * 160 or 2 * 80 or 4 * 40 or 5 * 32 or 8 * 20 or 10 * 16 Now you see that 8 * 20 is the only option. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13361 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The length of a rectangular floor is twice its width. The [#permalink] ### Show Tags 19 Jan 2015, 18:54 8 Hi All, This question can obviously be solved with a bit of Algebra and Geometry. You can also take those basic ideas, along with the answer choices (which are numbers) and TEST THE ANSWERS.... We're given a lot of information about a floor and a carpet on top of it: 1) The Floor's length is TWICE it's width. 2) The Carpet has the SAME length as the floor, but it's width is 2 feet less than the width of the floor 3) The area of the carpet is 160 ft^2. We're asked to find the length of the floor (which is the same as the length of the carpet). Since the area of the carpet is a "round number", it's likely that it's dimensions are probably round numbers. Let's TEST Answer B: Area of carpet is 160 If length = 16, then width = 10 Since the carpet width is 2 less than the floor width, the dimensions of the floor would be... Length = 16, width = 12. This does NOT match (the length is supposed to be TWICE the width. Eliminate B (and A, since a length of 8 would be way too small). Let's TEST Answer C: Area of carpet is 160 If length = 20, then width = 8 Since the carpet width is 2 less than the floor width.... Length = 20, width = 10. This DOES match (the length IS TWICE the width), so this MUST be the answer. Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Manager
Joined: 10 Feb 2015
Posts: 104
GMAT 1: 710 Q48 V38
Re: The length of a rectangular floor is twice its width. The  [#permalink]

### Show Tags

29 Oct 2015, 02:39
1
Straight algebra

L=2w
L(w-2)=160
Lw -2l =160
L^2/2 -2l =160 => l^2 -4l -320=0 . so l=20 or -16. Ans :C
Manager
Joined: 05 Jul 2015
Posts: 101
GMAT 1: 600 Q33 V40
GPA: 3.3
Re: The length of a rectangular floor is twice its width. The  [#permalink]

### Show Tags

21 Nov 2015, 17:25
2
I'm terrible at GMAT math so I always look for shortcuts...

Floor Area = 2w^2
Carpet Area = 160 which is slightly less than the floor.

So to guesstimate 2w^2=160..... w^2=80......w = around 9 ...
Length is a little bigger than 2*9....... 20 is closest answer.
Manager
Joined: 25 Mar 2013
Posts: 240
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
Re: The length of a rectangular floor is twice its width. The  [#permalink]

### Show Tags

20 Jan 2017, 07:46
Complete Rectangular floor
Width(W) = 10, Length = 2W
Carpet :
Width = W-2
same Length = 2W
A = 160 = 2W (W-2)
80 = W^2 - 2W
w^2 - 2W - 80 = 0
W = 10
Length = 2w = 20
C
_________________

I welcome analysis on my posts and kudo +1 if helpful. It helps me to improve my craft.Thank you

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4342
Location: India
GPA: 3.5
Re: The length of a rectangular floor is twice its width. The  [#permalink]

### Show Tags

20 Jan 2017, 10:33
Jem2905 wrote:
The length of a rectangular floor is twice its width. The floor is partially covered by a rectangular carpet whose length is the same as the lenfth of the floor and whose width is two feet less than the width of the floor. If the area of the carpet is 160 sq. feet, what is the length, in feet, of the floor?

A. 8
B. 16
C. 20
D. 24
E. 32

Floor :

Length = $$2w$$
Width = $$w$$

Area = $$2w^2$$

Carpet :

Length = $$2w$$
Width = $$w-2$$

Area = $$2w^2 - 4w$$

Quote:
If the area of the carpet is 160 sq. feet

$$2w ( w - 2 ) = 160$$

Or, $$w(w-2) = 80$$

So, $$w = 10$$

So, Length of the floor is $$2w = 20$$

Hence the length of floor is 20 , correct answer must be (C) 20
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Re: The length of a rectangular floor is twice its width. The &nbs [#permalink] 20 Jan 2017, 10:33
Display posts from previous: Sort by