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

It is currently 09 Dec 2019, 05:38

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If a rectangular billboard has an area of 104 square feet and a perime

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59624
If a rectangular billboard has an area of 104 square feet and a perime  [#permalink]

Show Tags

New post 27 Dec 2015, 10:47
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

76% (01:57) correct 24% (02:18) wrong based on 82 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
User avatar
B
Joined: 28 Feb 2014
Posts: 289
Location: United States
Concentration: Strategy, General Management
Reviews Badge
Re: If a rectangular billboard has an area of 104 square feet and a perime  [#permalink]

Show Tags

New post 27 Dec 2015, 21:55
If a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet, what is the length of each of the shorter sides?

l*w=104

2l+2w=42
l+w=21
l=21-w

(21-w)*w=104
solve for w.
w = 8 or 13

shorter side = 8

C. 8
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15675
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If a rectangular billboard has an area of 104 square feet and a perime  [#permalink]

Show Tags

New post 28 Dec 2015, 23:02
1
Hi All,

This question can be solved algebraically or by TESTing THE ANSWERS.

We're told that a rectangle has an area of 104 and a perimeter of 42. We're asked for the length of one of the SHORTER sides of the rectangle.

Since the answers are all INTEGERS, and the area is 104, the shorter side will almost certainly be less than 10 (since 10x10 = 100, but we're NOT dealing with a square). Answer B (7) does NOT divide evenly into 104, so the correct answer is probably A or C.

Let's TEST Answer C: 8

IF...
The shorter side = 8...
The area = 104....104/8 = 13 = the longer side
Perimeter = 8+8+13+13 = 42
This is an exact MATCH for what we were told, so this MUST be the answer.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com
Image


The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 384
Location: India
GMAT 1: 760 Q50 V44
Re: If a rectangular billboard has an area of 104 square feet and a perime  [#permalink]

Show Tags

New post 29 Dec 2015, 02:45
Bunuel wrote:
If a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet, what is the length of each of the shorter sides?

A. 4
B. 7
C. 8
D. 13
E. 26


Assume the sides to be x and y.

Perimeter = 2x + 2y = 42
Hence x + y = 21 - (i)

Area = xy = 104 - (ii)

Since these are the sides of a billboard, we are dealing with positive numbers only and the options tell us that they are integers.
104 can be written as a product of two numbers as 104*1 or 52*2 or 26*4 or 13*8

Of these, only 13*8 satisfies the equation (i)
Hence the lengths are 13 and 8

Length of shorter side = 8
Option C
Target Test Prep Representative
User avatar
V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8642
Location: United States (CA)
Re: If a rectangular billboard has an area of 104 square feet and a perime  [#permalink]

Show Tags

New post 14 Sep 2018, 17:37
Bunuel wrote:
If a rectangular billboard has an area of 104 square feet and a perimeter of 42 feet, what is the length of each of the shorter sides?

A. 4
B. 7
C. 8
D. 13
E. 26


We can create the following equations:

LW = 104

and

2L + 2W = 42

L + W = 21

W = 21 - L

Substituting, we have:

L(21 - L) = 104

21L - L^2 = 104

L^2 - 21L + 104 = 0

(L - 13)(L - 8) = 0

L = 13 or L = 8

Thus, the shorter side is 8.

Answer: C
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13731
Re: If a rectangular billboard has an area of 104 square feet and a perime  [#permalink]

Show Tags

New post 30 Nov 2019, 13:07
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: If a rectangular billboard has an area of 104 square feet and a perime   [#permalink] 30 Nov 2019, 13:07
Display posts from previous: Sort by

If a rectangular billboard has an area of 104 square feet and a perime

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne