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

It is currently 24 Apr 2019, 13:18

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

A rectangular floor measures a by b feet, where a and b are positive i

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54496
A rectangular floor measures a by b feet, where a and b are positive i  [#permalink]

Show Tags

New post 27 Mar 2019, 22:08
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

35% (02:52) correct 65% (03:02) wrong based on 20 sessions

HideShow timer Statistics

A rectangular floor measures a by b feet, where a and b are positive integers with b > a. An artist paints a rectangle on the floor with the sides of the rectangle parallel to the sides of the floor. The unpainted part of the floor forms a border of width 1 foot around the painted rectangle and occupies half of the area of the entire floor. How many possibilities are there for the ordered pair (a,b)?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

_________________
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7584
A rectangular floor measures a by b feet, where a and b are positive i  [#permalink]

Show Tags

New post 28 Mar 2019, 07:43
3
Bunuel wrote:
A rectangular floor measures a by b feet, where a and b are positive integers with b > a. An artist paints a rectangle on the floor with the sides of the rectangle parallel to the sides of the floor. The unpainted part of the floor forms a border of width 1 foot around the painted rectangle and occupies half of the area of the entire floor. How many possibilities are there for the ordered pair (a,b)?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5



Let us draw the two rectangles as below..

The area of bigger rectangle is a*b, and that of inner rectangle is (a-2)(b-2).
It is given that \((a-2)(b-2)=\frac{ab}{2}\)

Let us solve this.
\((a-2)(b-2)=\frac{ab}{2}..............2(ab-2(a+b)+4)=ab..........ab-4a-4b+8=0\)
\(..............ab-4a-4b+8+8-8=0.............ab-4a-4b+16-8=0.........a(b-4)-4(b-4)=8.\)

\((a-4)(b-4)=8=1*8=2*4\)
Now a and b are positive integers, and b>a, so two cases
1) a-4=1 and b-4=8, that is a=5 and b=12
2) a-4=2 and b-4=4, that is a=6 and b=8

Thus 2 cases

B
Attachments

10.png
10.png [ 45.63 KiB | Viewed 241 times ]


_________________
GMAT Club Bot
A rectangular floor measures a by b feet, where a and b are positive i   [#permalink] 28 Mar 2019, 07:43
Display posts from previous: Sort by

A rectangular floor measures a by b feet, where a and b are positive i

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.