GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
close
It is currently 18 May 2021, 18:07
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
As shown in the figure above 20 equal squares are arranged to form a
14 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
Tags:
Find Similar Topics 

Show Tags
Hide Tags

User avatar
AryamaDuttaSaikia
Jamboree GMAT Instructor
Joined: 15 Jul 2015
Status:GMAT Expert
Affiliations: Jamboree Education Pvt Ltd
Posts: 261
Location: India
As shown in the figure above 20 equal squares are arranged to form a [#permalink] New post  Updated on: 11 Oct 2015, 22:27
5
Kudos
17
Bookmarks
Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
00:00
A
B
C
D
E

Difficulty:

85% (hard)

Question Stats:

46% (02:00) correct 54% (02:13) wrong based on 194 sessions

Hide Show timer Statistics

Image
As shown in the figure above, 20 equal squares are arranged to form a large rectangle. How many total rectangles does the large rectangle contain?

(a) 20
(b) 40
(c) 90
(d) 150
(e) 190

Show Spoiler
Attachment:
1.jpg
1.jpg [ 11.69 KiB | Viewed 4192 times ]
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
Aryama Dutta Saikia
Jamboree Education Pvt. Ltd.
Signature Read More

Originally posted by AryamaDuttaSaikia on 11 Oct 2015, 22:24.
Last edited by Bunuel on 11 Oct 2015, 22:27, edited 1 time in total.
Edited the question.
Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
Most Helpful Community Reply
User avatar
AryamaDuttaSaikia
Jamboree GMAT Instructor
Joined: 15 Jul 2015
Status:GMAT Expert
Affiliations: Jamboree Education Pvt Ltd
Posts: 261
Location: India
As shown in the figure above 20 equal squares are arranged to form a [#permalink] New post  Updated on: 03 Dec 2015, 20:34
3
Kudos
7
Bookmarks
Jamboree way

If we choose any two horizontal lines and any two vertical lines the enclosed quadrilateral formed will be a rectangle.
The given figure has 5 horizontal lines and 6 vertical lines.
The number of ways we can select 2 horizontal lines out of 5 horizontal lines = 5C2 = 10
The number of ways we can select 2 vertical lines out of 6 vertical lines = 6C2 = 15

Total number of rectangles formed = (The number of ways we can select 2 horizontal lines) x (The number of ways we can select 2 vertical lines)

Total number of rectangles formed = 10 x 15 = 150
_________________
Aryama Dutta Saikia
Jamboree Education Pvt. Ltd.
Signature Read More

Originally posted by AryamaDuttaSaikia on 03 Dec 2015, 01:55.
Last edited by AryamaDuttaSaikia on 03 Dec 2015, 20:34, edited 1 time in total.
General Discussion
avatar
B
paulaalv11
Intern
Intern
Joined: 24 Aug 2015
Posts: 39
Location: Spain
Concentration: General Management, Technology
GMAT 1: 750 Q49 V42
GPA: 3.5
WE:Management Consulting (Consulting)
Re: As shown in the figure above 20 equal squares are arranged to form a [#permalink] New post  11 Oct 2015, 23:23
Hi Aryama,

could you kindly confirm if this type of question is likely to appear on the GMAT? I had not seen before anything like it in any of the CATs I've taken, or around here.

And is there a "formula"-way to solve it? Using combinatorics, maybe? Or are we supposed to simply count?

Many thanks in advance!

Paula
avatar
longfellow
Manager
Manager
Joined: 02 Jul 2015
Posts: 94
Schools: ISB '18
GMAT 1: 680 Q49 V33
Re: As shown in the figure above 20 equal squares are arranged to form a [#permalink] New post  12 Oct 2015, 06:33
Hi, Can you please share your approach. Though my answer is correct, I do not consider my way to be reliable in the long run.
User avatar
B
BrainLab
Current Student
Joined: 10 Mar 2013
Posts: 428
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A$)
GMAT 1: 580 Q46 V24
GPA: 3.7
WE:Information Technology (Consulting)
GMAT ToolKit User
As shown in the figure above 20 equal squares are arranged to form a [#permalink] New post  12 Oct 2015, 10:59
2
Kudos
3
Bookmarks
I don't think that such kind of problems appear in GMAT.
We can use this formula to solve this one: \(\frac{m(m+1)*n(n+1)}{4}\)==> \(\frac{4*5*5*6}{4}\)=150

Alternative solution:
In a rectangle m × n there are (m+1) vertical grid lines
and (n+1) horizontal grid lines (5 and in the example here).

To define any rectangle within the grid,
we must choose 2 of each and there are
( (m+1) choose 2 ) × ( (n+1) choose 2 ) ways to do that.

For 5 × 6 that gives us
2C5 × 2C6 = 10 * 21 = 150

What would the experts say about this question, isn't it too specific/hard for GMAT ?
User avatar
V
chetan2u
Math Expert
Joined: 02 Aug 2009
Posts: 9854
Reviews Badge Top Member of the Month
As shown in the figure above 20 equal squares are arranged to form a [#permalink] New post  03 Dec 2015, 03:28
1
Bookmarks
Expert Reply
AryamaDuttaSaikia wrote:
Jamboree way

If we draw two horizontal lines and two vertical lines the enclosed quadrilateral formed will be a rectangle.

The given figure has 4 horizontal lines and 3 vertical lines. The number of ways we can select 2 horizontal lines out of 4 horizontal lines = 4C2 = 6

The number of ways we can select 2 vertical lines out of 3 vertical lines = 3C2 = 3
Total number of rectangles formed = (The number of ways we can select 2 horizontal lines) x (The number of ways we can select 2 vertical lines)

Total number of rectangles formed = 6 x 3 = 18


Hi,
I think you require to change your answer as jamboree way, which is also the normal way, is correct but seems to be answering some other Q....

there is a grid of 6 by 5 and not 4 by 3..
for a rectangle we can choose 2 horizontal points and 2 vertical points...
total ways = 6C2 * 5C2=15*10=150
User avatar
AryamaDuttaSaikia
Jamboree GMAT Instructor
Joined: 15 Jul 2015
Status:GMAT Expert
Affiliations: Jamboree Education Pvt Ltd
Posts: 261
Location: India
Re: As shown in the figure above 20 equal squares are arranged to form a [#permalink] New post  03 Dec 2015, 20:33
The solution posted earlier has been updated.
_________________
Aryama Dutta Saikia
Jamboree Education Pvt. Ltd.
Signature Read More
User avatar
V
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5439
Location: India
GMAT: QUANT EXPERT
Schools: IIM (A)
GMAT 1: 750 Q51 V41
WE:Education (Education)
Reviews Badge
Re: As shown in the figure above 20 equal squares are arranged to form a [#permalink] New post  18 Jun 2017, 01:23
1
Bookmarks
Expert Reply
AryamaDuttaSaikia wrote:
Image
As shown in the figure above, 20 equal squares are arranged to form a large rectangle. How many total rectangles does the large rectangle contain?

(a) 20
(b) 40
(c) 90
(d) 150
(e) 190

Show Spoiler
Attachment:
1.jpg


For a rectangle we need two horizontal lines out of 5 and we need 2 vertical lines out of 6

= 6C2*5C2 = 15*10 = 150

Answer: option D
_________________
GMATinsight
Great Results (Q≥50 and V≥40) l Honest and Effective Admission Support l 100% Satisfaction !!!
One-on-One GMAT Skype classes l On-demand Quant Courses and Pricing l Admissions Consulting
Call/mail: +91-9999687183 l bhoopendra.singh@gmatinsight.com (for FREE Demo class/consultation)
SUCCESS STORIES: From 620 to 760 l Q-42 to Q-49 in 40 days l 590 to 710 + Wharton l GMAT730+ESCP
FREE Resources: 22 FULL LENGTH TESTS l OG QUANT 50 Qn+VIDEO Sol. l NEW:QUANT REVISION Topicwise Quiz
Signature Read More
avatar
B
meenakshibehera
Intern
Intern
Joined: 02 Aug 2016
Posts: 2
Re: As shown in the figure above 20 equal squares are arranged to form a [#permalink] New post  18 Jun 2017, 10:50
1
Kudos
but here the question asks for rectangles . I think this no 150 includes even squares also . like vertical grid line 2and 4 will give a square in combination with horizontal lines( 1,3) ; (2,4) ; (3,5) and so on should we not exclude them from this no .
avatar
S
arichinna
Intern
Intern
Joined: 24 Jun 2013
Posts: 32
Location: India
Schools: Stanford '22 (S)
GRE 1: Q170 V159
Reviews Badge
As shown in the figure above 20 equal squares are arranged to form a [#permalink] New post  04 Jan 2018, 14:23
meenakshibehera wrote:
but here the question asks for rectangles . I think this no 150 includes even squares also . like vertical grid line 2and 4 will give a square in combination with horizontal lines( 1,3) ; (2,4) ; (3,5) and so on should we not exclude them from this no .


You are right. The solution presented includes square as well. The formulae is blindly applied to include squares.
To prove, we can solve a simple combination.

Let's take a 2X3 rectangle grid made up of small squares.
Applying the same logic, it will be 3C2 X 4C2 = 3*6 = 18. This will include squares as well.

There are only 10 such rectangles which can be formed here.
rectangles with 1x2 = 2 per row = 4 in total
rectangles with 2x1 = 1 per column = 3 in total
rectangles with 1x3 = 1 per row = 2 in total
rectangle with 2x3 = 1 in total

Moreover, there are 8 such squares in total
squares 1x1 = 2*3 = 6
squares 2x2 = 1*2 = 2

Now, applying the same to the question.
Total quadrilaterals that can be formed is 5C2 * 6C2 = 10*15 = 150.
The number of squares in this will include = 4*5 + 3*4 + 2*3 + 1*2 = 40
Hence, the total number of rectangles will be 150 - 40 = 110

With respect to the question, I suppose (looking at the picture), the smaller units appear to be rectangle. Hence, the question was incorrectly worded as 20 equal squares instead of 20 equal rectangles. If it is the latter, 150 is right.
User avatar
B
castiel
Intern
Intern
Joined: 16 Jan 2017
Posts: 10
Re: As shown in the figure above 20 equal squares are arranged to form a [#permalink] New post  20 Oct 2018, 10:57
With respect to the question, I suppose (looking at the picture), the smaller units appear to be rectangle. Hence, the question was incorrectly worded as 20 equal squares instead of 20 equal rectangles. If it is the latter, 150 is right.[/quote]


I don't think that there's any problem with the wording of the question since 'A square is also a rectangle'.
avatar
lakshay21
Intern
Intern
Joined: 26 Apr 2019
Posts: 1
Re: As shown in the figure above 20 equal squares are arranged to form a [#permalink] New post  27 Aug 2019, 05:56
AryamaDuttaSaikia wrote:
Jamboree way

If we choose any two horizontal lines and any two vertical lines the enclosed quadrilateral formed will be a rectangle.
The given figure has 5 horizontal lines and 6 vertical lines.
The number of ways we can select 2 horizontal lines out of 5 horizontal lines = 5C2 = 10
The number of ways we can select 2 vertical lines out of 6 vertical lines = 6C2 = 15

Total number of rectangles formed = (The number of ways we can select 2 horizontal lines) x (The number of ways we can select 2 vertical lines)

Total number of rectangles formed = 10 x 15 = 150


This approach will also include squares formed by selecting 2 horizontal and 2 vertical lines(if distance between horizontal lines is equal to distance between vertical lines)
so answer should definitely be less than 150.
User avatar
V
Kinshook
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 4381
Location: India
Schools: HBS '22, CBS '22, Wharton '22
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Reviews Badge
Re: As shown in the figure above 20 equal squares are arranged to form a [#permalink] New post  28 Aug 2019, 06:33
meenakshibehera wrote:
but here the question asks for rectangles . I think this no 150 includes even squares also . like vertical grid line 2and 4 will give a square in combination with horizontal lines( 1,3) ; (2,4) ; (3,5) and so on should we not exclude them from this no .



Every square is a rectangle, but every rectangle is NOT a square.
A rectangle having its length equal to width is a square.
_________________
Kinshook Chaturvedi
Email: kinshook.chaturvedi@gmail.com
Signature Read More
User avatar
V
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 6981
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE:Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member Reviews Badge
Re: As shown in the figure above 20 equal squares are arranged to form a [#permalink] New post  28 Aug 2019, 09:15
possible lines from vertical 6c2 ; 15 and horizontal 5c2 ; 10 ; total 150
IMO D


AryamaDuttaSaikia wrote:
Image
As shown in the figure above, 20 equal squares are arranged to form a large rectangle. How many total rectangles does the large rectangle contain?

(a) 20
(b) 40
(c) 90
(d) 150
(e) 190

Show Spoiler
Attachment:
1.jpg
GMAT Club Bot
gmatclubot
Re: As shown in the figure above 20 equal squares are arranged to form a [#permalink]
28 Aug 2019, 09:15
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
chetan2u
Math Expert
9854 posts
Bunuel
Math Expert
75310 posts
yashikaaggarwal
Senior Moderator - Masters Forum
2480 posts
generis
Senior SC Moderator
4743 posts

cron

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

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions