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

 It is currently 20 Oct 2019, 14:32

### 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

# As shown in the figure above 20 equal squares are arranged to form a

Author Message
TAGS:

### Hide Tags

Jamboree GMAT Instructor
Status: GMAT Expert
Affiliations: Jamboree Education Pvt Ltd
Joined: 15 Jul 2015
Posts: 272
Location: India
As shown in the figure above 20 equal squares are arranged to form a  [#permalink]

### Show Tags

Updated on: 11 Oct 2015, 23:27
5
16
00:00

Difficulty:

85% (hard)

Question Stats:

47% (02:01) correct 53% (02:13) wrong based on 184 sessions

### HideShow timer Statistics

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

Attachment:

1.jpg [ 11.69 KiB | Viewed 3398 times ]

_________________
Aryama Dutta Saikia
Jamboree Education Pvt. Ltd.

Originally posted by AryamaDuttaSaikia on 11 Oct 2015, 23:24.
Last edited by Bunuel on 11 Oct 2015, 23:27, edited 1 time in total.
Edited the question.
Jamboree GMAT Instructor
Status: GMAT Expert
Affiliations: Jamboree Education Pvt Ltd
Joined: 15 Jul 2015
Posts: 272
Location: India
As shown in the figure above 20 equal squares are arranged to form a  [#permalink]

### Show Tags

Updated on: 03 Dec 2015, 21:34
3
7
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.

Originally posted by AryamaDuttaSaikia on 03 Dec 2015, 02:55.
Last edited by AryamaDuttaSaikia on 03 Dec 2015, 21:34, edited 1 time in total.
##### General Discussion
Intern
Joined: 24 Aug 2015
Posts: 41
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]

### Show Tags

12 Oct 2015, 00:23
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?

Paula
_________________

Don't worry about the world coming to an end today, it's already tomorrow in Australia
Manager
Joined: 02 Jul 2015
Posts: 101
Schools: ISB '18
GMAT 1: 680 Q49 V33
Re: As shown in the figure above 20 equal squares are arranged to form a  [#permalink]

### Show Tags

12 Oct 2015, 07:33
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.
Senior Manager
Joined: 10 Mar 2013
Posts: 465
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A)
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
As shown in the figure above 20 equal squares are arranged to form a  [#permalink]

### Show Tags

12 Oct 2015, 11:59
2
3
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

_________________
When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660
Math Expert
Joined: 02 Aug 2009
Posts: 7991
As shown in the figure above 20 equal squares are arranged to form a  [#permalink]

### Show Tags

03 Dec 2015, 04:28
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
_________________
Jamboree GMAT Instructor
Status: GMAT Expert
Affiliations: Jamboree Education Pvt Ltd
Joined: 15 Jul 2015
Posts: 272
Location: India
Re: As shown in the figure above 20 equal squares are arranged to form a  [#permalink]

### Show Tags

03 Dec 2015, 21:33
The solution posted earlier has been updated.
_________________
Aryama Dutta Saikia
Jamboree Education Pvt. Ltd.
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: As shown in the figure above 20 equal squares are arranged to form a  [#permalink]

### Show Tags

18 Jun 2017, 02:23

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

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

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern
Joined: 02 Aug 2016
Posts: 2
Re: As shown in the figure above 20 equal squares are arranged to form a  [#permalink]

### Show Tags

18 Jun 2017, 11:50
1
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 .
Intern
Joined: 24 Jun 2013
Posts: 32
As shown in the figure above 20 equal squares are arranged to form a  [#permalink]

### Show Tags

04 Jan 2018, 15:23
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.
Intern
Joined: 16 Jan 2017
Posts: 10
Re: As shown in the figure above 20 equal squares are arranged to form a  [#permalink]

### Show Tags

20 Oct 2018, 11:57
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'.
Intern
Joined: 26 Apr 2019
Posts: 1
Re: As shown in the figure above 20 equal squares are arranged to form a  [#permalink]

### Show Tags

27 Aug 2019, 06:56
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.
SVP
Joined: 03 Jun 2019
Posts: 1734
Location: India
Re: As shown in the figure above 20 equal squares are arranged to form a  [#permalink]

### Show Tags

28 Aug 2019, 07:33
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.
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
GMAT Club Legend
Joined: 18 Aug 2017
Posts: 5022
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: As shown in the figure above 20 equal squares are arranged to form a  [#permalink]

### Show Tags

28 Aug 2019, 10:15
possible lines from vertical 6c2 ; 15 and horizontal 5c2 ; 10 ; total 150
IMO D

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

Attachment:
1.jpg
Re: As shown in the figure above 20 equal squares are arranged to form a   [#permalink] 28 Aug 2019, 10:15
Display posts from previous: Sort by