Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Jul 2014, 08:38

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Rectangle ABCD is constructed in the coordinate plane parall

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
VP
VP
avatar
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1095
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Followers: 31

Kudos [?]: 243 [0], given: 67

Rectangle ABCD is constructed in the coordinate plane parall [#permalink] New post 11 Nov 2012, 15:58
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

49% (02:30) correct 51% (01:27) wrong based on 80 sessions
Rectangle ABCD is constructed in the coordinate plane parallel to the x- and y-axes. If the x- and y-coordinates of each of the points are integers which satisfy 3 ≤ x ≤ 11 and -5 ≤ y ≤ 5, how many possible ways are there to construct rectangle ABCD?

396
1260
1980
7920
15840
[Reveal] Spoiler: OA
4 KUDOS received
Intern
Intern
avatar
Joined: 02 Apr 2012
Posts: 32
Concentration: Finance, Strategy
GMAT 1: 710 Q50 V34
GMAT 2: 750 Q50 V41
Followers: 3

Kudos [?]: 19 [4] , given: 2

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink] New post 11 Nov 2012, 22:17
4
This post received
KUDOS
Just had a look- it is rather subtle. Here, we can choose 2 values of x and y as taking any 2 values of x and y will always yield a rectangle. For instance x=2 and x=3 are two lines parallel to y axis and y=1 and y=4 are two values parallel to x axis- plot these lines and you get a rectangle.

For the triangles query, we will need to constrain the values of the coordinates that x and y can take, say P is (x1,y1), Q(x1,y2) and R(x2,y1).

So we will need to pick one x to designate x1 and then we will have 9 more x values remaining from which we choose x2. Similarly we can do the same for y1 and y2.

That is why we get 11*10*10*9

If we choose 2 values directly , then we do not make a distinction in the order and if this happens we multiply the value by 4. Take x1=5, x2=8, y1=7 and y2=9 (so 8,5,7 and 9 can be arranged among one another and the combination does not take the changing values into account)

the four triangles you get are: (5,7), (8,7), (5,9) ; (8,7), (8,9), (5,7) ; (5,9), (8,9), (5,7) ; (8,9) , (5,9) , (5,7).

So we can also use : 4* 11C2*10C2 to get 9900

For the rectangle, choosing 2 values of x and y result in only 1 rectangle.
This is the only difference
3 KUDOS received
Intern
Intern
avatar
Status: ISB 14...:)
Joined: 25 May 2012
Posts: 30
Location: India
Concentration: Strategy
Schools: ISB '14 (A)
GMAT 1: 750 Q51 V39
GPA: 3.62
WE: Engineering (Energy and Utilities)
Followers: 1

Kudos [?]: 21 [3] , given: 10

Reviews Badge
Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink] New post 11 Nov 2012, 18:34
3
This post received
KUDOS
As the rectangle is parallel to coordinate axes, the coordinates of the points of the rectangle would be

(X1, Y1), (X2, Y1), (X2, Y2), (X1,Y2)

given that X1, X2 lie between 3 and 11..ie., 9 possible numbers

Possible combinations for X1,X2 would be 9C2 = 36

Similarly, Possible combinations for Y1, Y2 would be 11C2 = 55

Possible ways of constructing rectangle is by selecting any of the combination of X1,X2 and Y1,Y2

= 36 * 55 = 1980
Ans. C
1 KUDOS received
Intern
Intern
avatar
Joined: 02 Apr 2012
Posts: 32
Concentration: Finance, Strategy
GMAT 1: 710 Q50 V34
GMAT 2: 750 Q50 V41
Followers: 3

Kudos [?]: 19 [1] , given: 2

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink] New post 11 Nov 2012, 21:36
1
This post received
KUDOS
We need to choose 2 numbers from the x domain [3,11], since they will form two lines parallel to the y axis. Similarly, we need two values from the y domain [-5,5] to form two values parallel to the x axis. There are 9 integers for x and there are 11 numbers for y.

Choose 2 from 9 for the sides parallel to y axis: 9C2
Choose 2 from 11 for the sides parallel to x axis: 11C2

Multiply to get the overall number which should give you C.
1 KUDOS received
Intern
Intern
avatar
Joined: 02 Apr 2012
Posts: 32
Concentration: Finance, Strategy
GMAT 1: 710 Q50 V34
GMAT 2: 750 Q50 V41
Followers: 3

Kudos [?]: 19 [1] , given: 2

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink] New post 11 Nov 2012, 22:34
1
This post received
KUDOS
Sorry for the double post- but another easier way to think about this is as so: we can calculate the number of rectangles just as we have done for the original question you provided here.

Take any rectangle and you have two diagonals. Each diagonal divides the rectangle into two different right triangles. So taking the two diagonals into account, we can create 4 right triangles with each rectangle. So just multiply the number of rectangles by 4 to get the answer..
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18696
Followers: 3236

Kudos [?]: 22266 [1] , given: 2602

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink] New post 12 Nov 2012, 00:59
1
This post received
KUDOS
Expert's post
Archit143 wrote:
Rectangle ABCD is constructed in the coordinate plane parallel to the x- and y-axes. If the x- and y-coordinates of each of the points are integers which satisfy 3 ≤ x ≤ 11 and -5 ≤ y ≤ 5, how many possible ways are there to construct rectangle ABCD?

396
1260
1980
7920
15840


Similar questions to practice:
triangle-abc-will-be-constructed-in-a-xy-plane-according-to-132573.html
right-triangle-pqr-is-to-be-constructed-in-the-xy-plane-so-71597.html
right-triangle-pqr-is-to-be-constructed-in-the-xy-plane-so-88380.html
right-triangle-abc-is-to-be-drawn-in-the-xy-plane-so-that-88958.html
a-right-triangle-abc-has-to-be-constructed-in-the-xy-plane-94644.html
a-right-triangle-abc-has-to-be-constructed-in-the-xy-plane-100675.html
right-triangle-rst-can-be-constructed-in-the-xy-plane-such-137129.html

Hope it helps.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

VP
VP
avatar
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1095
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Followers: 31

Kudos [?]: 243 [0], given: 67

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink] New post 11 Nov 2012, 19:26
gnan wrote:
As the rectangle is parallel to coordinate axes, the coordinates of the points of the rectangle would be

(X1, Y1), (X2, Y1), (X2, Y2), (X1,Y2)

given that X1, X2 lie between 3 and 11..ie., 9 possible numbers

Possible combinations for X1,X2 would be 9C2 = 36

Similarly, Possible combinations for Y1, Y2 would be 11C2 = 55

Possible ways of constructing rectangle is by selecting any of the combination of X1,X2 and Y1,Y2

= 36 * 55 = 1980
Ans. C



Excellent explanation,

pls explain the similarity between between the triangle question and this, hope you would have solved it....I ll mention the question num for making it easy

OG 13 page num 185 question num 228
VP
VP
avatar
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1095
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Followers: 31

Kudos [?]: 243 [0], given: 67

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink] New post 11 Nov 2012, 21:41
seriousmonkey wrote:
We need to choose 2 numbers from the x domain [3,11], since they will form two lines parallel to the y axis. Similarly, we need two values from the y domain [-5,5] to form two values parallel to the x axis. There are 9 integers for x and there are 11 numbers for y.

Choose 2 from 9 for the sides parallel to y axis: 9C2
Choose 2 from 11 for the sides parallel to x axis: 11C2

Multiply to get the overall number which should give you C.



I used the same method to slove just wanted to know the distinction between the question in my preceding post and the the question in this thread.
VP
VP
avatar
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1095
Location: India
GMAT 1: 410 Q35 V11
GMAT 2: 530 Q44 V20
GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)
Followers: 31

Kudos [?]: 243 [0], given: 67

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink] New post 12 Nov 2012, 01:21
seriousmonkey wrote:
Sorry for the double post- but another easier way to think about this is as so: we can calculate the number of rectangles just as we have done for the original question you provided here.

Take any rectangle and you have two diagonals. Each diagonal divides the rectangle into two different right triangles. So taking the two diagonals into account, we can create 4 right triangles with each rectangle. So just multiply the number of rectangles by 4 to get the answer..



I was thinking on the same lines
Now another had the question mentioned how many different squares instead of rectangle than what will be our answer???????????
Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 14

Kudos [?]: 178 [0], given: 11

GMAT ToolKit User GMAT Tests User
Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink] New post 12 Nov 2012, 04:57
= Select 2 points along the x-axis * Select 2 points along the y-axis
= \frac{9!}{2!7!} * \frac{11!}{2!9!} = 1980

Answer: 1980

_________________

Impossible is nothing to God.

Manager
Manager
avatar
Joined: 20 Jun 2012
Posts: 96
Location: United States
Concentration: Finance, Operations
GMAT 1: 650 Q50 V28
GMAT 2: 700 Q50 V35
Followers: 1

Kudos [?]: 18 [0], given: 42

GMAT ToolKit User
Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink] New post 27 Jun 2013, 13:36
consider rectangle to be ABCD

choosing A's X and Y co-ordinate >> 10c1*9c1
choosing B's X and Y co-ordinate >> 9c1.1 (because one coordinate is fixed)
choosing C's X and Y co-ordinate >> 1.8c1 (because one coordinate is fixed)
choosing D's X and Y co-ordinate >> 1.1 (Because both coordinate are fixed)

this comes equal to 7920. I think I am considering some of the cases twice or even four times. Please tell me what am I doing wrong ..

_________________

Forget Kudos ... be an altruist

Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 15 Jun 2012
Posts: 992
Location: United States
Followers: 112

Kudos [?]: 1094 [0], given: 118

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink] New post 28 Jun 2013, 23:31
stunn3r wrote:
consider rectangle to be ABCD

choosing A's X and Y co-ordinate >> 10c1*9c1
choosing B's X and Y co-ordinate >> 9c1.1 (because one coordinate is fixed)
choosing C's X and Y co-ordinate >> 1.8c1 (because one coordinate is fixed)
choosing D's X and Y co-ordinate >> 1.1 (Because both coordinate are fixed)

this comes equal to 7920. I think I am considering some of the cases twice or even four times. Please tell me what am I doing wrong ..


Hi stunn3r

You have two errors:

(1) How did you come up with 7920, because 10C1*9C1*9C1*8C1 # 7920.
Because there are 9 ways to choose X, and 11 ways to choose Y

(2) I assume your equations are correct.
But the question here is "how many RECTANGLE?" not "how many combination of A,B,C and D ==> 4 points create only 1 rectangle ==> You should divide 7290/4 = 1980

Hope it helps.

_________________

Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Chris Bangle - Former BMV Chief of Design.

Re: Rectangle ABCD is constructed in the coordinate plane parall   [#permalink] 28 Jun 2013, 23:31
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic In the xy-coordinate system, rectangle ABCD is inscribed wit skamal7 10 14 Jul 2013, 21:27
1 Parallelogram ABCD is to be constructed in the xy-plane such cyberjadugar 10 05 Jul 2013, 03:08
30 Experts publish their posts in the topic A rectangle is plotted on the standard coordinate plane guygmat 23 19 Jun 2011, 22:18
2 Experts publish their posts in the topic A rectangle is plotted on the standard coordinate plane, JenniferClopton 13 02 Dec 2010, 12:13
In the xy-coordinate system, rectangle ABCD is inscribed kuristar 1 04 May 2006, 08:06
Display posts from previous: Sort by

Rectangle ABCD is constructed in the coordinate plane parall

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.