Author 
Message 
TAGS:

Hide Tags

VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1082
Location: India
GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)

Rectangle ABCD is constructed in the coordinate plane parall [#permalink]
Show Tags
11 Nov 2012, 16:58
17
This post was BOOKMARKED
Question Stats:
45% (02:29) correct
55% (01:44) wrong based on 300 sessions
HideShow timer Statistics
Rectangle ABCD is constructed in the coordinate plane parallel to the x and yaxes. If the x and ycoordinates 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
Official Answer and Stats are available only to registered users. Register/ Login.



Intern
Status: ISB 14...:)
Joined: 26 May 2012
Posts: 30
Location: India
Concentration: Strategy
GPA: 3.62
WE: Engineering (Energy and Utilities)

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink]
Show Tags
11 Nov 2012, 19:34
7
This post received KUDOS
4
This post was BOOKMARKED
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



VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1082
Location: India
GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink]
Show Tags
11 Nov 2012, 20:26
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



Intern
Joined: 02 Apr 2012
Posts: 32
Concentration: Finance, Strategy
GMAT 1: 710 Q50 V34 GMAT 2: 750 Q50 V41

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink]
Show Tags
11 Nov 2012, 22:36
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.



VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1082
Location: India
GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink]
Show Tags
11 Nov 2012, 22:41
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.



Intern
Joined: 02 Apr 2012
Posts: 32
Concentration: Finance, Strategy
GMAT 1: 710 Q50 V34 GMAT 2: 750 Q50 V41

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink]
Show Tags
11 Nov 2012, 23:17
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



Intern
Joined: 02 Apr 2012
Posts: 32
Concentration: Finance, Strategy
GMAT 1: 710 Q50 V34 GMAT 2: 750 Q50 V41

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink]
Show Tags
11 Nov 2012, 23:34
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..



Math Expert
Joined: 02 Sep 2009
Posts: 39589

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink]
Show Tags
12 Nov 2012, 01:59
2
This post received KUDOS
Expert's post
1
This post was BOOKMARKED



VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1082
Location: India
GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31
GPA: 3.84
WE: Engineering (Transportation)

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink]
Show Tags
12 Nov 2012, 02:21
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
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GPA: 3.23

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink]
Show Tags
12 Nov 2012, 05:57
= Select 2 points along the xaxis * Select 2 points along the yaxis = \(\frac{9!}{2!7!} * \frac{11!}{2!9!} = 1980\) Answer: 1980
_________________
Impossible is nothing to God.



Manager
Joined: 20 Jun 2012
Posts: 102
Location: United States
Concentration: Finance, Operations

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink]
Show Tags
27 Jun 2013, 14:36
consider rectangle to be ABCD choosing A's X and Y coordinate >> 10c1*9c1 choosing B's X and Y coordinate >> 9c1.1 (because one coordinate is fixed) choosing C's X and Y coordinate >> 1.8c1 (because one coordinate is fixed) choosing D's X and Y coordinate >> 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
Joined: 16 Jun 2012
Posts: 1127
Location: United States

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink]
Show Tags
29 Jun 2013, 00:31
1
This post received KUDOS
stunn3r wrote: consider rectangle to be ABCD
choosing A's X and Y coordinate >> 10c1*9c1 choosing B's X and Y coordinate >> 9c1.1 (because one coordinate is fixed) choosing C's X and Y coordinate >> 1.8c1 (because one coordinate is fixed) choosing D's X and Y coordinate >> 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 BMW Chief of Design.



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15918

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink]
Show Tags
10 Sep 2014, 09:30
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 Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Intern
Joined: 09 Sep 2014
Posts: 6

Rectangle ABCD is constructed in the coordinate plane parall [#permalink]
Show Tags
10 Sep 2014, 13:27
The way I solved this problem was by thinking about the points and lines on the graph.
I chose two points on the horizontal axis between 3 & 11 . Because it doesn't specify that the points are integers I considered EVERY point, including the first, making the choices (9)(9) you then multiply by 11 because there are 11 points on the y axis. (9)(9)(11)= 891
You do the same thing for the y axis. 11 possible points and 2 must be chosen considering also that there are 9 horizontal points. (11)(11)(9) = 1089
Added together. (9)(9)(11) + (11)(11)(9) = 1980
An interesting thing is that the answer is a little smaller than 1980 because the axis points cannot be the same on the graph... but since there are an infinite number of points between 3 & 11, the difference is negligible.



Manager
Joined: 03 May 2013
Posts: 75

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink]
Show Tags
04 Aug 2015, 06:04
hi experts please tell me what is wrong with it
9*11(no of ways to select first point) *8 (another point on x axis) * 10(no of ways for another point on y axis)
BTW OA is 9*11(no of ways to select first point) *8 (another point on x axis) * 10(no of ways for another point on y axis) / 2



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15918

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink]
Show Tags
26 Sep 2016, 13:39
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 Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: Rectangle ABCD is constructed in the coordinate plane parall
[#permalink]
26 Sep 2016, 13:39







