It is currently 17 Oct 2017, 12:14

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Rectangle ABCD is constructed in the coordinate plane parall

Author Message
TAGS:

### Hide Tags

VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1077

Kudos [?]: 646 [0], given: 70

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
00:00

Difficulty:

95% (hard)

Question Stats:

45% (01:28) correct 55% (01:43) wrong based on 304 sessions

### HideShow timer Statistics

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

Kudos [?]: 646 [0], given: 70

Intern
Status: ISB 14...:)
Joined: 26 May 2012
Posts: 30

Kudos [?]: 40 [8], given: 11

Location: India
Concentration: Strategy
Schools: ISB '14 (A)
GMAT 1: 750 Q51 V39
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
8
KUDOS
5
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

Kudos [?]: 40 [8], given: 11

VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1077

Kudos [?]: 646 [0], given: 70

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

Kudos [?]: 646 [0], given: 70

Intern
Joined: 02 Apr 2012
Posts: 32

Kudos [?]: 20 [1], given: 2

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
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.

Kudos [?]: 20 [1], given: 2

VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1077

Kudos [?]: 646 [0], given: 70

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.

Kudos [?]: 646 [0], given: 70

Intern
Joined: 02 Apr 2012
Posts: 32

Kudos [?]: 20 [4], given: 2

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
KUDOS
1
This post was
BOOKMARKED
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

Kudos [?]: 20 [4], given: 2

Intern
Joined: 02 Apr 2012
Posts: 32

Kudos [?]: 20 [1], given: 2

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
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..

Kudos [?]: 20 [1], given: 2

Math Expert
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128579 [2], given: 12180

Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink]

### Show Tags

12 Nov 2012, 01:59
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.
_________________

Kudos [?]: 128579 [2], given: 12180

VP
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 1077

Kudos [?]: 646 [0], given: 70

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???????????

Kudos [?]: 646 [0], given: 70

Senior Manager
Joined: 13 Aug 2012
Posts: 459

Kudos [?]: 540 [0], given: 11

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 x-axis * Select 2 points along the y-axis
= $$\frac{9!}{2!7!} * \frac{11!}{2!9!} = 1980$$

_________________

Impossible is nothing to God.

Kudos [?]: 540 [0], given: 11

Manager
Joined: 20 Jun 2012
Posts: 100

Kudos [?]: 45 [0], given: 52

Location: United States
Concentration: Finance, Operations
GMAT 1: 710 Q51 V25
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 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

Kudos [?]: 45 [0], given: 52

Verbal Forum Moderator
Joined: 16 Jun 2012
Posts: 1127

Kudos [?]: 3478 [1], given: 123

Location: United States
Re: Rectangle ABCD is constructed in the coordinate plane parall [#permalink]

### Show Tags

29 Jun 2013, 00:31
1
KUDOS
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 BMW Chief of Design.

Kudos [?]: 3478 [1], given: 123

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16758

Kudos [?]: 273 [0], given: 0

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.
_________________

Kudos [?]: 273 [0], given: 0

Intern
Joined: 09 Sep 2014
Posts: 6

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

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.

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

Manager
Joined: 03 May 2013
Posts: 76

Kudos [?]: 13 [0], given: 105

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

Kudos [?]: 13 [0], given: 105

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16758

Kudos [?]: 273 [0], given: 0

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.
_________________

Kudos [?]: 273 [0], given: 0

Re: Rectangle ABCD is constructed in the coordinate plane parall   [#permalink] 26 Sep 2016, 13:39
Display posts from previous: Sort by