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Arrow AB which is a line segment exactly 5 units along with

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Arrow AB which is a line segment exactly 5 units along with [#permalink]  24 Sep 2012, 21:48
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Arrow AB which is a line segment exactly 5 units along with an arrowhead at A is to be constructed in the xy-plane. The x and y coordinates of A and B are to be integers that satisfy the inequalities 0 ≤ x ≤ 9 and 0 ≤ y ≤ 9. How many different arrows with these properties can be constructed ?

A. 50
B. 168
C. 200
D. 368
E. 536
[Reveal] Spoiler: OA

Last edited by Bunuel on 25 Sep 2012, 01:02, edited 2 times in total.
Edited the question.
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Re: Arrow AB which is a line segment exactly 5 units along with [#permalink]  02 Oct 2012, 21:09
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harikris wrote:
Arrow AB which is a line segment exactly 5 units along with an arrowhead at A is to be constructed in the xy-plane. The x and y coordinates of A and B are to be integers that satisfy the inequalities 0 ≤ x ≤ 9 and 0 ≤ y ≤ 9. How many different arrows with these properties can be constructed ?

A. 50
B. 168
C. 200
D. 368
E. 536

Consider the diagram.
The arrows could be vertical, horizontal or diagonal.

Attachment:

Ques4.jpg [ 25.55 KiB | Viewed 15060 times ]

The vertical arrows are shown by the blue arrows. 5 of them will start from x = 0, 5 from x = 1 and so on till x = 9. So you have 50 of these blue arrows. You have another 50 vertical arrows which are the same arrows but with the arrow head on the opposite end (shown by the red arrow). So you have a total of 100 vertical arrows.
Similarly, you have 100 horizontal arrows.

Now check out the diagonal arrows. One co-ordinate should be of length 3 and another of 4 (so that the arrow length is 5 and all points are integers). Look at the purple arrows. The x co-ordinate is 3 and the y co-ordinate is 4. You can make 7*6 = 42 such arrows. Similarly, you can make 42 arrows with x cor-ordinate as 4 and y co-ordinate as 3. So you have 84 arrows. But you get another set of 84 arrows by keeping the arrows the same but putting the arrow head on the opposite end so you get a total of 2*84 = 168 arrows.

Similarly, you can make arrows in the opposite direction shown by the green arrows. So you have another 168 arrows.

Total = 100 + 100 + 168 + 168 = 536
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 20 Sep 2012 Posts: 51 Concentration: Finance, Entrepreneurship Schools: HSG '15 (A) GMAT 1: 750 Q50 V40 GPA: 3.37 Followers: 4 Kudos [?]: 35 [7] , given: 34 Re: Arrow AB which is a line segment exactly 5 units along with [#permalink] 25 Sep 2012, 00:01 7 This post received KUDOS 1 This post was BOOKMARKED ANSWER: E If A and B have the same x-coordinate then we have 10 pairs of y-coordinate of A and B per x-coordinate. (eg: 1-5, 2-6...) => 10*10 = 100 arrows. Similarly, if A and B have the same y-coordinate then we have another 100 arrows. If A(a,b) and B(c,d) don't have the same x-coordinate or y-coordinate then either |a-b|=3,|c-d|=4 or |a-b|=4,|c-d|=3 In the first case, there are 14 pairs of x-coordinate, and 12 pairs of y-coordinate. => 14*12 = 168 arrows. Similarly in the second case, there are 168 arrows. Therefore, We have 100 + 100 + 168 + 168 = 536 arrows. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6062 Location: Pune, India Followers: 1597 Kudos [?]: 8953 [2] , given: 195 Re: Arrow AB which is a line segment exactly 5 units along with [#permalink] 02 Oct 2012, 20:40 2 This post received KUDOS Expert's post daviesj wrote: I didn't get the explaination.... what i did was i formed the grid on xy plane with info provided. total grid points i got were 100 and we need to select 2 points to form an arrow...so 100C2 : 4950...which is nowhere near the answer....whr exactly i m making the mistake? Posted from my mobile device What you forgot to consider is that the length of the arrow must be 5 units. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Arrow AB which is a line segment exactly 5 units along with [#permalink]  22 Jul 2013, 20:56
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VeritasPrepKarishma wrote:
The vertical arrows are shown by the blue arrows. 5 of them will start from x = 0, 5 from x = 1 and so on till x = 9. So you have 50 of these blue arrows.

Responding to a pm:

This is what this statement means: Draw an arrow starting from (0, 0) to (0, 5). Head of the arrow is at (0, 5). Then draw another one starting from (0, 1) to (0, 6). Another from (0, 2) to (0, 7). Another from (0, 3 to 0, 8). Another from (0, 4) to (0, 9). You are able to draw these 5 arrows such that x co-ordinate is 0 in each case. You cannot go higher up because y co-ordinate cannot be more than 9.

Similarly, draw an arrow starting from (1, 0) to (1, 5). Another from (1, 1) to (1, 6) and so on... You will again be able to draw 5 such arrows.

Keep increasing x co-ordinate by 1 and you will get 5 arrows each time till you reach x = 9. So you will get 10 groups of 5 vertical arrows each i.e. 50 such arrows.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Status: Never ever give up on yourself.Period. Joined: 23 Aug 2012 Posts: 147 Location: India Concentration: Finance, Human Resources Schools: MBS '17 (A) GMAT 1: 570 Q47 V21 GMAT 2: 690 Q50 V33 GPA: 3.5 WE: Information Technology (Investment Banking) Followers: 9 Kudos [?]: 204 [1] , given: 35 Re: Arrow AB which is a line segment exactly 5 units along with [#permalink] 02 Oct 2012, 20:24 1 This post received KUDOS I didn't get the explaination.... what i did was i formed the grid on xy plane with info provided. total grid points i got were 100 and we need to select 2 points to form an arrow...so 100C2 : 4950...which is nowhere near the answer....whr exactly i m making the mistake? Posted from my mobile device Manager Status: Never ever give up on yourself.Period. Joined: 23 Aug 2012 Posts: 147 Location: India Concentration: Finance, Human Resources Schools: MBS '17 (A) GMAT 1: 570 Q47 V21 GMAT 2: 690 Q50 V33 GPA: 3.5 WE: Information Technology (Investment Banking) Followers: 9 Kudos [?]: 204 [0], given: 35 Re: Arrow AB which is a line segment exactly 5 units along with [#permalink] 03 Oct 2012, 03:44 Thanks for the wonderful explanation Karishma. Kudos for that. Now what my concern is, should we expect to get this type of problems in the real exam?...I mean in this problem we need to draw the figure and need to manually count the possibilities that is time consuming. Thanks. _________________ Don't give up on yourself ever. Period. Beat it, no one wants to be defeated (My journey from 570 to 690) : beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6062 Location: Pune, India Followers: 1597 Kudos [?]: 8953 [0], given: 195 Re: Arrow AB which is a line segment exactly 5 units along with [#permalink] 03 Oct 2012, 19:32 Expert's post 1 This post was BOOKMARKED daviesj wrote: Thanks for the wonderful explanation Karishma. Kudos for that. Now what my concern is, should we expect to get this type of problems in the real exam?...I mean in this problem we need to draw the figure and need to manually count the possibilities that is time consuming. Thanks. This question is based on an OG question. The OG question uses this concept though it doesn't require you to manually count the different cases. I have discussed that question in this post: http://www.veritasprep.com/blog/2011/09 ... o-succeed/ Given unlimited time, you should be able to do this question i.e. conceptually you should be clear with this. It is a time consuming laborious question so I wouldn't expect GMAT to give this. It is missing the excitement - you can do most GMAT in under a minute or perhaps even 30 secs. The fun is to be able to figure out the logical trick that makes it tick. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Arrow AB which is a line segment exactly 5 units along with [#permalink]  12 Oct 2012, 06:15
MonSama wrote:
If A and B have the same x-coordinate then we have 10 pairs of y-coordinate of A and B per x-coordinate. (eg: 1-5, 2-6...) => 10*10 = 100 arrows.
Similarly, if A and B have the same y-coordinate then we have another 100 arrows.
If A(a,b) and B(c,d) don't have the same x-coordinate or y-coordinate then either |a-b|=3,|c-d|=4 or |a-b|=4,|c-d|=3
In the first case, there are 14 pairs of x-coordinate, and 12 pairs of y-coordinate. => 14*12 = 168 arrows.
Similarly in the second case, there are 168 arrows.
Therefore, We have 100 + 100 + 168 + 168 = 536 arrows.

How did you find the coordinate pairs?

Thanks.
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Re: Arrow AB which is a line segment exactly 5 units along with [#permalink]  14 Jul 2013, 23:59
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Re: Arrow AB which is a line segment exactly 5 units along with [#permalink]  05 Nov 2013, 06:07
VeritasPrepKarishma wrote:
harikris wrote:
Arrow AB which is a line segment exactly 5 units along with an arrowhead at A is to be constructed in the xy-plane. The x and y coordinates of A and B are to be integers that satisfy the inequalities 0 ≤ x ≤ 9 and 0 ≤ y ≤ 9. How many different arrows with these properties can be constructed ?

A. 50
B. 168
C. 200
D. 368
E. 536

Consider the diagram.
The arrows could be vertical, horizontal or diagonal.

Attachment:
Ques4.jpg

The vertical arrows are shown by the blue arrows. 5 of them will start from x = 0, 5 from x = 1 and so on till x = 9. So you have 50 of these blue arrows. You have another 50 vertical arrows which are the same arrows but with the arrow head on the opposite end (shown by the red arrow). So you have a total of 100 vertical arrows.
Similarly, you have 100 horizontal arrows.

Now check out the diagonal arrows. One co-ordinate should be of length 3 and another of 4 (so that the arrow length is 5 and all points are integers). Look at the purple arrows. The x co-ordinate is 3 and the y co-ordinate is 4. You can make 7*6 = 42 such arrows. Similarly, you can make 42 arrows with x cor-ordinate as 4 and y co-ordinate as 3. So you have 84 arrows. But you get another set of 84 arrows by keeping the arrows the same but putting the arrow head on the opposite end so you get a total of 2*84 = 168 arrows.

Similarly, you can make arrows in the opposite direction shown by the green arrows. So you have another 168 arrows.

Total = 100 + 100 + 168 + 168 = 536

Hi, cant we make slanting arrows also in the opposite direction like vertical and horizontal arrows i.e. just reversing the coordinates of A and B.

thanks
Abhishek
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Re: Arrow AB which is a line segment exactly 5 units along with [#permalink]  06 Nov 2013, 05:30
Expert's post
Astral wrote:
VeritasPrepKarishma wrote:
harikris wrote:
Arrow AB which is a line segment exactly 5 units along with an arrowhead at A is to be constructed in the xy-plane. The x and y coordinates of A and B are to be integers that satisfy the inequalities 0 ≤ x ≤ 9 and 0 ≤ y ≤ 9. How many different arrows with these properties can be constructed ?

A. 50
B. 168
C. 200
D. 368
E. 536

Consider the diagram.
The arrows could be vertical, horizontal or diagonal.

Attachment:
Ques4.jpg

The vertical arrows are shown by the blue arrows. 5 of them will start from x = 0, 5 from x = 1 and so on till x = 9. So you have 50 of these blue arrows. You have another 50 vertical arrows which are the same arrows but with the arrow head on the opposite end (shown by the red arrow). So you have a total of 100 vertical arrows.
Similarly, you have 100 horizontal arrows.

Now check out the diagonal arrows. One co-ordinate should be of length 3 and another of 4 (so that the arrow length is 5 and all points are integers). Look at the purple arrows. The x co-ordinate is 3 and the y co-ordinate is 4. You can make 7*6 = 42 such arrows. Similarly, you can make 42 arrows with x cor-ordinate as 4 and y co-ordinate as 3. So you have 84 arrows. But you get another set of 84 arrows by keeping the arrows the same but putting the arrow head on the opposite end so you get a total of 2*84 = 168 arrows.

Similarly, you can make arrows in the opposite direction shown by the green arrows. So you have another 168 arrows.

Total = 100 + 100 + 168 + 168 = 536

Hi, cant we make slanting arrows also in the opposite direction like vertical and horizontal arrows i.e. just reversing the coordinates of A and B.

thanks
Abhishek

Look at the highlighted part above. We have already taken care of it.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 04 Nov 2013 Posts: 3 Followers: 0 Kudos [?]: 0 [0], given: 0 Re: Arrow AB which is a line segment exactly 5 units along with [#permalink] 07 Nov 2013, 01:07 VeritasPrepKarishma wrote: Now check out the diagonal arrows. One co-ordinate should be of length 3 and another of 4 (so that the arrow length is 5 and all points are integers). Look at the purple arrows. The x co-ordinate is 3 and the y co-ordinate is 4. You can make 7*6 = 42 such arrows. Similarly, you can make 42 arrows with x cor-ordinate as 4 and y co-ordinate as 3. So you have 84 arrows. But you get another set of 84 arrows by keeping the arrows the same but putting the arrow head on the opposite end so you get a total of 2*84 = 168 arrows. Similarly, you can make arrows in the opposite direction shown by the green arrows. So you have another 168 arrows. Total = 100 + 100 + 168 + 168 = 536 Hi, cant we make slanting arrows also in the opposite direction like vertical and horizontal arrows i.e. just reversing the coordinates of A and B. thanks Abhishek Look at the highlighted part above. We have already taken care of it.[/quote] Thanks a lot for the reply. There can be 4 different types of lines with 4 different slopes that may have 5 units as length (for eg. co-ordinates - (4,0)&(0,3); (3,0)&(0,4); (0,0)&(3,4); (0,0)&(4,3). Thus total number of lines 42*4=168. And if arrows are reversed number will be 168*2 = 336. Request you to please let me know if I am going wrong somewhere. thanks. Attachments Untitled.jpg [ 21.32 KiB | Viewed 13061 times ] Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 6062 Location: Pune, India Followers: 1597 Kudos [?]: 8953 [0], given: 195 Re: Arrow AB which is a line segment exactly 5 units along with [#permalink] 29 Jun 2014, 20:51 Expert's post Quote: VeritasPrepKarishma wrote: Now check out the diagonal arrows. One co-ordinate should be of length 3 and another of 4 (so that the arrow length is 5 and all points are integers). Look at the purple arrows. The x co-ordinate is 3 and the y co-ordinate is 4. You can make 7*6 = 42 such arrows. Similarly, you can make 42 arrows with x cor-ordinate as 4 and y co-ordinate as 3 (these are your blue and yellow arrows). So you have 84 arrows. But you get another set of 84 arrows by keeping the arrows the same but putting the arrow head on the opposite end so you get a total of 2*84 = 168 arrows. Similarly, you can make arrows in the opposite direction shown by the green arrows. (these are your red and black arrows) So you have another 168 arrows. Total = 100 + 100 + 168 + 168 = 536 There can be 4 different types of lines with 4 different slopes that may have 5 units as length (for eg. co-ordinates - (4,0)&(0,3); (3,0)&(0,4); (0,0)&(3,4); (0,0)&(4,3). Thus total number of lines 42*4=168. And if arrows are reversed number will be 168*2 = 336. Request you to please let me know if I am going wrong somewhere. thanks. Note that we have already taken all 4 of them them into account in the highlighted part above. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Arrow AB which is a line segment exactly 5 units along with [#permalink]  10 Jun 2015, 23:36
harikris wrote:
Arrow AB which is a line segment exactly 5 units along with an arrowhead at A is to be constructed in the xy-plane. The x and y coordinates of A and B are to be integers that satisfy the inequalities 0 ≤ x ≤ 9 and 0 ≤ y ≤ 9. How many different arrows with these properties can be constructed ?

A. 50
B. 168
C. 200
D. 368
E. 536

I guess it is more than 400. ans is E
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Re: Arrow AB which is a line segment exactly 5 units along with [#permalink]  22 Jun 2015, 10:45
Now check out the diagonal arrows. One co-ordinate should be of length 3 and another of 4 (so that the arrow length is 5 and all points are integers),..
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Arrow AB which is a line segment exactly 5 units along with [#permalink]  25 Jul 2015, 17:53
The way I did the diagonal arrows is... I drew a 3x4 (right 3, up 4) box from the origin. For each of those, you can have 4 sets of coordinates for A and B (e.g. A(0,0)+B(3,4); A(3,4)+B(0,0); A(3,0)+B(0,4); A(0,4)+B(3,0).

Moving up, you can make 5 more boxes, so that's 6 for the first column. Using the same 3x4 boxes, you can move right 6 times, so there are 7 of those. That's 6x7=42 times the box is made, with each box having 4 distinct arrows with their respective vectors. So, that's 42x4 = 168.

You can also make 4x3 squares from the origin. Using the same idea, you get another 168 distinct arrows.

So far in total that's 336 arrows.

Combine that with the 100 vertical and 100 horizontal arrows, then the total is 536 arrows.
Arrow AB which is a line segment exactly 5 units along with   [#permalink] 25 Jul 2015, 17:53
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