Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 11 Jul 2012
Posts: 24

Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
Updated on: 25 Sep 2012, 01:02
Question Stats:
22% (02:50) correct 78% (02:50) wrong based on 1431 sessions
HideShow timer Statistics
Arrow AB which is a line segment exactly 5 units along with an arrowhead at A is to be constructed in the xyplane. 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
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by harikris on 24 Sep 2012, 21:48.
Last edited by Bunuel on 25 Sep 2012, 01:02, edited 2 times in total.
Edited the question.




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10497
Location: Pune, India

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
02 Oct 2012, 21:09
harikris wrote: Arrow AB which is a line segment exactly 5 units along with an arrowhead at A is to be constructed in the xyplane. 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 38983 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 coordinate 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 coordinate is 3 and the y coordinate is 4. You can make 7*6 = 42 such arrows. Similarly, you can make 42 arrows with x corordinate as 4 and y coordinate 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
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Intern
Joined: 20 Sep 2012
Posts: 47
Concentration: Finance, Entrepreneurship
GPA: 3.37
WE: Analyst (Consulting)

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
25 Sep 2012, 00:01
ANSWER: E If A and B have the same xcoordinate then we have 10 pairs of ycoordinate of A and B per xcoordinate. (eg: 15, 26...) => 10*10 = 100 arrows. Similarly, if A and B have the same ycoordinate then we have another 100 arrows. If A(a,b) and B(c,d) don't have the same xcoordinate or ycoordinate then either ab=3,cd=4 or ab=4,cd=3 In the first case, there are 14 pairs of xcoordinate, and 12 pairs of ycoordinate. => 14*12 = 168 arrows. Similarly in the second case, there are 168 arrows. Therefore, We have 100 + 100 + 168 + 168 = 536 arrows.




Manager
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 129
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21 GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
02 Oct 2012, 20:24
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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10497
Location: Pune, India

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
02 Oct 2012, 20:40
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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 129
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21 GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
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) : http://gmatclub.com/forum/beatitnoonewantstobedefeatedjourney570to149968.html



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10497
Location: Pune, India

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
03 Oct 2012, 19:32
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 ... osucceed/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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 20 Jun 2011
Posts: 42

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
12 Oct 2012, 06:15
MonSama wrote: ANSWER: E If A and B have the same xcoordinate then we have 10 pairs of ycoordinate of A and B per xcoordinate. (eg: 15, 26...) => 10*10 = 100 arrows. Similarly, if A and B have the same ycoordinate then we have another 100 arrows. If A(a,b) and B(c,d) don't have the same xcoordinate or ycoordinate then either ab=3,cd=4 or ab=4,cd=3 In the first case, there are 14 pairs of xcoordinate, and 12 pairs of ycoordinate. => 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.



Math Expert
Joined: 02 Sep 2009
Posts: 64275

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
14 Jul 2013, 23:59
From 100 hardest questionsBumping for review and further discussion.
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10497
Location: Pune, India

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
22 Jul 2013, 20:56
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 coordinate is 0 in each case. You cannot go higher up because y coordinate 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 coordinate 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.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 04 Nov 2013
Posts: 19

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
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 xyplane. 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 coordinate 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 coordinate is 3 and the y coordinate is 4. You can make 7*6 = 42 such arrows. Similarly, you can make 42 arrows with x corordinate as 4 and y coordinate 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



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10497
Location: Pune, India

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
06 Nov 2013, 05:30
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 xyplane. 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 coordinate 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 coordinate is 3 and the y coordinate is 4. You can make 7*6 = 42 such arrows. Similarly, you can make 42 arrows with x corordinate as 4 and y coordinate 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.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 04 Nov 2013
Posts: 19

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
07 Nov 2013, 01:07
VeritasPrepKarishma wrote: Now check out the diagonal arrows. One coordinate 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 coordinate is 3 and the y coordinate is 4. You can make 7*6 = 42 such arrows. Similarly, you can make 42 arrows with x corordinate as 4 and y coordinate 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. coordinates  (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 36659 times ]



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10497
Location: Pune, India

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
29 Jun 2014, 20:51
Quote: VeritasPrepKarishma wrote: Now check out the diagonal arrows. One coordinate 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 coordinate is 3 and the y coordinate is 4. You can make 7*6 = 42 such arrows. Similarly, you can make 42 arrows with x corordinate as 4 and y coordinate 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. coordinates  (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
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 10 Jun 2015
Posts: 110

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
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 xyplane. 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



Intern
Joined: 15 Apr 2015
Posts: 7

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
22 Jun 2015, 10:45
Now check out the diagonal arrows. One coordinate should be of length 3 and another of 4 (so that the arrow length is 5 and all points are integers),.. Am not clear with this. Please help. Thanks in advance1



Manager
Joined: 08 Jun 2015
Posts: 99

Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
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.



Intern
Joined: 25 May 2016
Posts: 12

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
21 Jul 2016, 02:05
There is a much simpler way to do this, without having to visualise it.
The formula for distance between two points is d=Sqrt[(x2x1)^2+(y2y1)^2].
Now we know the distance is 5. so we get:
5=Sqrt[(x2x1)^2+(y2y1)^2].
25=[(x2x1)^2+(y2y1)^2]
Lets keep this aside, and look at our inequalities: 0 ≤ x ≤ 9 and 0 ≤ y ≤ 9.
This means the difference x2x1 and y2y1 can lie between 0 and 9.
Since our sum of the squares of the difference needs to be 25. The difference can be either 5 and 0, 0 and 5, 4 and 3 or 3 and 4.
The number of different coordinates for x1 and x2 which will give us a difference of:
5 is 10 0 is 10 4 is 12 3 is 14
Same for y coordinates.
So number of lines possible where the difference between x coordinates is 5 and y coordinates is 0 is 100. Interchange the differences and you get 100 more lines.
Number of lines possible where the difference between x coordinates is 4 and y coordinates is 3 is 168. Interchange the differences and you get 168 more lines.
Therefore total number of lines possible is  100+100+168+168 = 536.



Manager
Joined: 06 Oct 2015
Posts: 86
Location: Bangladesh
Concentration: Accounting, Leadership

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
24 Aug 2016, 13:09
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 xyplane. 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 coordinate 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 coordinate is 3 and the y coordinate is 4. You can make 7*6 = 42 such arrows. Similarly, you can make 42 arrows with x corordinate as 4 and y coordinate 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 Karishma, Can't the arrows start from point (1,2), (1,3), (2,3) etc.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10497
Location: Pune, India

Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
Show Tags
24 Aug 2016, 20:55
NaeemHasan 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 xyplane. 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 coordinate 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 coordinate is 3 and the y coordinate is 4. You can make 7*6 = 42 such arrows. Similarly, you can make 42 arrows with x corordinate as 4 and y coordinate 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 Karishma, Can't the arrows start from point (1,2), (1,3), (2,3) etc. Yes, they can. In the solution above: "...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. " 5 will start from x = 0. For these, y will be 0, 1, 2, 3 and 4. So the arrows will start from (0, 0), (0, 1), (0, 2) etc 5 will start from x = 1. For these too, y will be 0, 1, 2, 3 and 4. So the arrows will start from (1, 0), (1, 1), (1, 2) etc Similarly, arrows will start from (2, 0), ... (2, 4), ... (3, 0) ... etc Does this help?
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Re: Arrow AB which is a line segment exactly 5 units along with
[#permalink]
24 Aug 2016, 20:55



Go to page
1 2
Next
[ 36 posts ]

