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

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25 Aug 2016, 09:56

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

Very nice question. But took more than 5 mins to solve. Used the approach same as discussed above. Is there another way ?

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

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26 Aug 2016, 05:07

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,

Tried viewing the diagram but it seems diagram cannot be viewed. Please re-upload it, if possible.

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,

Tried viewing the diagram but it seems diagram cannot be viewed. Please re-upload it, if possible.

"The x co-ordinate is 3 and the y co-ordinate is 4. You can make 7*6 = 42 such arrows. "

Hi Karishma, Many thanks in advance... Will you please tell me how you got this ? " You can make 7*6 = 42 such arrows.[/color]"

How you got 7*6 ?

x is between 0 and 9 (inclusive) and y is between 0 and 9 (inclusive).

So if we need the length of x to be 3, we can start it anywhere from x = 0 to x = 6 (7 cases). If we start the arrow at x = 7, with a length of 3, it will mean that the end point of the arrow will have x co-ordinate of 10 (which is not allowed). So for the x co-ordinate, you have 7 options.

Similarly, the length of y should be 4 so we can start it anywhere from y = 0 to y = 5 (6 cases) If we start the arrow at y = 6, with a length of 4, it will mean that the end point of the arrow will have y co-ordinate of 10 (which is not allowed). So for the y co-ordinate, you have 6 options.

Hence you get a total of 7 * 6 = 42 acceptable cases.
_________________

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

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28 Aug 2016, 23:41

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 ?

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

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29 Aug 2016, 01:31

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 ?

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

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14 Sep 2017, 18:51

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