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Triangle integers

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Manager
Manager
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Joined: 08 Jul 2009
Posts: 172

Kudos [?]: 93 [0], given: 13

Triangle integers [#permalink]

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New post 10 Jul 2009, 20:30
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A
B
C
D
E

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Picture a triangle OPQ on a coordinate plane with the following coordinates P(0,30) O (0,0) Q (50,0)

In the figure above, how many of the points on line segment PQ have coordinates that are both integers?
(A) 5
(B) 8
(C) 10
(D) 11
(E) 20

Kudos [?]: 93 [0], given: 13

Senior Manager
Senior Manager
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Joined: 04 Jun 2008
Posts: 286

Kudos [?]: 162 [0], given: 15

Re: Triangle integers [#permalink]

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New post 10 Jul 2009, 20:44
After drawing/imagining the triangle, you will be able to find out the equation of the line PQ.

ie (Y-Y1)/(X-X1) = m..........m=slope

(30-0)/(0-50) = m
m = -3/5
so slope of PQ is -3/5

Now using Y = mx +C we get Y = -3x/5 + 30.......... equation of line PQ

for Y to be an integer, x must be a multiple of 5. You have 10 multiples of 5 upto 50 (50 is the highest value of x)

ans is 10

Kudos [?]: 162 [0], given: 15

Manager
Manager
avatar
Joined: 08 Jul 2009
Posts: 172

Kudos [?]: 93 [0], given: 13

Re: Triangle integers [#permalink]

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New post 10 Jul 2009, 21:23
The ans is 11 though

I see your point but you are not counting the extremes

50,0
45,3
40,6
35,9
30,12
25,15
20,18
15,21
10,24,
5,27
0,30

Kudos [?]: 93 [0], given: 13

Director
Director
User avatar
Joined: 01 Apr 2008
Posts: 872

Kudos [?]: 884 [0], given: 18

Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: Triangle integers [#permalink]

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New post 11 Jul 2009, 00:06
Yup.
X is from 0,5,10...50. so ans shud be 11.
sher676 wrote:
The ans is 11 though

I see your point but you are not counting the extremes

50,0
45,3
40,6
35,9
30,12
25,15
20,18
15,21
10,24,
5,27
0,30

Kudos [?]: 884 [0], given: 18

Senior Manager
Senior Manager
avatar
Joined: 04 Jun 2008
Posts: 286

Kudos [?]: 162 [0], given: 15

Re: Triangle integers [#permalink]

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New post 11 Jul 2009, 05:45
thanks for the correction.

missed out on x=0 :oops :-D

Kudos [?]: 162 [0], given: 15

Re: Triangle integers   [#permalink] 11 Jul 2009, 05:45
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Triangle integers

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