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# Triangle integers

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Manager
Joined: 08 Jul 2009
Posts: 160

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10 Jul 2009, 21:30
00:00

Difficulty:

(N/A)

Question Stats:

100% (00:25) correct 0% (00:00) wrong based on 5 sessions

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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

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Senior Manager
Joined: 04 Jun 2008
Posts: 279

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10 Jul 2009, 21:44
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
Manager
Joined: 08 Jul 2009
Posts: 160

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10 Jul 2009, 22:23
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
Director
Joined: 01 Apr 2008
Posts: 827
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014

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11 Jul 2009, 01:06
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
Senior Manager
Joined: 04 Jun 2008
Posts: 279

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11 Jul 2009, 06:45
thanks for the correction.

missed out on x=0 ops

--== Message from GMAT Club Team ==--

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If you would like to discuss this question please re-post it in the respective forum. Thank you!

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Re: Triangle integers   [#permalink] 11 Jul 2009, 06:45
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