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points on PQ

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by kanha81 » Wed May 27, 2009 10:35 am
In the attached figure, 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

Please explain.
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by sacx » Wed May 27, 2009 11:07 pm
I am getting 11 but I don't know if my method is correct

Slope of the line PQ = -3/5 or -0.6

so for every 0.6 increase in y-axis, x-axis decreases by 1

so the integer values for y-axis would be an interval of 3 (3,6,9,12,15,18,21,24,27,30)

So the points would be
(3,45)
(6,40)
(9,35)
(12,30)
(15,25)
(18,20)
(21,15)
(24,10)
(27,5)
(30,0)

and (50,0)

Whats the OA?
SACX
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by dumb.doofus » Wed May 27, 2009 11:12 pm
Just write the equation of the line..

y = -3/5x + 30..

Now for y to be an integer.. x needs to be a multiple of 5 or zero.

from 5 to 50 there are 10 multiples.. and when we include 0.. the total number of integers is 11..

so 11 points on the line are integers..

I have used the following formula to write the equation of a line..
When you have two points (x1,y1) and (x2,y2) .. then line joining these two points is

(x-x1)/(x2-x1) = (y-y1)/(y2-y1)
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Find the equation of line

by rah_pandey » Thu May 28, 2009 1:19 am
The equation of the line is x=50-5/3*y

for x and Y to be integers it is necessary from the equation above that y is a factor of 3 with the condition that y<=30 otherwise infinite solns exist.

the factors are 0,3,6,9.....30. Now if 0 and 30 are included than 11 is correct answer and if both are excluded than 9 such points exist. if only one than 10 such points exist.
(50,0),(45,3),(40,6) and so on...
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by kanha81 » Thu May 28, 2009 6:52 am
dumb.doofus wrote:Just write the equation of the line..

y = -3/5x + 30..

Now for y to be an integer.. x needs to be a multiple of 5 or zero.

from 5 to 50 there are 10 multiples.. and when we include 0.. the total number of integers is 11..

so 11 points on the line are integers..

I have used the following formula to write the equation of a line..
When you have two points (x1,y1) and (x2,y2) .. then line joining these two points is

(x-x1)/(x2-x1) = (y-y1)/(y2-y1)
Thank you all. The explanation makes sense. OA is [spoiler][D][/spoiler]
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