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# In the figure below, how many of the points on line segment

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In the figure below, how many of the points on line segment [#permalink]

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03 Apr 2004, 04:32
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In the figure below, 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

|P(0,30)
|\
| \
| \
| \
| \
|_____ \_______________________
Q(50,0)

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Joined: 02 Mar 2004
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03 Apr 2004, 04:51
Line eqn L: (x/50)+(y/30) = 1

3x+5y = 150

3x = 150-5y
x = 50-2y+(y/3)
y = 3k, x = 50-5k
0 <= 50-5k <= 50
0 <= 3k <= 30 or 0 <= k <= 10

Answer = |{0, 1, 2, ..., 10}| = 11

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Intern
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03 Apr 2004, 04:53
is the ans 11?

heres my solution:
use the two-point form to find the equation of the line
(y - y1)/(y1 - y2) = (x - x1)/(x1 - x2)

i got 3x + 5y = 150
when x = 0, y = 30
when x = 5, y = 27
so x multiples of 5 will give y in integers.
max x = 50
so 11 points...

awaiting corrections....

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03 Apr 2004, 04:53
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