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# Q : In a XY Coordinate plane Point P has (0, 30) coordinates

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Intern
Joined: 13 Jun 2004
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Q : In a XY Coordinate plane Point P has (0, 30) coordinates [#permalink]  21 Mar 2006, 21:34
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Q : In a XY Coordinate plane Point P has (0, 30) coordinates and Point Q has (50, 0). How many of the points on line seqment PQ have coordinates that are both integers ?

A : 5
B : 8
C : 10
D : 11
E : 20
Manager
Joined: 09 Feb 2006
Posts: 129
Location: New York, NY
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Kudos [?]: 3 [0], given: 0

In a XY Coordinate plane Point P has (0, 30) coordinates and Point Q has (50, 0). How many of the points on line seqment PQ have coordinates that are both integers ?

First, let's set up the equation: y=mx+b

30 = b
m = -3/5

So the line can be stated as y = -(3/5)x + 30

So we know that for every 5 integers, x and y will be integers. The range of x is 0 to 50. This would lead us to 10, but we need to add 1 because it is inclusive.
Intern
Joined: 13 Jun 2004
Posts: 4
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Kudos [?]: 0 [0], given: 0

Yep..But OA is 10
Senior Manager
Joined: 29 Jun 2005
Posts: 403
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Kudos [?]: 15 [0], given: 0

jcgoodchild wrote:
In a XY Coordinate plane Point P has (0, 30) coordinates and Point Q has (50, 0). How many of the points on line seqment PQ have coordinates that are both integers ?

First, let's set up the equation: y=mx+b

30 = b
m = -3/5

So the line can be stated as y = -(3/5)x + 30

So we know that for every 5 integers, x and y will be integers. The range of x is 0 to 50. This would lead us to 10, but we need to add 1 because it is inclusive.

You should add Point Q and Point P. then you will get 10.
Manager
Joined: 09 Feb 2006
Posts: 129
Location: New York, NY
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Kudos [?]: 3 [0], given: 0

Well all I can say is that the OA is wrong. I've bolded the integer pairs. If you count, you'll see that it is 11.

X Y
0 30
1 29.4
2 28.8
3 28.2
4 27.6
5 27
6 26.4
7 25.8
8 25.2
9 24.6
10 24
11 23.4
12 22.8
13 22.2
14 21.6
15 21
16 20.4
17 19.8
18 19.2
19 18.6
20 18
21 17.4
22 16.8
23 16.2
24 15.6
25 15
26 14.4
27 13.8
28 13.2
29 12.6
30 12
31 11.4
32 10.8
33 10.2
34 9.6
35 9
36 8.4
37 7.8
38 7.2
39 6.6
40 6
41 5.4
42 4.8
43 4.2
44 3.6
45 3
46 2.4
47 1.8
48 1.2
49 0.6
50 0
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