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# How many integer points lie between points A and B on the

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Manager
Joined: 07 May 2007
Posts: 178

Kudos [?]: 81 [0], given: 0

How many integer points lie between points A and B on the [#permalink]

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17 Jun 2007, 16:15
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How many integer points lie between points A and B on the line segment AB, if A is (5, 7) and B is (10, -3)?
(A) 4
(B) 5
(C) 6
(D) 10
(E) 15

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Director
Joined: 14 Jan 2007
Posts: 775

Kudos [?]: 175 [0], given: 0

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17 Jun 2007, 17:01

Equation of the line passing through the (5,7) and (10,-3) is -
y + 2x = 17

Now we have to find the integer points lying on the above line and between the above given points.
Range of x and y of the points between (5,7) and (10,-3)-
x< 10
-3<x<7

Now find the values of x and y in the above range and satisfying the equation.
These points are (6,5), (7,5), (8,1) and (9,-1).

Can anybody suggest a better method.

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Manager
Joined: 07 May 2007
Posts: 178

Kudos [?]: 81 [0], given: 0

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17 Jun 2007, 19:47
This is the right approach. But why did you not include points A and B in the set of points?

Should they be included only if the question states explicitly?

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Manager
Joined: 22 May 2006
Posts: 179

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18 Jun 2007, 01:01
I agree with iamba. I would have chosen A and B as well. Does the term between exclude A and B?

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Director
Joined: 14 Jan 2007
Posts: 775

Kudos [?]: 175 [0], given: 0

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18 Jun 2007, 01:49
iamba wrote:
This is the right approach. But why did you not include points A and B in the set of points?

Should they be included only if the question states explicitly?

The question says - points lie between A and B. That's why I have NOT included the points A and B in count.

Kudos [?]: 175 [0], given: 0

Manager
Joined: 07 May 2007
Posts: 178

Kudos [?]: 81 [0], given: 0

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18 Jun 2007, 16:35
OA is # of points = 4

A point to remember - look for term between

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18 Jun 2007, 16:35
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