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

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How many integer points lie between points A and B on the [#permalink] New post 03 Nov 2007, 18:48
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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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Answer E [#permalink] New post 03 Nov 2007, 20:09
Ravshonbek wrote:
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


I would say 15.

Along y axis 7+3=10 distinct integer points example 7,6,5,4,...0,-1,-2,-3
Along x axis 10-5=5 distinct points exmaple 5,6,7,8,9,10

Total 15 distinct x,y points
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 [#permalink] New post 03 Nov 2007, 23:42
Hi,
The equation of the line is y=-2*x+17 substituting for x= 6,7,8 and 9 we get values for y 5,3,1 and -2 then the ans to the question is 4
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 [#permalink] New post 03 Nov 2007, 23:57
Get the equation of the line which pass through the points A and B....
we get 2x+y=17 now start substituting x and y values where the x lies between +5 and +10.........5<x<10 and find all the possible integer solutions of y....similarly find all possible integral solutions of x where y ranges from +7 and -3...i.e 7<y<-3.......
so we have 4 such possible integral solutions....

hence the answer is A
  [#permalink] 03 Nov 2007, 23:57
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