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# How many integer points lie between points A and В on the line segment

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Manager
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How many integer points lie between points A and В on the line segment [#permalink]

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18 Feb 2011, 10:25
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How many integer points lie between points A and В on the line segment AB, if A is (5, 7) and В is (10, –3)?

(A) 4
(B) 5
(C) 6
(D) 10
(E) 15
[Reveal] Spoiler: OA
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Re: How many integer points lie between points A and В on the line segment [#permalink]

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18 Feb 2011, 10:55
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equation of line passing through two points (x1,y1) and (x2,y2)

$$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$$

$$(x_1,y_1) = (5,7)$$
$$(x_2,y_2) = (10,-3)$$

$$y-7=\frac{-3-7}{10-5}(x-5)$$

$$y-7=-2(x-5)$$

$$y+2x=17$$

Plug in values for x from 6 to 9 and see whether y will be an integer.

x=6; y=5
x=7; y=3
x=8; y=1
x=9; y=-1

Total 4 points that are integers.

Ans: "A"
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Re: How many integer points lie between points A and В on the line segment [#permalink]

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18 Feb 2011, 11:07
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banksy wrote:
204. How many integer points lie between points A and В on the line segment AB, if A is (5, 7) and В is (10, –3)?
(A) 4
(B) 5
(C) 6
(D) 10
(E) 15

You can notice that while we moved 5 units to the right (from x=5 to x=10) we moved 10 units down (from y=7 to y=-3) thus every unit to the right = exactly 2 units down. So each of 4 integer coordinates of x between 5 and 10 (6, 7, 8 and 9) will have an integer pair of y (5, 3, 1, and -1).

To demonstrate:
x=5, y=7;
x=5+1=6 --> y=7-2=5;
x=6+1=7 --> y=5-2=3;
x=7+1=8 --> y=3-2=1;
x=8+1=9 --> y=1-2=-1;
x=9+1=10 --> y=-1-2=-3.

So there are 4 points with integer co-ordinates: (6, 5), (7, 3), (8, 1), and (9, -1).

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Re: How many integer points lie between points A and В on the line segment [#permalink]

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29 Jun 2015, 10:58
Hello from the GMAT Club BumpBot!

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Re: How many integer points lie between points A and В on the line segment [#permalink]

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07 Jul 2016, 02:15
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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21 Oct 2016, 02:38
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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Re: How many integer points lie between points A and В on the line segment [#permalink]

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21 Oct 2016, 02:46
duahsolo 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

Merging topics. Please refer to the discussion above.
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Posts: 37669
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Kudos [?]: 99888 [1] , given: 11068

Re: How many integer points lie between points A and В on the line segment [#permalink]

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21 Oct 2016, 02:47
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Bunuel wrote:
duahsolo 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

Merging topics. Please refer to the discussion above.

Similar questions to practice:
in-the-figure-above-how-many-of-the-points-on-line-segment-108673.html
how-many-points-x-y-lie-on-the-line-segment-between-22-12-2-3-an-103881.html

Hope it helps.
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Manager
Joined: 02 Jun 2015
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How many integer points lie between points A and В on the line segment [#permalink]

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24 Oct 2016, 01:55
Bunuel wrote:
Bunuel wrote:
duahsolo 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

Merging topics. Please refer to the discussion above.

Similar questions to practice:
in-the-figure-above-how-many-of-the-points-on-line-segment-108673.html
how-many-points-x-y-lie-on-the-line-segment-between-22-12-2-3-an-103881.html

Hope it helps.

Hi Bunuel,

Sorry I had to post a question already on the platform. I should have searched well enough before posting.

Thanks
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Kudos [?]: 3 [0], given: 4

Re: How many integer points lie between points A and В on the line segment [#permalink]

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10 Jan 2017, 20:20
Between the points (5,7) and (10,-3) I got the slope as -2. I then kept increasing x by 1 and accordingly reduced y by -2. Got 4 integer points until (10,-3)
Re: How many integer points lie between points A and В on the line segment   [#permalink] 10 Jan 2017, 20:20
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