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In the figure above, 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

The equation of a straight line passing through points \(P(x_1, y_1)\) and \(Q(x_2, y_2)\) is: \(\frac{y-y_1}{x-x_1}=\frac{y_1-y_2}{x_1-x_2}\) (check here: math-coordinate-geometry-87652.html).

For P(0, 30) and Q(50, 0): \(\frac{y-30}{x-0}=\frac{30-0}{0-50}\) --> \(3x + 5y = 150\).

If x is a multiple of 5, then y will be an integer. x ranges from 0 to 50, inclusive. There are total of 11 multiples of 5 in this range: 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50.

Re: In the figure above, how many of the points on line segment [#permalink]

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14 Oct 2013, 10:17

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This post received KUDOS

First develope the equation of line with coordinates given:- Y = MX + C

When X =0, Y=30, putting the values in above equation of line gives the value of C 30 = C

When Y=0, X=30, putting the values in above equation of line gives the value of M M= - 3/5

The equation of Line is Y= (-3/5)X +30, Now from this equation it is clear that if we want to have both X and Y to be integers, then all values of X has to be multiple of 5, so starting from X=0 to X=50 (Coordinate limits of line PQ), we note that there are 11 integer values of X for which 11 integer values of Y exists in line PQ

Re: In the figure above, how many of the points on line segment [#permalink]

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29 Jun 2015, 11:03

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Re: In the figure above, how many of the points on line segment [#permalink]

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21 Aug 2016, 01:53

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