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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
In the figure above, how many of the points on line segment PQ have co
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05 Nov 2021, 05:25
05 Nov 2021, 05:25
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66% (02:37) correct
33% (04:00) wrong based on 6 sessions
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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
Re: In the figure above, how many of the points on line segment PQ have co
[#permalink]
08 Nov 2021, 14:05
08 Nov 2021, 14:05
Expert Reply
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: http://gmatclub.com/forum/math-coordina ... 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.
Answer: D.
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.
Answer: D.
gmatclubot
Re: In the figure above, how many of the points on line segment PQ have co [#permalink]
08 Nov 2021, 14:05
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