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In the figure above, how many of the points on line segment PQ have [#permalink]
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Updated on: 10 Feb 2018, 16:09
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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 Attachment:
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Originally posted by GMATD11 on 03 Feb 2011, 12:18.
Last edited by Bunuel on 10 Feb 2018, 16:09, edited 2 times in total.
Renamed the topic, edited the question and added the OA.



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Re: In the figure above, how many of the points on line segment PQ have [#permalink]
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03 Feb 2011, 20:54
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m = (30  0)/(050) m = 30/50 = 3/5 y = mx + c c = 30 y = (3/5)x + 30 For y to be an integer, the term (3/5)x must be an integer. Thus, x must be divisible by 5. The value of x ranges from 0 to 50 So we need to find the number of multiples of 5 between 0 and 50 (Exclusive) 5, 10, 15, 20, 25, 30, 35, 40 & 45 Ans: 9 points between A and B will have integer values for both the coordinates!
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Re: In the figure above, how many of the points on line segment PQ have [#permalink]
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26 Jun 2011, 16:05
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I think the answer should be 11. Why are 0 & 11 excluded?. Please explain.
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Re: In the figure above, how many of the points on line segment PQ have [#permalink]
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27 Jun 2011, 04:22
maheshsrini wrote: I think the answer should be 11. Why are 0 & 11 excluded?. Please explain. You are right. thanks.
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Re: In the figure above, how many of the points on line segment PQ have [#permalink]
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09 Sep 2013, 00:43
Ok Including 0 we will get an Int but how will 11 help?



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Re: In the figure above, how many of the points on line segment PQ have [#permalink]
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09 Sep 2013, 02:42
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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: \(\frac{yy_1}{xx_1}=\frac{y_1y_2}{x_1x_2}\) (check here: mathcoordinategeometry87652.html). For P(0, 30) and Q(50, 0): \(\frac{y30}{x0}=\frac{300}{050}\) > \(3x + 5y = 150\). 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. Hope this helps.
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Re: In the figure above, how many of the points on line segment PQ have [#permalink]
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14 Oct 2013, 10:17
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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



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Re: In the figure above, how many of the points on line segment PQ have [#permalink]
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10 Feb 2018, 17:31
GMATD11 wrote: 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 We have  \(3x + 5y = 150\) \(5y = 150  3x > y = 30  (3x/5)\) As, \(x & y\) has to be integers x has to be multiple of y. Also, \(x & y\) has to be postie as it lies in the first quadrant. \(x = {0,5,10,15,20,25,30,35,40,45,50}\)
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