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How many points on line with equation x/13+y/52=1 have both non-negati

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Joined: 30 May 2018
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How many points on line with equation x/13+y/52=1 have both non-negati  [#permalink]

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New post 21 Mar 2019, 10:52
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A
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Difficulty:

  55% (hard)

Question Stats:

61% (02:02) correct 39% (01:40) wrong based on 23 sessions

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How many points on line with equation x/13+y/52=1 have both non-negative integer coordinates?
(A) 10
(B) 12
(C) 13
(D) 14
(E) Infinite
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Re: How many points on line with equation x/13+y/52=1 have both non-negati  [#permalink]

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New post 21 Mar 2019, 11:28
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If u multiply both sides of the equation by 52 i.e.(LCM OF 13&52), the equation becomes
4x+y=52.or y=-4x+52

The equation says it's a negative slope. To be more specific, slope =-4 means if u increase x by 1 unut, y will decrease by 4 units.
The equation also says y intercept is 52 that when x =0, y=52.

Thousands of points may be available on this equation. But, the question says
INTEGER & NON NEGATIVE. SO, there is a defined number of points by connecting which the straight line has been created.
So the points of (x,y) are (0,52),(1,48),(2,44),.....(12,4) & (13,0).
So, how manys points there?
=14.

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Joined: 11 Feb 2013
Posts: 229
Location: United States (TX)
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
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How many points on line with equation x/13+y/52=1 have both non-negati  [#permalink]

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New post 21 Mar 2019, 11:34
1
There is a shortcut to find out number of integer points.

number of integer points in a single quadrant of (y=mx+c) equation= (Y intercept/ ABSOLUTE value of SLOPE)+1.

Here, equation is Y=-4x+52
So, number of integer points in a QUADRANT = {52/(|-4|)}+1
=(52/4)+1
=14

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How many points on line with equation x/13+y/52=1 have both non-negati   [#permalink] 21 Mar 2019, 11:34
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