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Line M has x-intercept as -40 and y-intercept as 70. If the line M

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Line M has x-intercept as -40 and y-intercept as 70. If the line M  [#permalink]

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New post 04 Mar 2017, 02:47
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Line M has x intercept as -40 and y intercept as 70. If the line M cuts x-axis at point P and y-axis at point Q,then how many points on line segment PQ have both x coordinate and y coordinate as integers?

a)40
b)70
c)10
d)11
e)30
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Re: Line M has x-intercept as -40 and y-intercept as 70. If the line M  [#permalink]

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New post 04 Mar 2017, 04:00
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Bhalla wrote:
Line M has x intercept as -40 and y intercept as 70. If the line M cuts x-axis at point P and y-axis at point Q,then how many points on line segment PQ have both x coordinate and y coordinate as integers?

a)40
b)70
c)10
d)11
e)30


The equation of a straight line whose x and y intercepts are a and b, respectively, is: \(\frac{x}{a}+\frac{y}{b}=1\) (check for more here: https://gmatclub.com/forum/math-coordin ... 87652.html)

Thus, the equation of line M is -x/40 + y/70 = 1.

Image

y = 7x/4 + 70. For y to be an integer 7x/4 must be an integer, thus x must be a multiple of 4, from 0 to -40 inclusive. There are 11 multiples of 4 in this range: 0, -4, -8, -12, -16, -20, -24, -28, -32, -36, and -40.

Answer: D.

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Line M has x-intercept as -40 and y-intercept as 70. If the line M  [#permalink]

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New post Updated on: 05 Mar 2017, 07:34
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Bhalla wrote:
Line M has x intercept as -40 and y intercept as 70. If the line M cuts x-axis at point P and y-axis at point Q,then how many points on line segment PQ have both x coordinate and y coordinate as integers?

a)40
b)70
c)10
d)11
e)30


We know two points through which the line PQ passes through: (-40,0) and (0,70).

Equation of a line passing through two points can be found using the formula (y-y1)/(y2-y1) = (x-x1)/(x2-x1).

Equation of the line PQ is 4y-7x=280.

y=7(40+x)/4.

For y to be an integer (40+x)/4 should be an integer. So 40+x should be divisible by 4. Here x can vary from -40 to 0. All multiples of 4 between 0 and -40 will satisfy the condition. So there are 11 such numbers, including 0.

Hence D.

Cheers!

Originally posted by Diwakar003 on 04 Mar 2017, 09:07.
Last edited by Diwakar003 on 05 Mar 2017, 07:34, edited 1 time in total.
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Re: Line M has x-intercept as -40 and y-intercept as 70. If the line M  [#permalink]

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New post 04 Aug 2019, 13:35
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Re: Line M has x-intercept as -40 and y-intercept as 70. If the line M   [#permalink] 04 Aug 2019, 13:35
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