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Bhalla
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Line M has x-intercept as -40 and y-intercept as 70. If the line M 04 Mar 2017, 02:47
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D
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75% (hard)

Question Stats:

56% (02:29) correct 44% (02:26) wrong based on 230 sessions

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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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D
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Bunuel
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Line M has x-intercept as -40 and y-intercept as 70. If the line M 04 Mar 2017, 04:00
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Bhalla
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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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.



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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Diwakar003
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Line M has x-intercept as -40 and y-intercept as 70. If the line M Updated on: 05 Mar 2017, 07:34
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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Bhalla
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
Show more

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.

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Line M has x-intercept as -40 and y-intercept as 70. If the line M 22 Feb 2021, 22:52
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Bunuel
Bhalla
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.



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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Bunuel can you elaborate on this: "from 0 to -40 inclusive." I suppose this coincides with my lack of understanding of what this part of the question means: "then how many points on line segment PQ have both x coordinate and y coordinate as integers"
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Line M has x-intercept as -40 and y-intercept as 70. If the line M 23 Feb 2021, 00:50
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Bunuel
Bhalla
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.



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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Bunuel can you elaborate on this: "from 0 to -40 inclusive." I suppose this coincides with my lack of understanding of what this part of the question means: "then how many points on line segment PQ have both x coordinate and y coordinate as integers"
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Check the line segment PQ. It consists of infinitely many points (x, y). Notice that for PQ, x there is from -40 to 0 and y there is from 0 to 70. We need to find out how many of these points have both x and y coordinates as integers: (integer, integer). There are 11 such points:

(0, 70)
(-4, 63)
(-8, 56)
(-12, 49)
(-16, 42)
(-20, 35)
(-24, 28)
(-28, 21)
(-32, 14)
(-36, 7)
(-40, 0)
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KarishmaB
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Line M has x-intercept as -40 and y-intercept as 70. If the line M 23 Feb 2021, 02:27
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Bhalla
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
Show more

First check:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2016/0 ... line-gmat/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... -vertices/

If x and y intercepts are -40 and 70, slope of the line = -70/-40 = 7/4

This means that for every 1 unit increase in x, y will increase by 7/4. So when x goes from -40 to -39, y becomes 7/4 which is not an integer. At next 1 unit increase of x, y will increase by another 7/4 giving 14/4, again not an integer. Only on the fourth increase of x by 1 unit will y increase to 4*7/4 = 7 units (another integer).
Similarly, at every fourth increase of x, y will give an integer value.
So when x = -40, -36, -32... 0 you will get integer values for y co-ordinate.

This gives us 11 points.

Answer (D)
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Line M has x-intercept as -40 and y-intercept as 70. If the line M 01 Mar 2025, 11:59
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