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If a line which has the equation 7x + 17y = 1000 is plotted on XY pla [#permalink]
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Updated on: 13 May 2017, 07:57
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If a line which has the equation 7x + 17y = 1000 is plotted on XY plane then how many points will fall on the line in 1st quadrant which will have both x and y coordinates Integers? A) 6 B) 7 C) 8 D) 9 E) 10
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Originally posted by GMATinsight on 13 May 2017, 06:13.
Last edited by Bunuel on 13 May 2017, 07:57, edited 1 time in total.
Edited the OA.




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Re: If a line which has the equation 7x + 17y = 1000 is plotted on XY pla [#permalink]
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13 May 2017, 06:52
GMATinsight wrote: If a line which has the equation 7x + 17y = 1000 is plotted on XY plane then how many points will fall on the line in 1st quadrant which will have both x and y coordinates Integers?
A) 6 B) 7 C) 8 D) 9 E) 10 Hi, First quadrant is the quadrant where both x and y are POSITIVE... Let's see the equation.. 7x+17y=1000 You have to find the first set of x and y that satisfies the equation and thereafter the remaining can be found.. Here subtract multiples of 7 from 1000 and check if remaining amount is div by 17.. When x is 2, y is 58... This is the first set.. Remaining values of y will be 587t, where t is integer.. When t is 9, 7t becomes 7*9=63 and 587t will become negative.. Hence t<9.. So t will take all values from 0 to 8 so 9 values.. D GMATinsight pl relook at the OA provided by you. Ans will be 9 and not 10.. So D is the answer and Not E
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Re: If a line which has the equation 7x + 17y = 1000 is plotted on XY pla [#permalink]
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14 May 2017, 07:41
I guess it must be D the sets will have values as 58, 2 51,19 44, 36 37, 53 30, 70 23, 87 16, 104 9, 121 2, 138 Chetan how can u include 0 in your answer as x and y both cant be equal to zero, or even if one is zero then other wont be an integer...if u even try drawing the line it wont pass from origin.
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If a line which has the equation 7x + 17y = 1000 is plotted on XY pla [#permalink]
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14 May 2017, 07:50
GMATinsight wrote: chetan2u wrote: GMATinsight wrote: If a line which has the equation 7x + 17y = 1000 is plotted on XY plane then how many points will fall on the line in 1st quadrant which will have both x and y coordinates Integers?
A) 6 B) 7 C) 8 D) 9 E) 10 Hi, First quadrant is the quadrant where both x and y are POSITIVE... Let's see the equation.. 7x+17y=1000 You have to find the first set of x and y that satisfies the equation and thereafter the remaining can be found.. Here subtract multiples of 7 from 1000 and check if remaining amount is div by 17.. When x is 2, y is 58... This is the first set.. Remaining values of y will be 587t, where t is integer.. When t is 9, 7t becomes 7*9=63 and 587t will become negative.. Hence t<9.. So t will take all values from 0 to 8 so 9 values.. D GMATinsight pl relook at the OA provided by you. Ans will be 9 and not 10.. So D is the answer and Not E OA is correct. Here is the solution... Posted from my mobile deviceHi, OA is correct now because Bunuel has edited it from E to D. sananoor I have mentioned exactly that in the post that there will be 9 and not 10. The OA originally was E which now has been changed to D by Bunuel And I have taken t as 0 and not x and y..
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Re: If a line which has the equation 7x + 17y = 1000 is plotted on XY pla [#permalink]
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14 May 2017, 08:20
chetan2u wrote: GMATinsight wrote: If a line which has the equation 7x + 17y = 1000 is plotted on XY plane then how many points will fall on the line in 1st quadrant which will have both x and y coordinates Integers?
A) 6 B) 7 C) 8 D) 9 E) 10 Hi, First quadrant is the quadrant where both x and y are POSITIVE... Let's see the equation.. 7x+17y=1000 You have to find the first set of x and y that satisfies the equation and thereafter the remaining can be found.. Here subtract multiples of 7 from 1000 and check if remaining amount is div by 17.. When x is 2, y is 58... This is the first set.. Remaining values of y will be 587t, where t is integer.. When t is 9, 7t becomes 7*9=63 and 587t will become negative.. Hence t<9.. So t will take all values from 0 to 8 so 9 values..D GMATinsight pl relook at the OA provided by you. Ans will be 9 and not 10.. So D is the answer and Not E Chetan last question...can u explain he above highlighted and underlined part? how come 0?
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Re: If a line which has the equation 7x + 17y = 1000 is plotted on XY pla [#permalink]
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14 May 2017, 08:48
sananoor wrote: chetan2u wrote: GMATinsight wrote: If a line which has the equation 7x + 17y = 1000 is plotted on XY plane then how many points will fall on the line in 1st quadrant which will have both x and y coordinates Integers?
A) 6 B) 7 C) 8 D) 9 E) 10 Hi, First quadrant is the quadrant where both x and y are POSITIVE... Let's see the equation.. 7x+17y=1000 You have to find the first set of x and y that satisfies the equation and thereafter the remaining can be found.. Here subtract multiples of 7 from 1000 and check if remaining amount is div by 17.. When x is 2, y is 58... This is the first set.. Remaining values of y will be 587t, where t is integer.. When t is 9, 7t becomes 7*9=63 and 587t will become negative.. Hence t<9.. So t will take all values from 0 to 8 so 9 values..D GMATinsight pl relook at the OA provided by you. Ans will be 9 and not 10.. So D is the answer and Not E Chetan last question...can u explain he above highlighted and underlined part? how come 0? Hi, I found the max value of y as 58 and the next values will be 58 multiples of 7... Now instead of finding values one by one, I have taken y=587t... Here y would become<0, when 7t>=58.. So 7t<58... Max value of t is 8 as 7*8=56... t can take value of 0 because y=587t=587*0=58... So y is not 0 but t is..
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Re: If a line which has the equation 7x + 17y = 1000 is plotted on XY pla [#permalink]
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04 Jun 2017, 15:07
I did the problem slightly differently, can someone help where i went wrong? I got the answer as 8:
7x + 17y = 1000 rearrange to get: y = (7/17)x + (1000/17) solve for x intercept: (7/17)x = 1000/17 x intercept = (1000/7) or 142.XXX
then 17*(number of points on line) must be <142 17*8 = 136 so that's the number of points, 8



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Re: If a line which has the equation 7x + 17y = 1000 is plotted on XY pla [#permalink]
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06 Jun 2017, 05:06
mdacosta wrote: I did the problem slightly differently, can someone help where i went wrong? I got the answer as 8:
7x + 17y = 1000 rearrange to get: y = (7/17)x + (1000/17) solve for x intercept: (7/17)x = 1000/17 x intercept = (1000/7) or 142.XXX
then 17*(number of points on line) must be <142 17*8 = 136 so that's the number of points, 8 x min = 2 x max = 138 You are missing counting the smallest solution... Word of caution: Find the first solution for real before you take a leap to the last solution like you did.
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Re: If a line which has the equation 7x + 17y = 1000 is plotted on XY pla [#permalink]
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07 Jun 2017, 14:39
this question is not so hard, but it does take time, and it may confuse test takers. If ones look at the options, you can easily get a wrong choice by accident. Stay awake!



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If a line which has the equation 7x + 17y = 1000 is plotted on XY pla [#permalink]
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26 Nov 2017, 10:09
I solved the problem like this:
Like chetan mentioned, we have to find first multiple of 7, for which 1000  first multiple of 7 is divisible by 17, which is 14 and remaining is 986
Now we can find the number of next multiples of 7 for which remainining is divisible by 17, by taking quotient of 1000 / LCM(7,17) 1000/119 = 8, so there are 8 multiples of 7 after 14 for which remaining is divisible by 17. so multiple of 7 after 14 will be \(14+119, 14 + 2*119, 14 + 3 * 119, ..... 14 + 8*119\)
So total is 9, Answer (C)



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Re: If a line which has the equation 7x + 17y = 1000 is plotted on XY pla [#permalink]
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09 Dec 2017, 14:40
I solved it the hard way . Took like 3 minutes, blame the lack of coordinate grey cells. if we simplify the 17y = 1000  7x > y = 1000/17 + 7/17x so if y = 0, x= 142 so if x = 0, y is 142 out of these, we will see there is a downward sloping line. So, between the two coordinates we need to find integer coordinates on the hypotenuse. So for 2 points we get 1 coordinate > 142*2 = 284 I kept dividing by 2 till I got a remainder too small to be divided by 2. 284/2, 142/2, 71/2, 35/2, 17/2, 8/2,4/2, 2/2; and one more as it is inclusive of the points (it anyway cannot exceed beyond 10 points) > around 9 times. Please press kudos, if this solution made sense for you




Re: If a line which has the equation 7x + 17y = 1000 is plotted on XY pla
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