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If a line which has the equation 7x + 17y = 1000 is plotted on X-Y plane then how many points will fall on the line in 1st quadrant which will have both x and y co-ordinates Integers?

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If a line which has the equation 7x + 17y = 1000 is plotted on X-Y plane then how many points will fall on the line in 1st quadrant which will have both x and y co-ordinates 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 58-7t, where t is integer.. When t is 9, 7t becomes 7*9=63 and 58-7t 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
_________________

Re: If a line which has the equation 7x + 17y = 1000 is plotted on X-Y pla [#permalink]

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14 May 2017, 06:41

2

This post received KUDOS

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.
_________________

Push yourself again and again. Don't give an inch until the final buzzer sounds. -Larry Bird Success isn't something that just happens - success is learned, success is practiced and then it is shared. -Sparky Anderson -S

If a line which has the equation 7x + 17y = 1000 is plotted on X-Y plane then how many points will fall on the line in 1st quadrant which will have both x and y co-ordinates 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 58-7t, where t is integer.. When t is 9, 7t becomes 7*9=63 and 58-7t 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 device

Hi, 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..
_________________

Re: If a line which has the equation 7x + 17y = 1000 is plotted on X-Y pla [#permalink]

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14 May 2017, 07:20

1

This post received KUDOS

chetan2u wrote:

GMATinsight wrote:

If a line which has the equation 7x + 17y = 1000 is plotted on X-Y plane then how many points will fall on the line in 1st quadrant which will have both x and y co-ordinates 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 58-7t, where t is integer.. When t is 9, 7t becomes 7*9=63 and 58-7t 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?
_________________

Push yourself again and again. Don't give an inch until the final buzzer sounds. -Larry Bird Success isn't something that just happens - success is learned, success is practiced and then it is shared. -Sparky Anderson -S

If a line which has the equation 7x + 17y = 1000 is plotted on X-Y plane then how many points will fall on the line in 1st quadrant which will have both x and y co-ordinates 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 58-7t, where t is integer.. When t is 9, 7t becomes 7*9=63 and 58-7t 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=58-7t... 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=58-7t=58-7*0=58... So y is not 0 but t is..
_________________

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. _________________

Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html

Re: If a line which has the equation 7x + 17y = 1000 is plotted on X-Y pla [#permalink]

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07 Jun 2017, 13:39

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!

If a line which has the equation 7x + 17y = 1000 is plotted on X-Y pla [#permalink]

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26 Nov 2017, 09:09

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 \(14+119, 14 + 2*119, 14 + 3 * 119, ..... 14 + 8*119\)

Re: If a line which has the equation 7x + 17y = 1000 is plotted on X-Y pla [#permalink]

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09 Dec 2017, 13:40

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