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

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

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New post Updated on: 13 May 2017, 07:57
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A
B
C
D
E

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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

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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 X-Y pla  [#permalink]

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New post 13 May 2017, 06:52
4
1
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
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Re: If a line which has the equation 7x + 17y = 1000 is plotted on X-Y pla  [#permalink]

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New post 14 May 2017, 07:41
2
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 X-Y pla  [#permalink]

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New post 14 May 2017, 07:50
GMATinsight wrote:
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


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..
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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

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New post 14 May 2017, 08:20
1
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?
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Re: If a line which has the equation 7x + 17y = 1000 is plotted on X-Y pla  [#permalink]

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New post 14 May 2017, 08:48
1
sananoor wrote:
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?


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..
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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

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New post 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 X-Y pla  [#permalink]

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New post 06 Jun 2017, 05:06
1
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 X-Y pla  [#permalink]

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New post 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 X-Y pla  [#permalink]

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New post 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 X-Y pla  [#permalink]

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New post 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 :)
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Re: If a line which has the equation 7x + 17y = 1000 is plotted on X-Y pla &nbs [#permalink] 09 Dec 2017, 14:40
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