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

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..

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.

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!

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)

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

sir , can you please explain why " Remaining values of y will be 58-7t"
I'm really confused , it took so long for me to answer this question , here's my way :
7x + 17y = 1000
y = (-7x + 1000 )/17
now , + 1000-7x must be divisable by 17 , I'm stuck here , we know that x=<142 but how we can know how many valuse of (-7x + 1000 ) that are divisable by 17 where x=<142 ?
i tried back and forth ,(-7x + 1000 ) can be written as ( 1000+10x -17x )
now , -17x is no problem , let's take care only of 1000+10x which can be written as 10(100+x)
now , since 0=< x =< 142
100=< 100+x =< 242
let's find how many numbers divisable by 17 between 100, 242 in the classic way , the answer is 9

I appreciate any detailed explanation of other methods
Thanks

For any linear equation such as 7x+17y = 1000 The solutions always differ by co-efficient of other variables
i.e. values of x will differ by co-efficient of y i.e 17 in this case and
i.e. values of y will differ by co-efficient of x i.e 7 in this case


Likewise if the equation is 3x+4y = 120
then values of x will differ by 4 and values of y will differ by 3

foryearss

[quote=


For any linear equation such as 7x+17y = 1000 The solutions always differ by co-efficient of other variables
i.e. values of x will differ by co-efficient of y i.e 17 in this case and
i.e. values of y will differ by co-efficient of x i.e 7 in this case


Likewise if the equation is 3x+4y = 120
then values of x will differ by 4 and values of y will differ by 3

foryearss[/quote]
Thanks a lot , that really makes sense

The detailed video solution of the problem is here.

Answer: Option D

Asked: 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?

x = (1000 - 17y)/7
(x,y) = {(138,2),(121,9),(104,16),(87,22),(70,29),(53,36),(36,43),(19,50),(2,57)} : 9 solutions

IMO D

chetan2u i didnt understand 58-7t .. plz explain the logic