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A line passes through point p(1,1) and q(100,1000). How many other poi [#permalink]
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28 Jan 2015, 08:00
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A line passes through point p(1,1) and q(100,1000). How many other points with integer coordinates are on the line and strictly between points p and q ? a) 0 b) 2 c) 3 d) 8 e) 9
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Re: A line passes through point p(1,1) and q(100,1000). How many other poi [#permalink]
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28 Jan 2015, 08:23
ans D..... p(1,1) and q(100,1000)... so the ratio in which the increase is ,increase of x by 10 results in increase of 100 in y coord.. so for x, there are 8 such points for which y is also int...
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Re: A line passes through point p(1,1) and q(100,1000). How many other poi [#permalink]
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28 Jan 2015, 09:09
chetan2u wrote: ans D..... p(1,1) and q(100,1000)... so the ratio in which the increase is ,increase of x by 10 results in increase of 100 in y coord.. so for x, there are 8 such points for which y is also int... Can you please elaborate?



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Re: A line passes through point p(1,1) and q(100,1000). How many other poi [#permalink]
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28 Jan 2015, 09:25
DesiGmat wrote: chetan2u wrote: ans D..... p(1,1) and q(100,1000)... so the ratio in which the increase is ,increase of x by 10 results in increase of 100 in y coord.. so for x, there are 8 such points for which y is also int... Can you please elaborate? hi... the Y coord is increasing by(10001) or999 as x increases by (1001) or 99.. so the ratio of increase is 99:999 or 11:111... it means with every increase of x by 11 , y increases by 111.. so the value of 12(1+11) will have y as 112(1+111).. 23(12+11) will have 223(112+111) and so on till 89 will have 889.. value of x as 1 and 100 is not taken so 8 values 12,23,34,45,56,67,78,89 with corresponding int values for Y
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Re: A line passes through point p(1,1) and q(100,1000). How many other poi [#permalink]
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29 Jan 2015, 05:49
Let's say point p is at the origin and q is at the (99,999) (this does not change the problem). The line pq has the equation y =\(\frac{999}{99}x\)= \(\frac{111}{11}x\) .
Now the coordinates of y will be integer, when x takes the value of 11,22,33,44,55,66,77,88.
hence answer is D.



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Re: A line passes through point p(1,1) and q(100,1000). How many other poi [#permalink]
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29 Jan 2015, 07:11
Line equation y = mx + c....Using the inform...m = 111/11....so y = 111/11x + c......put y=x= 1....c = 100/11 Line eqn :11y = 111x  100......x = (11y+100)/111...limit x till 100....only 8 values permissible



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Re: A line passes through point p(1,1) and q(100,1000). How many other poi [#permalink]
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08 Mar 2015, 00:50
Hi,
I didnt get the solution.Why can't 99 also be the value ?? When x is 99 ,y can still be an integer..?? Can some1 please explain the problem



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Re: A line passes through point p(1,1) and q(100,1000). How many other poi [#permalink]
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30 Jun 2015, 07:03
the slope we will get as 11/111. Then equation of the line y=11/111x+c if we take for every mulitple of 111, the value of y is integer, then we will have 9 values.
Can someone pls tell me where i am going wrong?



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Re: A line passes through point p(1,1) and q(100,1000). How many other poi [#permalink]
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10 Aug 2015, 21:54
jayanthjanardhan wrote: the slope we will get as 11/111. Then equation of the line y=11/111x+c if we take for every mulitple of 111, the value of y is integer, then we will have 9 values.
Can someone pls tell me where i am going wrong? Hi, The error is that c is not an integer. Am I right in suggesting that you have assumed c to be an integer?



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Re: A line passes through point p(1,1) and q(100,1000). How many other poi [#permalink]
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17 Aug 2015, 12:14
The slope is y2y1/x2x1. So, it is 10001/1001 = 999/99 = 111/11 Also, the value of C needs to be calculated (to check whether it is integer). In this case, the value of C is not an integer = 100/11. Hope this helps.
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Re: A line passes through point p(1,1) and q(100,1000). How many other poi [#permalink]
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18 Sep 2015, 04:58
AryamaDuttaSaikia wrote: The slope is y2y1/x2x1. So, it is 10001/1001 = 999/99 = 111/11
Also, the value of C needs to be calculated (to check whether it is integer). In this case, the value of C is not an integer = 100/11.
Hope this helps. Hi Aryama, Can you extend your explanation further I mean now we have got the equation of the line as y= (11/111)x 100/11 Now how to go ahead with this from here What values one should place here to get integer value of y Thanks Kani



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A line passes through point p(1,1) and q(100,1000). How many other poi [#permalink]
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18 Sep 2015, 14:53
Hi folks, here is how i solved the problem :
From the two point coordinates, we obtain the following equation Y= (111/11)*X  100/11; This equation can be written as follow : (111*X  100)/11 or More better (100(X1) + 11 X)/11 .
Now the problem here is that we should obtain an INTEGER Y, in other words (100(X1) + 11 X) should be divisible by 11.
11X is obviously divisible by 11 so we can neglect it, now our unique friend is 100(X1) which should be divisible by 11.
X ranges from 1 to 100 , thus the possible values for X to be divisible by 11 are : 12, 23,34,45,56,67,78,89 . So we have 8 values, thus Answer (D) is correct.
Hope it helps



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Re: A line passes through point p(1,1) and q(100,1000). How many other poi [#permalink]
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21 Sep 2015, 23:14
Slope is calculated by using the formula : m = y2y1/x2x1 Slope intercept format (Equation of the line) Y = mx+c In this equation substitute the values of " m "and one of the given coordinates (x,y) to get the value of C. c= 100/11 So y becomes y=(111/11)x100/11 = (111x100) /11 X =1 So we get Y = 1 (given coordinates). We want values between (1,1) and (100, 1000) The next values of X that make Y as integer is 11 (divisor is 11) more than the first value. 12,23 (12+11),34,45,56,67,78,89 = Total 8 values. HOPE IT HELPS!!
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