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28 Jan 2015, 08:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
37% (02:28) correct
63%
(02:30)
wrong
based on 176
sessions
History
Date
Time
Result
Not Attempted Yet
A line passes through point p(1,1) and q(100,1000). How many other points with integer co-ordinates are on the line and strictly between points p and q ?
a) 0
b) 2
c) 3
d) 8
e) 9
a) 0
b) 2
c) 3
d) 8
e) 9
29 Jan 2015, 05:49
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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 co-ordinates of y will be integer, when x takes the value of 11,22,33,44,55,66,77,88.
hence answer is D.
The line pq has the equation y =\(\frac{999}{99}x\)= \(\frac{111}{11}x\) .
Now the co-ordinates of y will be integer, when x takes the value of 11,22,33,44,55,66,77,88.
hence answer is D.
18 Sep 2015, 14:53
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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(X-1) + 11 X)/11 .
Now the problem here is that we should obtain an INTEGER Y, in other words (100(X-1) + 11 X) should be divisible by 11.
11X is obviously divisible by 11 so we can neglect it, now our unique friend is 100(X-1) 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
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(X-1) + 11 X)/11 .
Now the problem here is that we should obtain an INTEGER Y, in other words (100(X-1) + 11 X) should be divisible by 11.
11X is obviously divisible by 11 so we can neglect it, now our unique friend is 100(X-1) 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
