edited by
1,828 views
12 votes
12 votes

Imagine the first quadrant of the real plane as consisting of unit squares. A typical square has $4$ corners: $(i, j), (i+1, j), (i+1, j+1),$and $(i, j+1)$, where $(i, j)$ is a pair of non-negative integers. Suppose a line segment $l$ connecting $(0, 0)$ to $(90, 1100)$ is drawn. We say that $l$ passes through a unit square if it passes through a point in the interior of the square. How many unit squares does $l$ pass through?

  1. $98,990$
  2. $9,900$
  3. $1,190$
  4. $1,180$
  5. $1,010$
edited by

2 Answers

Best answer
11 votes
11 votes

Answer will be (d) 1,180

If a line segment passes through unit square from $(0,0)$ to $(i,j)$ the line intersects $(i+j-gcd(i,j))$

no. of squares =$ (90+1100-10)=1180.$

edited by
0 votes
0 votes

I think (B) answer will be 99000

(0,0) to(90,1100) total rowwise 91 points and columnwise 1101 points

Each 2 points makes 1 square

So, total no. of unit square are 90* 1100 = 99000 

Answer:

Related questions