# CAT Practice : Coordinate Geometry

Take Geometry, add one unit of algebra; take a diagram, explain it with x's and y's. For the purists, it is geometry without the romance, for the pragmatists it is Geometry with expanded scope.

## Coordinate geometry and greatest integer function

Q.3: Region Q is defined by the equation 2x + y < 40. How many points (r, s) exist such that r is a natural number and s is a multiple of r?
1. 84
2. 92
3. 105
4. 72

Choice B. 92

## Detailed Solution

When r = 1, s can take 37 values $\left[ {{37 \over 1}} \right]$

When r = 2, s can take 17 values $\left[ {{35 \over 2}} \right]$

When r = 3, s can take 11 values $\left[ {{33 \over 3}} \right]$

When r = 4, s can take 7 values $\left[ {{31 \over 4}} \right]$

When r = 5, s can take 5 values $\left[ {{29 \over 5}} \right]$

When r = 6, s can take 4 values $\left[ {{27 \over 6}} \right]$

When r = 7, s can take 3 values $\left[ {{25 \over 7}} \right]$

When r = 8, s can take 2 values $\left[ {{23 \over 8}} \right]$

When r = 9, s can take 2 values $\left[ {{21 \over 9}} \right]$

When r = 10, s can take 1 values $\left[ {{19 \over 10}} \right]$

When r = 11, 12, 13 s can take one value each.

Totally, there are 92 values possible.

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## More questions from Coordinate Geometry

Take Geometry, add one unit of algebra; take a diagram, explain it with x's and y's. For the purists, it is geometry without the romance, for the pragmatists it is Geometry with expanded scope.