CAT Quantitative Aptitude Questions | Questions for CAT - Coordinate Geometry

CAT Questions | CAT Coordinate Geometry | greatest integer function
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The question is from CAT Coordinate Geometry. It combines coordinate geometry with functions. Our task is to find out the number of points which lies in the given region and also satisfies the given condition. 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. CAT exam does test one on ideas from CAT Coordinate Geometry once in a while.

Question 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

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Explanatory Answer

Method of solving this CAT Question from CAT 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.

When r = 1, s can take 37 values [$$frac{37}{1}\\$] When r = 2, s can take 17 values [$\frac{35}{2}\\$] When r = 3, s can take 11 values [$\frac{33}{3}\\$] When r = 4, s can take 7 values [$\frac{31}{4}\\$] When r = 5, s can take 5 values [$\frac{29}{5}\\$] When r = 6, s can take 4 values [$\frac{27}{6}\\$] When r = 7, s can take 3 values [$\frac{25}{7}\\$] When r = 8, s can take 2 values [$\frac{23}{8}\\$] When r = 9, s can take 2 values [$\frac{21}{9}\\$] When r = 10, s can take 1 values [$\frac{19}{10}\\$] When r = 11, 12, 13 s can take one value each. Totally, there are 92 values possible. The question is "How many points$r, s) exist such that r is a natural number and s is a multiple of r?"

Hence, the answer is 92.

Choice B is the correct answer.

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