# CAT Practice : Number System

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The greatest integer function is brilliant, it is not-intrusive(discrete) and takes you to a higher level (step function).

## Greatest integer function

Q.6: [x] is the greatest integer less than or equal to x. Find the number of positive integers n such that $\left[ {{{\rm{n}} \over {{\rm{11}}}}} \right]{\rm{ = }}\left[ {{{\rm{n}} \over {{\rm{13}}}}} \right]$.
1. 31
2. 25
3. 35
4. 40

Choice C. 35

## Detailed Solution

This is a classic case of brute-force counting.
When n = 1, 2, 3....10, both values will be equal to 0. 10 possibilities
When n = 13, 14, ....21, both values will be equal to 1. 9 possibilities
When n = 26, 27, ....32, both values will be equal to 2. 7 possibilities
When n = 39, 27, ....43, both values will be equal to 3. 5 possibilities
When n = 52, 53, 54, both values will be equal to 4. 3 possibilities
when n = 65, both will be equal to 5. 1 possibility

So, totally there are 1 + 3 + 5 + 7 + 9 + 10 = 35 possibilities.

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## More questions from Number System

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