CAT Quantitative Aptitude Questions | CAT Number Theory - Digits questions

CAT Questions | Number Theory | Greatest integer function

The question is about Greatest integer function. Another question on possible values. We need to find out the possible values of 'n' which satisfies of the equation of greatest integer function. Dealing with digits and base system of a number is a vital component in CAT Number Systems. A range of CAT questions can be asked based on this simple concept in the CAT Exam.

Question 6: [x] is the greatest integer less than or equal to x. Find the number of positive integers n such that [\\frac{n}{11}\\)] = [\\frac{n}{13}\\)].

  1. 31
  2. 25
  3. 35
  4. 40

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Explanatory Answer

Method of solving this CAT Question from Number Theory - Digits: The greatest integer function is brilliant, it is not-intrusive(discrete) and takes you to a higher level (step function).

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.

The question is Find the number of positive integers n such that [\\frac{n}{11}\\)] = [\\frac{n}{13}\\)].

Hence the answer is "35 possibilities"

Choice C is the correct answer.


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