# CAT Quantitative Aptitude Questions | CAT Algebra - Functions questions

###### CAT Questions | Algebra | Functions - Greatest Integer Function CAT Questions

The question is about Greatest Integer Function. A question which combines the function with the probability. Greatest integer function with square in it.. Functions is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept of Functions questions in the CAT Exam. Make sure you practice a lot of questions in CAT Functions Algebra to push your CAT preparation in the right direction. Functions as an idea is a fabulous idea if one can wrap their head around it the right way, and it has been one of the staple ideas tested by the CAT exam historically.

Question 4: [x] = greatest integer less than or equal to x. If x lies between 3 and 5, 5 inclusive, what is the probability that [x2] = [x]2?

1. Roughly 0.64
2. Roughly 0.5
3. Roughly 0.14
4. Roughly 0.36

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##### Method of solving this CAT Question from CAT Algebra - Functions: The greatest integer function is one of the most interesting around. Input can be anything, output is discrete - this function is a logician's delight. You can create gazillion questions; none of which can be solved by plugging in formulae.

Let us take a few examples.
 = 2
[3.52] = 12 [3.5]2 = 9
 = 16 2 = 16
For x ∈ (3, 5). [x]2 can only take value 9, 16 and 25.

Let us see when [x2] will be 9, 16 or 25.
If [x2] = 9,
x2 ∈ [9, 10)
=> x ∈ [3, √10)

[x2] = 16
x2 ∈ [16, 17)
=> x ∈ [4, √17)
In the given range [x2] = 25 only when x = 5
So [x2] = [x]2 when x ∈ [3, √10] or [4, √10) or 5.
Probability = $$frac{10 - 3 + √17 - 4}{2}\\$ $\frac {3.16 - 3 + 4.12 - 4}{2}\\$ = $\frac{0.28}{2}\\$ = 0.14 The question is "If x lies between 3 and 5, 5 inclusive, what is the probability that [x2] = [x]2?" ##### Hence the answer is "Roughly 0.14" Choice C is the correct answer. ###### 2IIM's Online CAT CoachingGet CAT Last Mile Prep Course for 799 /- Signup Now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 44,000/- Next Weekend Batch Starts Sat, Nov 2nd, 2019 ###### Best CAT Coaching in ChennaiRegister Online, get Rs 4000/- off Attend a Demo Class ## CAT Online Coaching | CAT Algebra Videos On YouTube #### Other useful sources for Algebra Questions | Functions Sample Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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