CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

CAT Questions | Permutation Probability | Distribution

The question is from Permutation and Combination. It is from the topic probabilty. We need to find out the probability of a particular event. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 20: A boss decides to distribute Rs. 2000 between 2 employees. He knows X deserves more that Y, but does not know how much more. So he decides to arbitrarily break Rs. 2000 into two parts and give X the bigger part. What is the chance that X gets twice as much as Y or more?

  1. \\frac{2}{5}\\)
  2. \\frac{1}{2}\\)
  3. \\frac{1}{3}\\)
  4. \\frac{2}{3}\\)

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Explanatory Answer

Method of solving this CAT Question from Permutation and Combination: A tough question which becomes easy if you get the basics right!!

The bigger part could be any number from 1000 to 2000.
Now, if the bigger part is to be at least twice as much as the smaller part, we have
X ≥ 2Y or X ≥ 2(2000 – X)
Or X ≥ \\frac{4000}{3}\\)
Given that X lies between 1000 and 2000, what is the probability that X lies between \\frac{4000}{3}\\) and 2000?
This probability is equal to \\frac{2000 − 4000/3}{2000 − 1000}\\) = \\frac{2}{3}\\)

The question is "What is the chance that X gets twice as much as Y or more?"

Hence the answer is "\\frac{2}{3}\\)"

Choice D is the correct answer.


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