CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

CAT Questions | Permutation Probability | Sum of Rearrangements

The question is from Permutation and Combination. This question is about Sum of Rearrangements. We need to find out the sum of all possible numbers when a four digit number is rearranged. 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 27: What is sum of all rearrangements of the 4-digit number 3321?

  1. 29999
  2. 27777
  3. 28888
  4. 29997

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Explanatory Answer

Method of solving this CAT Question from Permutation and Combination: Clue - FInd the number of rearrangements and then focus on the number of digits

Each of the four digits is likely to appear in the units place , but the digit 3 will appear twice as that of 2 and 1.
Therefore, sum of units place = 3*2 +3*1 + 6*3 = 27.
Sum of tens place = 270
Sum of hundreds place = 2700
Sum of thousands place =27000
Sum of all arrangements of 3321 = 29997.

The question is "What is sum of all rearrangements of the 4-digit number 3321?"

Hence the answer is "29997"

Choice D is the correct answer.


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