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CAT Previous Year Paper | CAT Quants Questions | Question 10

The question is about the mean of all four-digit natural numbers. All the numbers are in the form of aabc. In CAT exam one can expect 2-3 questions from Number Theory. One needs lots of practice to master this topic. 2IIM Online CAT Coaching provides exactly that. Make good use of 2IIM CAT question bank and get a kick-ass CAT score.

Question 10 : The mean of all 4 digit even natural numbers of the form 'aabb', where a>0, is

  1. 5544
  2. 4466
  3. 4864
  4. 5050

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Explanatory Answer

Even numbers so b = 0
1100 1122 1144 1166 1188
2200 2222 2244 … …
.
.
.
9900 … … … …
By adding
\\frac{5(1100 + ... + 9900) + 9(22 + 44 + 66 + 88)}{45}) {Since the term is common 5 times and 9 times}
\\frac{(5 × 100 × 11 × 45) + 9 × 22(1 + 2 + 3 + 4)}{45})
= 5544


The question is "The mean of all 4 digit even natural numbers of the form 'aabb', where a>0, is"

Hence, the answer is, "5544"

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