14 thoughts on “Writer’s Block – CAT Scan 4

  1. pleasr explain this concept.
    Two consecutive no.s are removed from a list of first n natuaral no.s . The average of the remaining no .s is 64/3. What is the product of the two no. that have been removed?

    Averge of consecutive numbers.

    • Karuni, I guess the product will be 210 (as Viren has already said).

      Suppose there are n numbers initially. That means after removing 2 of them the total is n-2. Also if the average of a set of first n (mostly) consecutive numbers is 64/3 (which is 21.33..) the value of n should be near double this i.e around 42 to 43. Also, n-2 should be a multiple of 3 (since the average has a 3 left in the denominator). So let’s try n-2 = 42 and 39.

      Trying n-2 = 42, n becomes 44. Now the 42 numbers sum up to 42 * 64/3 = 896 while the sum of the first 44 numbers is 44 * 45/2 = 990. The two missing numbers would then add to 94 (which cannot be the total for two consecutive numbers and is also too high)

      Trying n-2 = 39, n becomes 41. So the 39 numbers add to 39 * 64/3 = 832 while the 41 numbers add to 41 * 42/2 = 861. So the two missing numbers add to 961 – 832 = 29 and so must be 14 and 15. The product will therefore be 210…

      Hope this helps!


      • Hey J,
        “Also if the average of a set of first n (mostly) consecutive numbers is 64/3 (which is 21.33..) the value of n should be near double this i.e around 42 to 43.”

        I did not understand this. Could you please explain?

        Thanks πŸ™‚

  2. Ratish, try it for yourself. First, take a set of “n” natural numbers starting from 1. Find the average; this will turn out to be the middle number (or the average of the middle two, for even “n”). So it will be near n/2.

    Then remove one of the numbers. Since this removed number will be at most “n”, the average will change by less than n/n i.e. 1. Try it for yourself and see.

    By this kind of experimentation, you will develop the “feel” necessary for that statement of mine to make immediate sense.


    • Ok, I understood what you are trying to say. That when 2 numbers are removed from a set of numbers, the range of the new average varies between (a+ or – 1), where a is the original average of all numbers.
      Now, you’ve stated above that “if the average of a set of first n (mostly) consecutive numbers is a, the value of n should be near double this” (This is after we have removed two numbers)

      So, suppose I take the numbers 1,2,3,4,5. Here, n is 5.
      When I remove 1 and 2, I am left with an average of 4. So, according to your logic above, n should be nearly double of 4, i.e., 8. But 5 and 8 arent close enough.

      Please correct me. Not able to wrap my head around this. 😦

  3. Too small a set Ratish. What we are doing is approximation, it will give us a reasonable answer when we take n = 20 or 100, since removing 1 or 2 numbers is a tiny fraction, but if you take say n = 5 you are removing 40% of the numbers at one fell swoop!


  4. Sir, this is not related to your above post, but will there be apost on question like ‘There are 200 boys.. 150 Got grade A in Maths, 170 got grade A in Science …. what is the minimum number of boys who got Grade A in all subjects? ‘ I just can’t seem to grasp this concept.

    • This kind of question is based on the Pigeonhole Principle (though one can also use the Venn diagram logic – Inclusion-Exclusion principle). I am hoping to do a post or three on the PP sometime but so far haven’t managed….

      In simple terms, if the above question has 3 subjects and asks 150 in Maths, 170 in Science and 180 in History for example, then say 150 + 170 + 180 – (200*2) = 100. (Idea being we are making all 200 pass in 2 subjects and seeing how many extra “passes” are left over.


  5. Would you please elaborate on the 4th question? The cat and tunnel one…
    I didn’t understand the explanation provided in the answers.

    Also, your posts are wonderful! Thank you, keep posting! πŸ™‚

  6. Pingback: How to solve CAT questions in 60 seconds? | IMS VKpedia

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