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!

      regards
      J

      • 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.

    regards
    J

    • 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!

    regards
    J

  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.

      regards
      J

  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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