17 thoughts on “CAT 15 Lead-up – 3

    • I’ve assumed you’ve already read (and understood!) my previous posts on PnC – specifically the ones on the Theory of Partitioning. If you haven’t please go through them, it will be clear I guess 🙂

      regards
      J

  1. sir, in 1st question if (a – 1) will be 9, then “a” will be equal to 10 which, which is not possible….please tell me where am i going wrong??

  2. Seema, if you are considering those solutions you will also need to arrange (1, 5, 8) in 6 ways and (1, 1, 40) in 3 ways as the question asks for (a, b, c) so we need ordered triplets. I will also suggest you consider the next case where two numbers are divisible by 2 and one not. See if that adds anything to your set of solutions.

    regards
    J

    • yes, (2,20,1) will also be there, but do we need to arrange them? u mean it matters weather a =2, b=20, c=1 and a=20, b=2 and c=1?

      • OK let me clarify.

        If the question asks “how many pairs of natural numbers multiply to give 30” then the answer will be 4 i.e. (1, 30), (2, 15), (3,10) and (5,6) [here order is not important]

        If the question asks “how many natural number solutions exist for (a, b) such that ab = 30”, then the answer will be 8 [here order is important as a = 15 and b = 2 is different from a = 2 and b = 15]

        The latter question could also be asked as “how many ordered pairs of natural numbers exists such that their product is 30”

        regards
        J

  3. Dear sir,
    Please correct me if wrong but won’t the answer to 2nd question be 2002-1=2001 as there will one case where all the digits are zero resulting in the number 0?
    After all, we are looking for natural numbers.

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