16 thoughts on “Singles – 4

    • Any specific topic, Aditya? Number Theory is pretty vast πŸ™‚ I have already discussed remainders and P&C in some detail, and plan to talk about the pigeonhole principle at some time in the future…


      • Sir, it would be very helpful if you discuss few questions on the application of:
        1.Euler’s theorem on Remainders.
        2.Fermat’s little theorem.
        3.Wilson theorem.
        4.Questions on HCF and LCM, as in: how to find hcf and lcm of : 2222….(30 times) and 33333…(70 times).
        Thanks a ton.

      • Aditya, these topics are way beyond CAT level. I have briefly mentioned Fermat’s little theorem (and the Chinese Remainder Approach) in a couple of earlier posts, but I believe that they are way beyond what is needed for a CAT/XAT. Ditto for Euler’s and Wilson’s (I have never seen a problem that needed these theorems, and I have been seeing the CAT since, oh, 15 years? HCF and LCM one, I will try, but it might not happen before this year’s CAT as I have some stuff planned for the coming weeks….

  1. In the example of Indrayani express, we halved the saved time and complemented it with the total time taken (i.e. 90 minutes.) So, 12 minutes/2 = 6 minutes : 84 minutes. So, speed ratio is 1:14

    There was a question in a recent mock–

    “Anwar leaves home by car everyday at 4 pm to pick up his son from school and returns home at 6 pm. One day, the school was over at 4 pm and the son, instead of waiting for his father as usual, started walking home from school. Anwar, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes earlier than usual. If the speed of Anwar’s car is 35 kmph, find the speed (in kmph) of his son.”

    Now, I tried implementing the same logic here:

    15 minutes over total journey, so saved 7.5 minutes to and fro the actual point.

    Hence, speed ratio = 7.5 / 112.5 = 1/15

    But there seems to be something wrong with this.

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