# Singles – 4

## 16 thoughts on “Singles – 4”

1. Girish |

amazing problems… solving them using equations would be equal to 2 month worth practice of equations.

• Any specific topic, Aditya? Number Theory is pretty vast π 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…

regards
J

• 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….

2. 1.total no. of factors.
2. ways in which no. can be written as a product of two even no.(or one even and one odd no.)
Plz explain the process (steps involved in this).

3. invictus2013 |

one word: WOW

4. sahil katoch |

i think answer for above question should be 8:1 instead of 7:1.

5. Harsh Vardhan |

Explained clearly π Thanks for the post!

6. gaurav |

Julie had been running for 120 min. Why v have taken that as 105 min..

• Nope, read carefully. her mom picks her up up 15 minutes earlier than usual. So 105 minutes!

regards
J

7. gaurav |

oh..sorry i got it

8. Raj Patel |

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 Anwarβ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.

• Here Anwar returns home at 6 p.m., not reaches the school at 6 pm. So, he must have reached the school at 5 p.m. So it will be 7.5 : 52.5 = 1 : 7

regards
J

9. Raj Patel |

Oh okay! Got it sir, thank you π