Quant Concepts thread for CAT 2014

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Hey puys, As we all are geared up to prepare ALL NEW CAT 2014, let us refresh our quant concepts bit by bit. All we need to do is just mention the topic name followed by the concept and illustrate it with an example or two. So, let's get started...
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If 201 digits were used to number the pages of a book, starting from 1, find the number of pages in the book.

Do pls share your logic friends


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The capital of a company, Estyle, is made of 75,000 preferred shares with a dividend of 15% and 20,000 common shares, with the par value of each type of share as Rs 10. The total profit of Estyle was Rs 2,40,000 of which Rs. 40,000 was kept in a reserve fund. The remaining profit was distributed to the shareholders. What would be the difference in the dividend percentage given to the common shareholders if the amount kept away in the reserve fund was reduced to Rs 25,000?


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Tryst with destiny!
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harshcat91
@harshcat91  ·  4,242 karma

@shojazz phew ! done!

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shojazz
@shojazzIIM Raipur  ·  3,298 karma

haan ab dikha ki funda kaha pe tha 😃 gud one 👍 

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FRACTIONAL PART AND INTEGRAL PART

R=(5*rt5+11)^2n+1 find fractional part of this number . 

 let f is fractional part of this f=R-[R] 

 let a number X=(5*rt5-11)^2n+1

 X will lie in 0

 so R-X=(5*rt5+11)^2n+1-(5*rt5-11)^2n+1

 so R-X=2*(2n+1c1*(5*rt5)^2n*11+2n+1c3*(5rt5)^2n-2* (11)^3......

 so R-X=even number

 so [R]+f-X=even 

 so f-X=even-[R]

 so f-X=an integer (odd or even both possible)

 so f-X=0 

 bcz 0

 0

so f-X=0 

so f=X=(5rt5-11)^2n+1

so fractional part is (5rt5-11)^2n+1

 ___________________________________________________________________________________________

2nd question 

R=(5+2*rt6)^n=[R]+f

let X=(5-2rt6)^n

so[R}+f+X=((5+2*rt6)^n+(5-2rt6)

so R+f+G=2*(nc0*5^n+nc2*5^n-2*(2rt6)^2....

so [R]+f+X=even 

so f+X=integer 

so f+X=1 

so f=1-x so 1-(5-2rt6)^n________________________

Note - 1) in R=(a+b*rtc)^kif k is odd then f=X

fractional part will be f=(a-b*rtc)^n

2) and if k is even then f+X=1

f=1-(a-b*rtc)^k 

example )find greatest integer less than or equal to (rt2+1)^6 

ANS- here n=6 means even 

so f+X =1 so 

f=1-x =1-(rt2-1)^6

so (rt2+1)^6 =integer+fraction

so integer=(rt2+1)^6-fraction

   = (rt2+1)^6-(1-(rt2-1)^6

  = (rt2+1)^6+(rt2-1)^6-1

Now solve (rt2+1)^6+(rt2-1)^6 by simple binomial expansion 

so integer=198-1

  =197 

-By hunny malhotra

Tryst with destiny!
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@harshcat91 sir thanks a lot for teaching so many concepts in a simpler way 😃 hope u nail it tom..all the very best ..u really deserve to be in iim a..

P.S. sir toh bolna banta hai 😛

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harshcat91
@harshcat91  ·  4,242 karma

thank you all the best ! @charu.goyal22 :)

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Twenty years from now you will be more disappointed by the things you didn't do than by the ones you did. So throw off the bowlines, Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover !!!!!!! Cheers!!
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Guys what is the solution to the generalized eqn a/x+b/y = c/n ??

XLRI Jamshedpur
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D.Uchiha
@D.Uchiha  ·  0 karma

So c does not affect the ans??

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Find the sum of all the 4 digit nos that can be formed using 0,1,3,5,7 (No repetition) . @harshcat91 plz post direct formula for this ???

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hemante
@hemante  ·  0 karma

11th is 3rd window...2nd toh shyd 3-4th nov tk hi thi...

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Ash227
@Ash227  ·  366 karma

415968 aaega.....took some time to understand the concept,,,,,but finally...

😁

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Karan wanted to go to a Sonu Nigam concert at Ambala. Unfortunately, he could not get a ticket because the concert was sold out. He located a tout who was willing to sell him a ticket at a premium. The tout begins by asking Rs. 1000 for the ticket. Karan countered by offering Rs. 500. The tout, knowing that Karan was a Bulls Eye Math faculty, always countered by asking Karan to pay the average of the two offers. Karan countered by always asking the average of his previous offer and the tout's new offer. At what price did Karan finally buy the ticket? (rounded to the nearest Rupee) 667 888 725 NOTA

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anilkrishna
@anilkrishnaIIM Calcutta  ·  0 karma

667

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hardy.divya
@hardy.divya  ·  0 karma

Its just like  inserting the arithmetic means between the 2 extremes

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Does anybody have the Totdal Gadha PDF on PNC and Probability

Please share

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