Official Quant thread for CAT 2013

MBA CAT 2024
23787
@bodhi_vriksha said:
f(1)f(0)= 2f(1)=> f(1){f(0)-2}=0=> f(0)=2Also, {f(x)}^2 =f(2x)+f(0)=f(2x)+2 => f(2)=3^3 - 2 =7 and f(4)=7^2 -2 =47 Also, f(2)f(1)=f(3)+f(1)=>f(3)=18 Hence, 47*18=f(7) + 3=> f(7)=843
@ravi.theja said:
843??
@catahead said:
843

plug in 0 as x and y in c
f(0)^2 = 2f(0)
we have two values for f(0) = 0,2 but f(0)=/0, so f(0) = 2

Given that f(1) = 3
let x=1,y=1
so,
f(1)^2 = f(2) + f(0)
9 = f(2) + 2.
f(2) = 7

Now, x=2,y=1
f(2)f(1) = f(3) + f(1)
(7)(3) = f(3) + 3.
f(3) = 18

x=2,y=2
f(2)^2 = f(4) + f(2)
49 = f(4) + 7.
f(4) = 42

x=4,y=3
f(4)f(3) = f(7) + f(1)
(42)(18) = f(7) + 3.
f(7) = 753
23788
@jain4444 said:

f(2)^2 = f(4) + f(2)49 = f(4) + 7.f(4) = 42
You have made an error in the above underlined part. Basically we have {f(x)}^2 =f(2x)+f(0).

So, f(4)= 49-2=47
23789
@chillfactor said:
In how many ways one can choose 2 white squares and one black square from a chessboard ?
We need to choose two of 32 whites AND choose 1 of 32 blacks.

32C2 * 32C1

Now solve this:

In how many ways three white squares can be selected on a chessboard such that no two squares are in same row or column?
23790
All possible words from the letters of the word "TRUNK", used without repetition, are written down in alphabetical order. What is the rank of the word RUN?
23791
@bodhi_vriksha said:
We need to choose two of 32 whites AND choose 1 of 32 blacks.32C2 * 32C1
Oops sorry my bad! I meant to ask that

In how many ways one can choose two white squares and one black square in chessboard such that no two lies in same row or column ?
23792
@chillfactor said:
In how many ways one can choose 2 white squares and one black square from a chessboard ?
32C2 * 31C1

sir jii aur kuch banta hai kya
23793
@ani6 said:
All possible words from the letters of the word "TRUNK", used without repetition, are written down in alphabetical order. What is the rank of the word RUN?
Edit: Too many errors starting from scratch...

Total words = 5 + 5*4 + 5*4*3 + 5*4*3*2 * 5! = 325. So 65 words starting with each letter. 65 with K and N means 130 before R.
Within Rs
R - 1
RK... - 1 + 3 + 6 + 6 - 16
RN... - 16
RT... - 16
RU - 1
RUK - 1 + 2 + 2
RUN - 1
= 186

regards
scrabbler
23794
@scrabbler 186
23795
@scrabbler said:
142? recheckingregardsscrabbler
Try again! It should be186.
23796
@ani6 said:
All possible words from the letters of the word "TRUNK", used without repetition, are written down in alphabetical order. What is the rank of the word RUN?
47?
23797
@bodhi_vriksha said:
We need to choose two of 32 whites AND choose 1 of 32 blacks.32C2 * 32C1Now solve this:In how many ways three white squares can be selected on a chessboard such that no two squares are in same row or column?
32*25*18/3! = 4800 ways
@ani6 said:
All possible words from the letters of the word "TRUNK", used without repetition, are written down in alphabetical order. What is the rank of the word RUN?
K N R T U

Starting with K -> 1 + 4 + 2*C(4, 2) + 3!*C(4, 3) + 4! = 1 + 4 + 12 + 24 + 24 = 65
Starting with N -> 65 letters
Starting with R ->
1 + starting with RK + starting with RN + starting with RT + RU + starting with RUK
= 1 + 3(1 + 3 + 2*C(3, 2) + 3!) + 1 + (1 + 2 + 2)
= 1 + 48 + 6
= 55

So rank of RUN will be 65 + 65 + 55 + 1 = 186
23798
@chillfactor said:
Oops sorry my bad! I meant to ask thatIn how many ways one can choose two white squares and one black square in chessboard such that no two lies in same row or column ?
32C1 * 25C1 * 16C1/3!

but this is not an integer

@chillfactor sir kahan galti ki
23799
@jain4444 said:
32C1 * 25C1 * 16C1/3! but this is not an integer @chillfactor sir kahan galti ki
Here order in which you are choosing squares will also play a role, try BWW instead of WWB
23800
@chillfactor said:
Here order in which you are choosing squares will also play a role, try BWW instead of WWB
32C1 = black square
(32 - 8)C1 = 1st white
(32 - 8 - 7)C1 = 2nd white

32*24*17/3! = 2176 ??
23801
@chillfactor said:
Here order in which you are choosing squares will also play a role, try BWW instead of WWB
is it 32c1*25c1*13c1/3!?
23802
@iLoveTorres said:
is it 32c1*25c1*13c1/3!?
@jain4444
Why are you both dividing by 3!, here its 2 white and one black so shouldn't we divide by 2 instead of 3!

@iLoveTorres Still you won't get the correct answer
23803
@chillfactor said:
@jain4444Why are you both dividing by 3!, here its 2 white and one black so shouldn't we divide by 2 instead of 3!Still you won't get the correct answer
for the three different cases i am getting
WWB 32c1*25c1*13c1/2
BWW 32c1*24c1*6c1/2
WBW 32c1*24c1*9c1/2

Whats the error here?
23805
@chillfactor said:
32*25*18/3! = 4800 ways
This is not correct. Please try again.

Think in terms of positioning of the subsequent left over squares.
23806
@chillfactor said:
In how many ways one can choose two white squares and one black square in chessboard such that no two lies in same row or column ?
6912?

Choose a black square : 32C1
Choose a white square : (32 - 8)C1 = 24C1
Choose another white square : (23- (8 - 1)) = 18C1
(Removing 1 because there will be one common white with a row or column of both black and white squares selected.)

Total = 32 * 24 * 18 / 2 = 6912
23807
@chillfactor can you plz elaborate how you got 65 for K??