Official Quant thread for CAT 2013

@VSK1608 said:
@vbhvgupta Taking S.P as 100 we get C.P as 80 and 75. So difference in profits in 5. So for diff in Profit to be 100, S.P shud be 2000. Is it correct????
correct

@albiesriram said:
I think it shud be C...!!!
@albiesriram said:
B??
@Joey_Sharma
We see the numbers without the squares are of the type
1 2 3 5 8 i.e Fibonacci series ( number= sum of previous 2 numbers)
S = 1 2 3 5 8 .......Xn
S = 1 2 3 5 ...........Xn
Subtracting both the series we get

0 = 1+1+(1+2+3+......n-2 terms) - Xn

=> Xn = 2+(n-2)(n-1)/2 ....we have got the sequence of Fibonacci series starting from the second number....so the series becomes

S = 1 as the first term and next terms as 2+(n-2)(n-1)/2 which is n^2/2 -3n/2 + 3 ( n starts from 2 )

so sum would be 1^2 + Sigma(n^2/2 -3n/2 +3) n varies from 2 to 100

now it becomes a sum of square of numbers, sum of n numbers and appropriate formula can be used.....

The method is lengthier than remembering the formula but this approach comes in handy if u don't remember them and doesn't take too much time as well.... 😃 😃
@ravi.theja said:
B??
A
@pratyush9811 said:
B?
@VSK1608 said:
I think it shud be C...!!!
@albiesriram said:
A
@albiesriram i think its B but t should be greater than 1 bcz for the first hour the cost of parking is constant..i.e. 3 .....plz post the answer also asap...

@albiesriram

Take t = 3.7 hrs
so the total cost becomes = 3+2+2 = 7
checking options
a) 3+2*(3) = 9
b) 3+2*2 = 7
c) 3+2(4) = 11
d) 3+2(3) = 9

so has to be B i believe.....If we take 3.4 instead of 3.7 , a would also satisfy so I modified it to 3.7 coz for all the ranges from a.0 to a.5 , the greatest and the rounding function becomes the same, so we take the other range as our case....

suppose u park for 2.5 hs then fee is 3+2+2 = 7

by A, We have,
3+|2.5 -1| = 3+2|1.5| =7
Others wont work i guess.
@Crysis said:
@albiesriramTake t = 3.7 hrs so the total cost becomes = 3+2+2 = 7checking optionsa) 3+2*(3) = 9b) 3+2*2 = 7c) 3+2(4) = 11d) 3+2(3) = 9so has to be B i believe.....If we take 3.4 instead of 3.7 , a would also satisfy so I modified it to 3.7 coz for all the ranges from a.0 to a.5 , the greatest and the rounding function becomes the same, so we take the other range as our case....
sorry...the cost at 3.7 is 3(0-1) +2(1-2) +2(2-3) + 2(3-3.7) = 3+2+2+2 = 9

but at 3.3, the cost remains 9 but
option a gives 3+2*2 = 7 and option d gives 3+2(3) = 9
so has to be d i believe 😃
@scrabbler said:
2*8C4 +4(7C4+6C4+5C4+4C4) = 364 in the numerator?Diagonal on a chessboard is not only the longest diagonal (not the geometry waala definition) on a square...it is any path on which a bishop moves na...so 2 diagonals of length 8 hai, but next to them 4 of length 7, and 4 of length 6, 5, 4, 3, etc....regardsscrabbler
bhai cant it be ,say , diagonals of all 4 —4 square on a chess board
@albiesriram Can u pls explain what do u mean by rounding off function... I was confused b/w A and C...!!! And am still..!!!

like 1.45 = 1, 1.49 = 1, 1.5 = 2, 1.99 = 2. 00


Guys i am confused as well
@Crysis said:
@albiesriramTake t = 3.7 hrs so the total cost becomes = 3+2+2 = 7checking optionsa) 3+2*(3) = 9b) 3+2*2 = 7c) 3+2(4) = 11d) 3+2(3) = 9so has to be B i believe.....If we take 3.4 instead of 3.7 , a would also satisfy so I modified it to 3.7 coz for all the ranges from a.0 to a.5 , the greatest and the rounding function becomes the same, so we take the other range as our case....
For 3.7hrs ,the total cost is 9 ,not 7.

first hour =3
second hour = 2
third hour = 2
and the next 0.7hrs = 2 (it says "or a part thereof")
so total is 9.

Hence A

and that is assuming ,rounding off leads to the next higher integer..

@albiesriram I feel it should be B only, beacuse suppose we park for 3.4 hours
total cost for 1st hr= 3rs 2nd hr=2rs 3rd hr=2rs 4th hr=2rs total= 9 rs
by a 3+ [3.4-1=2.4 (2 after rounding of)] which makes it total 7 rs
by B 3+ [3.4-1=2.4 (3 after greatest inetger)] which makes it 9 rs.

One from my side :

A square of unit diagonal is cut along one of the diagonals, and the two parts are moved towards each other along the line of the other diagonal. What is the maximum possible area of the overlapping region?


Team BV--Pratik Gauri
@bodhi_vriksha said:
One from my side : A square of unit diagonal is cut along one of the diagonals, and the two parts are moved towards each other along the line of the other diagonal. What is the maximum possible area of the overlapping region?Team BV--Pratik Gauri
half of the square's area? It wont be. getting back with the solution.
@albiesriram said:
half of the square's area?
No 😞 Think again ..Draw the figure and then try it :)

Team BV--Pratik Gauri

Q1