Official Quant thread for CAT 2013

@ScareCrow28 no,
and plz share approaches too...atleast galti kaha ho rhi he pata bhi chale so dat others can b caeful on that
@soumitrabengeri said:
A locker at a famous bank can be opened by dialing a fixed 3 digit code(between 000 and 999). Dawood, a terrorist, only knows that the number is a 3 digit number and has only one six. Using this he tries to open the lock by dialing 3 digits at random. The probability that he succeeds in this is..1) 1/2432) 1/9003) 1/2164) 1/1000
1/243
@ScareCrow28 said:
"Dawood, a terrorist, only knows that the number is a 3 digit number and has only one six."If it starts with "0", then its not a 3 digit -no... Question language me JHOL
deko, if u have ever locked ur suitcase, by key lock,,it has default lock at 000...now its a combination of 3 digit..dont go by a 3 digit number..if u have a suitcase whose lock code is 42, u have to give 042..u cant say der, no its a 2 digit no.so what ll u put at hundred place in ur suitcase...i think it shud be clear now
@soumitrabengeri 1/243?
@rkshtsurana said:
@ScareCrow28 no, and plz share approaches too...atleast galti kaha ho rhi he pata bhi chale so dat others can b caeful on that
(0.0769874)^8 = (769874*10^-7)^8 = X
log X = 8log769874 - 56 = 5.8864 * 8 - 56 = -8.9088
Also, (0.1234) = (1234 * 10^-4)^n = Y
log Y = n*3.0912 - 4n = -8.9088
=> n= 9.8 something :(
@wovfactorAPS said:
3?36*24!arrrange 24 memebers u have 18 positions for and b with 2! arrangemements between them.
can you please explain a bit more in detail?
Out of 24 members we have to arrange 7..so it should be 24P7 right?

Q. What are the last two digits of the sum obtained by adding all the possible remainders of numbers of the form 2^n, n being a non-negative integer, when divided by 100?


No OA available. Please discuss in details !!
@ScareCrow28 said:
(0.0769874)^8 = (769874*10^-7)^8 = Xlog X = 8log769874 - 56 = 5.8864 * 8 - 56 = -8.9088 Also, (0.1234) = (1234 * 10^-4)^n = Ylog Y = n*3.0912 - 4n = -8.9088=> n= 9.8 something
see log X = -8.9088 = 0.0912 - 9
also given log 1.234 = 0.0912
so log 1.234 - log10^9 = X
so log 1.234* 10^-9 = x
iske baad me bhi atak gaya..ans D diya he

@staaalinnn said:
Q. What are the last two digits of the sum obtained by adding all the possible remainders of numbers of the form2^n, n being a non-negative integer, when divided by100?No OA available. Please discuss in details !!
2, 4 ,8 , 16 , 32 ,64, 28, 56 , 12, 24 , 48 , 96, 92 , 84 , 68, 36 , 72, 44 , 88, 76 , 52 , // repetition 04 , 8 ,
dis is bekar approach
@rkshtsurana said:
2, 4 ,8 , 16 , 32 ,64, 28, 56 , 12, 24 , 48 , 96, 92 , 84 , 68, 36 , 72, 44 , 88, 76 , 52 , // repetition 04 , 8 ,dis is bekar approach
right bhai..I also tried in the same lines but yeh to bahut lamba ho jayega..
@rkshtsurana said:
2, 4 ,8 , 16 , 32 ,64, 28, 56 , 12, 24 , 48 , 96, 92 , 84 , 68, 36 , 72, 44 , 88, 76 , 52 , // repetition 04 , 8 ,dis is bekar approach
even i used the same approach..:P
@staaalinnn
@soumitrabengeri ha aur koi approach dundte he
@soumitrabengeri said:
can you please explain a bit more in detail? Out of 24 members we have to arrange 7..so it should be 24P7 right?
na ..iam not doing that way..

first i arrange 24 alphabets excepting a and b

1 2 3 4 5 6 7 8.....

now if i place A before 1 i have to place b immediatetly after 7( which is 1+6)

so till 18 (18+6=24) i can place one of the alphabets..either A/B IN 2 ways

so 24!*18*2!

regarding ur approach of getting

24p7*18!*2! there is a small flaw..

consider this A B the alphabets between them be 1 2 3 4 5 6 7 (consider this as group Q)

so when u write 18! u r arranging the remaining 18 alphabets

say the alphabets be x y z ..

so ur arrangement would be

( x y z...'s arrangement)*(arrangement of Q)

u didnt consider the arrangement where Q can be placed between the letters of the other group say( x,y)

i think this clears..else revert..

p.s:slow reply bcz of too many g k notifications and missed urs






edited the typos

@soumitrabengeri
@staaalinnn
ek pattern dikh gaya..
x 2 = x can be 1 3 5 7 9 ( exception 0 bhi hga)
x 4 = x can be all even 0 2 4 6 8
x 6 = x all odd 1 3 5 7 9
x 8 = x all even 0 2 4 6 8
now we can add
@soumitrabengeri said:
Seems to be correct and even i got the same answer but the OA has been given as (c)The explanation is given as follows..question is from Arun SharmaA and B can occupy 1st and 9th places..2nd and 10th...3rd and 11th places and so on..This can be done in 18 waysA and B can be arranged in 2 waysAll the other 24 alphabets can be arranged in 24! ways..how is this possible?Hence their answer comes out to be 2*18*24! = 36*24!Option (c)
@rkshtsurana :
2*P(24, 7)*18!
=2*24!*18!/17!
=2*24!*18
=36*24!

ye Arun Sharma ka bharosa thoda kam karo.
I've seen the book. Mistakes se bhari padi h :splat:

@wovfactorAPS said:
na ..iam not doing that way..first i arrange 24 alphabets excepting a and b1 2 3 4 5 6 7 8.....now if i place A before 1 i have to place b immediatetly after 7( which is 1+6)so till 18 (18+6=24) i can place one of the alphabets..either A/B IN 2 waysso 24!*18*2!regarding ur approach of getting24p7*18!*2! there is a small flaw..consider this A B the alphabets between them be 1 2 3 4 5 6 7 9(consider this as group Q)so when u write 18! u r arranging the remaining 18 alphabetssay the alphabets be x y z ..so ur arrangement would be( x y z...'s arrangement)*(arrangement of Q)u didnt consider the arrangement where Q can be placed between the letters of the other group say( x,y)i think this clears..else revert..p.s:slow reply bcz of too many g k notifications and missed urs
@rkshtsurana dekho bhai..kuch samajh aata hai toh
@wovfactorAPS Thanks for the solution..i still feel that my answer is correct..lets just agree to disagree..:)
@rkshtsurana said:
@soumitrabengeri@staaalinnnek pattern dikh gaya.. x 2 = x can be 1 3 5 7 9 ( exception 0 bhi hga)x 4 = x can be all even 0 2 4 6 8x 6 = x all odd 1 3 5 7 9x 8 = x all even 0 2 4 6 8now we can add

@wovfactorAPS said:
na ..iam not doing that way..first i arrange 24 alphabets excepting a and b1 2 3 4 5 6 7 8.....now if i place A before 1 i have to place b immediatetly after 7( which is 1+6)so till 18 (18+6=24) i can place one of the alphabets..either A/B IN 2 waysso 24!*18*2!regarding ur approach of getting24p7*18!*2! there is a small flaw..consider this A B the alphabets between them be 1 2 3 4 5 6 7 9(consider this as group Q)so when u write 18! u r arranging the remaining 18 alphabetssay the alphabets be x y z ..so ur arrangement would be( x y z...'s arrangement)*(arrangement of Q)u didnt consider the arrangement where Q can be placed between the letters of the other group say( x,y)i think this clears..else revert..p.s:slow reply bcz of too many g k notifications and missed urs
we have consider the case when Q will be in between x y z
18! me yahi toh hga
like yaha 4! me ho rha he..x yz Q
xQzy , xzQy..and so on..
@vijay_chandola said:
@rkshtsurana : Does this formula hold true for every case....?I mean, if we take a case of let say, three persons and one person is taking 6 hours more than the all three working together, second person takes 3 horse more than all three working together, and third takes 12 hours more than all three working together.What would be the answer of time taken by all three working together in this case?
its not valid ..i checked now :)
consider an examlpe
1/2+1/3+1/4=13/12

so x=12/13

so a=2-12/13=14/13

b=27/13

c=40/13

(abc)^(1/3)=((14*27*40)^1/3)/13 which is not equal to 12/13

@soumitrabengeri said:
2 women Katrina and Deepika are working on an embroidery design. If Deepika worked alone, she would need 8 hours more to complete the design than if they both worked together. Now, if Katrina worked alone, she would need 4.5 hours more to complete the design than if they were working together. What time would it take for Katrina alone to complete the design?1) 10.5 hours2) 12.5 hours3) 14.5 hours4) 18.5 hours

k+d=1/t (where t is the time taken when both work together)

k=1/(t+4.5)

d=1/(t+8)

1/(t+4.5) +1/(t+8) = 1/t

t=6
so time taken by katrina only=t+4.5=10.5