Official Quant thread for CAT 2013

@amresh_maverick said:
Three horses : Kanishka, Silver Streak and Arabian Knight are the only horses competing in a race and only one of these three can win the race. If Kanishka is twice as likely to win as Silver Streak and Sliver Streak is twice as likely to win as Arabian Knight, then what is the probability of Arabian Knight losing this race?
@albiesriram said:
4x,2x,x be the probabilties of winning of respective horses. Now since Only three of them are there, 7x = 1,x=1/7;Hence probability of losing is 6/7
oa : 6/7
Mandeep has to create a password having 5 distinct characters using at least 2 digits (from 7 to 9) and at least 2 English vowels (from A, E, I, O and U). No character other than digits from 7 to 9 and vowels of English alphabets are allowed in that password. If the password starts with a digit, then it must end with an alphabet and if it starts with an alphabet, then it must end with a digit. Find the number of possible passwords that Mandeep can create.
@CrookDinu said:
In how many ways 5 rings can be placed in 4 fingers ??
For first ring there are 4 ways ... for second ring there are 5 ways ..(3 fingers that are left plus above and below the first ring put in some finger ).... for third ring we have 6 ways .. and so on ...

So .. 4*5*6*7*8=6720 ways :)


Team BV--Pratik Gauri
@amresh_maverick said:
Mandeep has to create a password having 5 distinct characters using at least 2 digits (from 7 to 9) and at least 2 English vowels (from A, E, I, O and U). No character other than digits from 7 to 9 and vowels of English alphabets are allowed in that password. If the password starts with a digit, then it must end with an alphabet and if it starts with an alphabet, then it must end with a digit. Find the number of possible passwords that Mandeep can create.
1440?

C(3,2)*C(5,3)*(C(2,1)*C(3,1)*3! + C(3,3)*C(5,2)*(C(3,1)*C(2,1)*3!)
@amresh_maverick said:
Mandeep has to create a password having 5 distinct characters using at least 2 digits (from 7 to 9) and at least 2 English vowels (from A, E, I, O and U). No character other than digits from 7 to 9 and vowels of English alphabets are allowed in that password. If the password starts with a digit, then it must end with an alphabet and if it starts with an alphabet, then it must end with a digit. Find the number of possible passwords that Mandeep can create.
3*2*3*4C2*2!*5 = 1080
5*3*1*4C2*3*2! = 360

One way = 1440

Hence, Total ways = 1440*2 = 2880?
@amresh_maverick said:
Mandeep has to create a password having 5 distinct characters using at least 2 digits (from 7 to 9) and at least 2 English vowels (from A, E, I, O and U). No character other than digits from 7 to 9 and vowels of English alphabets are allowed in that password. If the password starts with a digit, then it must end with an alphabet and if it starts with an alphabet, then it must end with a digit. Find the number of possible passwords that Mandeep can create.
3600
@bodhi_vriksha said:
For first ring there are 4 ways ... for second ring there are 5 ways ..(3 fingers that are left plus above and below the first ring put in some finger ).... for third ring we have 6 ways .. and so on ...So .. 4*5*6*7*8=6720 ways Team BV--Pratik Gauri
sir , can we assume here that the rings are diff ? This is if rings are diff , right ?
@amresh_maverick said:
Mandeep has to create a password having 5 distinct characters using at least 2 digits (from 7 to 9) and at least 2 English vowels (from A, E, I, O and U). No character other than digits from 7 to 9 and vowels of English alphabets are allowed in that password. If the password starts with a digit, then it must end with an alphabet and if it starts with an alphabet, then it must end with a digit. Find the number of possible passwords that Mandeep can create.
OA: 2880
When Sunil will be as old as his father is at present, Sunil will be five times as old as his son is at present. Also, by then Sunil €™s son will be six years older than the age of Sunil at present. The sum of the ages of Sunil €™s father and Sunil is 85 years at present. What is the sum of the ages of Sunil €™s son and Sunil at present?
@amresh_maverick Sir jee _/\_ You are always posting questions here and are one of the reasons that this thread never gets dried up! :)
@CrookDinu said:
In how many ways 5 rings can be placed in 4 fingers ??
8C3 * 5!

Treat rings as identical, then make then distinct.

regards
scrabbler

@albiesriram said:
Last three digits of 3^3^3^3 or (% 1000)?
let's find remainder by 125 and 4 ..
3^odd will give remainder -1 by 4 ..so rem is of form 4k-1..
now rem by 125 : phi(125)=100..
so basically 3^27 mod 100 or we need to find last 2 digits of 3^27 ..
(3^4)^6.3^3 mod 100 == last 2 digits of 81^6*27 ==>last 2 digits of 81*47 ==87
so rem is 4k-1=125k'+87
smallest no satisfying is 87 :)
hence remainder is 87 :)


Team BV -- Pratik Gauri
@amresh_maverick said:
sir , can we assume here that the rings are diff ? This is if rings are diff , right ?
If rings are identical it will be 8C3 (partitioning 5 identical objects into 4 distinct groups)

regards
scrabbler

inclusion-exclusion:
Total pool : 5+3= 8 characters are there..

if it starts of with a digit:-
3* 6*5*4*5 =1800 ways( filling the fifth character is given precedence)

If it starts of with a alphabet:-
Similar will be the case if we create a password that start of with a albhabet and ends in a digit. ->1800 ways.

Now, exclude the violating cases, we cant create p/w with 4 digits as we are having only 3 with us . so we will anyway have 2 albhabetss in the p/w
Consider the cases we have created pws with 4 albhabets.
6*4*3*2* 5= 720 ways.
in total 3600-720 =2880ways?

@amresh_maverick said:
sir , can we assume here that the rings are diff ? This is if rings are diff , right ?
yes amresh ..here the rings are different ..in these types of questions you have to assume them different ..

The logic i have used is the best logic to use in such questions. Method is short and crisp :)

Team BV--Pratik Gauri
@amresh_maverick said:
When Sunil will be as old as his father is at present, Sunil will be five times as old as his son is at present. Also, by then Sunil's son will be six years older than the age of Sunil at present. The sum of the ages of Sunil's father and Sunil is 85 years at present. What is the sum of the ages of Sunil's son and Sunil at present?
41? trying orally...

11, 30, 55

Edit: Adding logic:

When Sunil will be as old as his father is at present, Sunil will be five times as old as his son is at present.

=> Sunil's father is 5 times the ages of the son say 5x and x.

Also, by then Sunil's son will be six years older than the age of Sunil at present.

If Sunil had been 3x to start, son would be at that age later. So Sunil must be 3x - 3 initially so that later son will be 3x+3 i.e. 6 years more.

The sum of the ages of Sunil's father and Sunil is 85 years at present.

So 5x + (3x-3) = 85 and so x = 11. hence 11, 30 and 55 are the ages so Sunil + son = 41

regards
scrabbler

@scrabbler said:
41? trying orally...11, 30, 55regardsscrabbler
One day u will be awarded Noble prize for Environment (if this is ever instituted) for saving trees (paper) as u solve most of the q's orally ,

P is the product of first 30 multiples of 30. N is the total number of factors of P. In how many ways N can be written as the product of two natural numbers such that the HCF of these two natural numbers is 19?

@amresh_maverick 41

@amresh_maverick said:
When Sunil will be as old as his father is at present, Sunil will be five times as old as his son is at present. Also, by then Sunil's son will be six years older than the age of Sunil at present. The sum of the ages of Sunil's father and Sunil is 85 years at present. What is the sum of the ages of Sunil's son and Sunil at present?
OA : 41

PS : @sujamait sir, pranam
@amresh_maverick said:
One day u will be awarded Noble prize for Environment (if this is ever instituted) for saving trees (paper) as u solve most of the q's orally ,P is the product of first 30 multiples of 30. N is the total number of factors of P. In how many ways N can be written as the product of two natural numbers such that the HCF of these two natural numbers is 19?
N will be 19^2 * 2^x *3^y * 5^z so the 2s, 3s and 5s can be distributed in 2^(3-1) = 4 ways?

regards
scrabbler