Official Quant thread for CAT 2013

@Budokai001 said:
A and B are the two opposite ends of a swimming pool and the distance between them is420 metres. Ankur and Manu start swimming towards each other at the same time from A and B,with speeds in the ratio 5 : 9 respectively. As soon as any of them reaches an end, he turns backand starts swimming towards the other end. At what distance (in metres) from A will they meet whenManu is in his 13th round? Note: A to B is considered one round and B to A another round.(a) 405 (b) 330 (c) 240 (d) 280
b)
@vbhvgupta said:
Grass in lawn grows equally thick and in a uniform rate. It takes 40 days for 40 cows and 60 days for 30 cows to eat the whole of the grass. How many days does it take for 20 cows to do the same?
Let
a=Initial amt of grass
d=amount of grass added each day
r=rate at which 1 cow eats grass per day

So, r=(a+39d)/1600=(a+59d)/1800

1800*(a+39d)=1600*(a+59d)
200a=24200d
a=121d

Let 20 cows take n days.

then 20*r*n=121d+(n-1)d
20*(1/10)*n=120+n
n=120

@Zedai said:
In a number system 12, 20,24 are in an arithmetic progression. What is the base of the number system?
a very interesting question indeed and my take is that if the concepts of number system are known well it is less than 45 sec question.

Trying to explain how to do it verbally

1. when we move from 20 to 24 effectively we move 4 units, because the 10's place (i.e 2) hasn't changed after adding 4 hence we haven't crossed the base number. for example when we add 15 to 8 in decimal system we cross the base i.e we cross a multiple of 10. hence the ten's place is changes from 1 to 2 (i.e. 15+8 =23).

Based on this argument we can conclude that in the given question common difference is 4.

2. Now that we know that common difference is 4 so in the given base system we get 12+4=20. This means that when we added 2+4 it became 0 and gave a carry of 1. (the same way when we add 2+8 in decimal system we get 0 and a carry of 1 )

hence the base of number system must be 4+2 = 6.

No calculations or paper pen work required here

ATDH.
@shattereddream said:
Q. Each computer system has a password which is 6 to 8 digits long, and contains of alphabets and digits. Each password must have atleast one digit. How many passwords are possible ?
26^6*9^6+26^7*9^7+26^8*9^8
@aimiift2012 said:
N is the largest 3-digit number which when divided by 11 and 9 leaves 9 and 7 as the respective remainders. The sum of the digits of N is
99k-2
988 for k=10
@pirateiim478 said:
Number of divisors of form 4n+2 for 240 is.....
2^4*3*5
(4n+2)=>4 numbers

(4n+3)=>1 number
(4n+1)=>1 number

(4n+2)
(4n+2)*(4n+1)
(4n+3)*(4n+2)

3 divisors
@gnehagarg said:
26^6*9^6+26^7*9^7+26^8*9^8
Approach plz..
@vbhvgupta said:
Grass in lawn grows equally thick and in a uniform rate. It takes 40 days for 40 cows and 60 days for 30 cows to eat the whole of the grass. How many days does it take for 20 cows to do the same?
80?
let the initial length of grass: L1
it grows @ T

40 cows eat: L1+(T)*40
so 1cow/day eats: (L+40T)/(40*40)....(1)

similarly 30 cows eats: (L1+60T)
so, 1cow/day eats: (L1+60T)/(30*60)....(2)

equate 1 and 2
we get L1=120T.... (3)

let 20 cows take x days to eat
so using eqn1:

[(L+40T)/(40*40)] *20x= L1+(T)*40 (because, total amount of grass= L1+(T)*40)

substitute (3)

we get x=80
@vbhvgupta said:
Grass in lawn grows equally thick and in a uniform rate. It takes 40 days for 40 cows and 60 days for 30 cows to eat the whole of the grass. How many days does it take for 20 cows to do the same?
Making the question a little bit more challenging:
Grass in lawn grows at a rate which is proportional to the amount of grass already present. It takes 40 days for 40 cows and 60 days for 30 cows to eat the whole of the grass. How many days does it take for 20 cows to do the same? Assume that some grass was already there initially.
@sbharadwaj said:
Approach plz..
Upper case letters = 26
Digits = 10
Total characters = 36

If pswrd contains 6 characters, we can have 36P6 possibilities.
We need to remove cases when only letters are used. So, remove 26P6 cases.

Same for 7 and 8 character pswrd.

Hence total ways = (36P6 + 36P7 + 36P8 ) - (26P6 + 26P7 + 26P8 )
@nagpal9 said:
dinesh is seated 7th from left and satish is seated 12 from right. when they interchange their positions, dinesh is seated at 22nd from left. how many people are there?
n-11=22
n=33
@vbhvgupta said:
Grass in lawn grows equally thick and in a uniform rate. It takes 40 days for 40 cows and 60 days for 30 cows to eat the whole of the grass. How many days does it take for 20 cows to do the same?
120
@getupsid said:
Q1.N=7!^3. How many factors of N are multiples 10?a) 736b) 1008c) 1352d) 894Q2.how many zeroes are at the end of36!^36!?a)7*6!b)8*6!c)7*36!d)8*36!
( 2^3*3^2*5*7)^3
2^9*3^6*5^3*7^3

10(2^8*3^6*5^2*7^3)

9*7*3*4
63*12
756

count number of 5 beacuse it is minimum

8*36!
Bill and Clinton take the square of a certain decimal number and express it in base 5 and 6 respectively. Then Bush comes and he takes the two representations and assuming that the expressions are in base 10, adds the numbers. Which of the following cannot be the value of the unit's digit of the sum obtained?
a. 0
b. 2
c. 8
d. 6
e. 3


The product of two numbers '231' and 'ABA' is 'BA4AA' in a certain base system (where base is less than 10), where A and B are distinct digits. What is the base of that system.
a. 5
b. 6
c. 7
d. 8
e. 4


@anytomdickandhary __/\__ please help
@getupsid said:

Q1.N=7!^3. How many factors of N are multiples 10?

a) 736

b) 1008

c) 1352

d) 894


Q2.how many zeroes are at the end of36!^36!?

a)7*6!

b)8*6!

c)7*36!

d)8*36!

1) 7! = (1*2*3*2^2*5*(2*3)*7)^3 = (2^4*3^2*5*7)^3 = (2^12*3^6*5^3*7^3) = 10(2^11*3^6*5^2*7^3)
hence, (12*7*3*4) = 1008 factors..
2) 36/5 = 7/5 = 1 = 8 zeores
hence, 8*36! zeroes...
@Zedai said:
Bill and Clinton take the square of a certain decimal number and express it in base 5 and 6 respectively. Then Bush comes and he takes the two representations and assuming that the expressions are in base 10, adds the numbers. Which of the following cannot be the value of the unit's digit of the sum obtained?

The product of two numbers '231' and 'ABA' is 'BA4AA' in a certain base system (where base is less than 10), where A and B are distinct digits. What is the base of that system.

@anytomdickandhary __/\__ please help
1) Options missing.
sqaure of a number always ends in 0 1 4 5 6
Let the number taken by Bill be X
so x^2 ends in 0 1 4 5 6
now when he expresses in base 5, the numbers have to be 0 1 4 10 11
Similarly for Clinton the number will end in 0 1 4 5 10
when these are added in base 10, the sum can be 0 1 2 4 5 6 8 9
so 3 and 7. Based ont he options i would select my answer.
@Zedai said:
Bill and Clinton take the square of a certain decimal number and express it in base 5 and 6 respectively. Then Bush comes and he takes the two representations and assuming that the expressions are in base 10, adds the numbers. Which of the following cannot be the value of the unit €™s digit of the sum obtained?



square of a number ends with 1 4 5 6 and 9

expressed in base 5 gets converted into 1 4 0 1 4

expressed in base 6 gets converted into 1 4 5 0 3

SO ADDING THEM LAST DIGIT CANNOT BE 3 AND 7
@chandrakant.k said:BHAI 2 ND WALA KAISE HOGA?
@chandrakant.k said:
1) Options missing.sqaure of a number always ends in 0 1 4 5 6Let the number taken by Bill be Xso x^2 ends in 0 1 4 5 6now when he expresses in base 5, the numbers have to be 0 1 4 10 11Similarly for Clinton the number will end in 0 1 4 5 10when these are added in base 10, the sum can be 0 1 2 4 5 6 8 9 so 3 and 7. Based ont he options i would select my answer.
@joyjitpal said:
square of a number ends with 1 4 5 6 and 9expressed in base 5 gets converted into 1 4 0 1 4expressed in base 6 gets converted into 1 4 5 0 3 SO ADDING THEM LAST DIGIT CANNOT BE 3 AND 7
have put the OPTIONS up.
@Zedai said:
Bill and Clinton take the square of a certain decimal number and express it in base 5 and 6 respectively. Then Bush comes and he takes the two representations and assuming that the expressions are in base 10, adds the numbers. Which of the following cannot be the value of the unit €™s digit of the sum obtained? a. 0b. 2c. 8d. 6e. 3







6. coz squares in base 5 end with 0,1,4 and square in base 6 end with 0,1,4,3. so we can't obtain the sum 6.
OA?