Official Quant thread for CAT 2013

@vbhvgupta said:
Q1
20c+30s)*30 = 720
if 20C eats which costs you x rs per day
then x+2x = 24
3x =24
x = 8
so 30 sheep costs you 16rs
so 20 sheep = 16*20/30 = 16*2/3
for 15 days = 16*2/3*15 = 16*10 = 160
A cat takes 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?
1) 11:15
2) 15:11
3) 16:15
4) 15:16

Plz give answer along with explanation.
@Exodia said:
A cat takes 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?1) 11:152) 15:113) 16:154) 15:16Plz give answer along with explanation.
let the size of cat leap be c and dog leap be d
cat travels at 5c
dog travels at 4d
3d=4c
d=4c/3
5c/4d
15/16
@Exodia said:
A cat takes 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?1) 11:152) 15:113) 16:154) 15:16Plz give answer along with explanation.
(5*3)/(4*4) = 15:16...
@Exodia
4cat= x unit
3dog=x unit


5 cat / 4 dog
= (5x/4)/(4x/3)
= 15/16



@Exodia said:
A cat takes 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?1) 11:152) 15:113) 16:154) 15:16Plz give answer along with explanation.
say dog one leap = 10kms
so 3 leasps = 30kms
now this is = to 4 leaps of cat so
1 leap of cat = 30/4 = 7.5kms

now when cat travels 7.5*5 = 37.5
dog travels 40kms
cat : dog = 15:16

A^2-B^2=1125
How many integer solution is possible?
1.12
2.24
3.18.
4.36

A cat takes 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?1) 11:152) 15:113) 16:154) 15:16Plz give answer along with explanation.

OA: 15:16
All approaches mentioned above are correct. Happy CATing
@DespicableA said:
A^2-B^2=1125How many integer solution is possible?1.122.243.18.4.36
24??
1125 = 5^3*3^2
x = 5^a*3^b
y = 5^c*3^d
a+c = 3 -> 4solutions
b+d = 2 -> 3 solutions...
total = 4*3 = 12
but need to cconsider -ve integers. hence 12*2 = 24...
@ani4588 nicely done
@DespicableA said:
A^2-B^2=1125
How many integer solution is possible?
1.12
2.24
3.18.
4.36
(A+B)(A-B)=1125
1125=5^3*3^2
all odd factors of 1125
4*3=12
and negative integers
12*4=48
@Logrhythm said:
24??
1125 = 5^3*3^2
x = 5^a*3^b
y = 5^c*3^d
a+c = 3 -> 4solutions
b+d = 2 -> 3 solutions...
total = 4*3 = 12
but need to cconsider -ve integers. hence 12*2 = 24...
u also need to consider cases when one is negative and the other positive
@Subhashdec2 said:
u also need to consider cases when one is negative and the other positive
i knw...but 48 was not in the options hence 24 seemed most likely...
warna 48 is perfect...
coz *4 ho jata hai...
@Logrhythm said:
i knw...but 48 was not in the options hence 24 seemed most likely...
warna 48 is perfect...
coz *4 ho jata hai...
yep that is what i wanted to say

Q1

Q2
raman and rajan efficiency = 50/18 = 2.78
rajan and rajiv efficiency = 50/12 = 4.17
rajiv efficiency = 100/36 = 2.78
so rajan efficiency = 4.17 - 2.78 = 1.39
raman efficiency = 2.78 - 1.39 = 1.39

so raman time = 100/1.39 = 71.94 = 72

I want some different approach..

@Subhashdec2 @Logrhythm @scrabbler @anytomdickandhary
last 2 non zero digit of factorial of any number??

sab so rahe hai...

@vbhvgupta said:
Q2
raman and rajan efficiency = 50/18 = 2.78
rajan and rajiv efficiency = 50/12 = 4.17
rajiv efficiency = 100/36 = 2.78
so rajan efficiency = 4.17 - 2.78 = 1.39
raman efficiency = 2.78 - 1.39 = 1.39

so raman time = 100/1.39 = 71.94 = 72

I want some different approach..
Let Raman do a units of work per day
rajan do b units per day. similary rajiv be c
now in 18days they do 18(a+b) units
so total amount of work to be done = 36(a+b)
(b+c)*12 = 18(a+b) -(2)
12b + 12c = 18a+18b
=>6b +18a = 12c
b+3a = 2c -(3)
36c = 36(a+b)
so c = a+b
sub this in (3)
b+3a = 2a+2b
=> a = b
which means 25% of the work is done by raman in 18 dyas
so 100% will be done in 72 days 😁 :D

Q3