Official Quant thread for CAT 2013

@krum said:
yaar ye sab to theek hai, J ko kaise B ke sath laga diya?
B ka shaadi ni hua tho.. L and F kaha se ayengee ? isliye marry older ones fst
@techsurge said:
@krum if you put J with M how many sons are there who are married ??
B is the father of F who is his only married child, F's child can be married
@catter2011 said:
B ka shaadi ni hua tho.. L and F kaha se ayengee ? isliye marry older ones fst
dadi unki swarg sidhar gayi hogi

chodo yaar, ye dusron ke family ke ladfde mien nai padna
@catter2011 said:
tu avi ni samjha.. L is B's married chid, whoz unmarried
Got it..what a question!!!!!
The savings of Ramesh and Varun are in the ratio 3 : 2, while their expenditures are in the ratio 3 :4 in the same order. Also the ratio of their incomes in the given order is 4 : 5. What is the ratio of saving of Ramesh to his expenditure?
here's an easy one :
Find all positive integers n for which 1 + 2^n + 3^n + 4^n is divisible by 5.

| attitude is more important than facts |
@surajmenonv said:
here's an easy one :Find all positive integers n for which 1 + 2^n + 3^n + 4^n is divisible by 5.| attitude is more important than facts |
all odd natural numbers
@catter2011 said:
The savings of Ramesh and Varun are in the ratio 3 : 2, while their expenditures are in the ratio 3 :4 in the same order. Also the ratio of their incomes in the given order is 4 : 5. What is the ratio of saving of Ramesh to his expenditure?
is it 6:7??????
@19rsb hmm.. donno the answer.. i am getting 1:7 , post ur approach @19rsb
@catter2011 said:
The savings of Ramesh and Varun are in the ratio 3 : 2, while their expenditures are in the ratio 3 :4 in the same order. Also the ratio of their incomes in the given order is 4 : 5. What is the ratio of saving of Ramesh to his expenditure?
ans : 1/7
@catter2011 said:
The savings of Ramesh and Varun are in the ratio 3 : 2, while their expenditures are in the ratio 3 :4 in the same order. Also the ratio of their incomes in the given order is 4 : 5. What is the ratio of saving of Ramesh to his expenditure?
(4i-3e)/(5i-4e)=3/2
=>8i-6e=15i-12e
=>7i=6e
=>i/e=6/7

4i-3e=3s
=>24/7e-3e=3s
=>3/7e=3s
=>s/e=1/7
r v
savings 3s 2s
exp 3e 4e
income 4i 5i

now income = exp + sav

so,
4i = 3s + 3e
5i = 2s + 4e

solve to get s/e = 1/7


| attitude is more important than facts |



@krum said:
all odd natural numbers
i am afraid not....think again
infact try for n = 2... its valid

| attitude is more important than facts |

@catter2011 said:
@19rsb hmm.. donno the answer.. i am getting 1:7 , post ur approach @19rsb
yaa buddy it is 1/7....some calc mistake.....lost in d world of mistakes..but trying hard 2 come out of it........
@surajmenonv said:
i am afraid not....think againinfact try for n = 2... its valid| attitude is more important than facts |
(1+2^n+3^n+4^n)mod5
==>(1+(2)^n+(-2)^n+(-1)^n)mod5
1+(2)^n+(-2)^n+(-1)^n =0 ; n=odd

1+(2)^n+(-2)^n+(-1)^n
==>2+2*2^n ; n=even
==>2+2*2^n=5k

as sum of two even numbers is always even, we need numbers of the form 10k
==>2*2^n=__8
==>2^n=__4
==>n=2,6,10,14,....

including all the odd numbers , we get all numbers except multiples of 4

@surajmenonv said:
i am afraid not....think againinfact try for n = 2... its valid| attitude is more important than facts |
all natural no. except multiple of 4?
@krum said:
all odd+ 2,6,10...
ya thats correct....in simpler words all nos which are not multiles of 4.
post ur approach too for others help

| attitude is more important than facts |


In a group of 130 players numbered 1 to 130, all even numbered players choose Cricket, whose numbers are divisible by 5 choose Football and those whose numbers are divisible by 7 choose Hockey. How many choose none of the three sports?
@catter2011 said:
In a group of 130 players numbered 1 to 130, all even numbered players choose Cricket, whose numbers are divisible by 5 choose Football and those whose numbers are divisible by 7 choose Hockey. How many choose none of the three sports?
45?
EDITED
@catter2011 said:
In a group of 130 players numbered 1 to 130, all even numbered players choose Cricket, whose numbers are divisible by 5 choose Football and those whose numbers are divisible by 7 choose Hockey. How many choose none of the three sports?
cricket - 130/2=65
football - 130/5=26
hockey - 130/7=18

cricket + football - 13
football + hockey - 3
cricket + hockey - 9

all 3=1

none=130-(65+26+18-13-3-9+1) = 45
@krum yes 45, making a venn .. gives answer.