Official Quant thread for CAT 2013

@vishcat said:
guys pleASE help me out with this question-two vessels contain spirit and water mixed respectively in the ratio 1:3 and 3:5. Find the ratio in which these are to be mixed to get a new mixture in which the ratio of spirit to water is 1:2?
1:2?
let quantity in vessel I be x
..............................II be y
quantity of spirit taken from vessel I = 1/4x
quantity of water taken from vessel I = 3/4x

quantity of spirit taken from vessel II = 3/8y
quantity of water taken from vessel II = 5/8y

total quantity of spirit in new mix = (1/4x+3/8y)
total quantity of water in new mix = (3/4x+5/8y)

ratio of this is equal to 1:2

so..(1/4*x+3/8*y)/(3/4*x+5/8*y)=1/2
x/y=1/2@vishcat
@vishcat said:
guys pleASE help me out with this question-two vessels contain spirit and water mixed respectively in the ratio 1:3 and 3:5. Find the ratio in which these are to be mixed to get a new mixture in which the ratio of spirit to water is 1:2?
1:2..??
@mailtoankit plz elaborate the concepts applied

@vishcat said:
guys pleASE help me out with this question-two vessels contain spirit and water mixed respectively in the ratio 1:3 and 3:5. Find the ratio in which these are to be mixed to get a new mixture in which the ratio of spirit to water is 1:2?
Say the fraction of spirit in the two bottles is 1/4 and 3/8 and thre reqd value is 1/3
So the ratio = (3/8-1/3) : (1/3-1/4) = 1:2
@vishcat said:
@Logrhythm no
oh srry...typo 1:2 i meant..

(x/4 + 3y/8)/(3x/4 + 5y/8) = 1/2
x:y = 1:2
@Logrhythm bro a method is also given for the weeks question ..
1989=1600+300+89
1600 years have zero odd days
300 years has one odd days
89 years have six odd days (89+22=111=6)
total of 7 odd days
therefore by the end of the year ,the number of odd days is zero
therefore 1 jan 1990 is monday
therefore 10 december is a sunday

can u explain how 1600 years have zero odd days and 300 years 1 odd days
@fireatwill said:
In a triangle ABC, AD , BE ,AND CF are internal angle bisectors of the angles A,B AND C respectively . if D divides BC in the ratio 1:2 and E divides AC in the ratio 3:4, what is the ratio in which F divides AB? PLEASE HELP
Let BC=3x and AC=7y
Now AB/7y = 1/2 =>AB/y=7/2
And AB/3x=3/4=>AB/x=9/4

So divide one by the other and get y/x = 9/14
Now AF/FB = 7y/3x = (7/3)(9/14) = 3/2
Hence 3:2
@catahead I really appreciate your methodology as it reduces the steps drastically. But can you explain a bit more in detail?? i mean how did u take 1/3 in there?
@vishcat said:
@catahead I really appreciate your methodology as it reduces the steps drastically. But can you explain a bit more in detail?? i mean how did u take 1/3 in there?
1:2 => Total parts = 1+2=3 So first part proportion = 1/3 and second part is 2/3
In such questions where you have more than one item, it is better to find the proportion for one item and proceed.

Hope this helps!
@catahead i am asking about that (3/8-1/3)/(1/3-1/4) ....
@vishcat said:
@catahead i am asking about that (3/8-1/3)/(1/3-1/4) ....
So the proportion in 1st is 1/4 and in second is 3/8 and we need to use the property of alligation to get 1/4
So 1/4___________3/8
_________1/3_________
(3/8-1/3)______(1/3-1/4)
The ratio of the last 2 terms is 1:2

You can refer the rule of alligation here http://quantexpert.co.in/qenotes/quantnotes/mixtures/77-mixtures.html
@fireatwill it is 3/2 ..
@catahead thanks a ton ...i didnt knew that rule :)
@vishcat said:
guys pleASE help me out with this question-two vessels contain spirit and water mixed respectively in the ratio 1:3 and 3:5. Find the ratio in which these are to be mixed to get a new mixture in which the ratio of spirit to water is 1:2?
1:2
use property of allegations...
@vishcat 1/2

@sos2god ya
its 3:2
@The_Loser 2+4+8+16+32....256 .. till 8 digit... for 9 digit less and than 2x10^8 ... 256

766..?
@catahead what if the ratios are replaced by- 5:2 and 7:6..........& 8:5 in the question??.....here the allegation rule is giving -ve ratios which are cancelling out in the end....but my question is will the allegation rule change for -ve ratios?
@vishcat said:
@catahead what if the ratios are replaced by- 5:2 and 7:6..........& 8:5 in the question??.....here the allegation rule is giving -ve ratios which are cancelling out in the end....but my question is will the allegation rule change for -ve ratios?
U will not get negative if you place the smaller on the left and larger on the right
So 7/13_______________5/7
_____________8/13_________
__(5/7 - 8/13) : (8/13 - 7/13)

Shud be +ive . I didnt calculate
@The_Loser
@The_Loser said:
hw many 6 digit no are dre having 3 odd & 3 even digits?
number of ways 6!5*5*5*5*5*5
how ever we will have to remove the cases with first digit as 0
so 5!*5*5*5*5*5

so ans 6!5*5*5*5*5*5 - 5!5*5*5*5*5
what am i doin wrong here??