Official Quant thread for CAT 2013

MBA CAT 2022
1501
@Messy_19 said:
The chance of India winning a cricket match against Australia is 1/6. What is the minimum number of matches India should play against Australia so that there is a fair chance of winning at least one match?
Is it 4?

Fair chance means 50-50 chance, so they should play one more than half to make sure India wins at least 1.
1502
@rkshtsurana said:
cos 18 cos 36 cos 72 cos 144 = ?
cos 36 = -cos 144
cos 72 = sin 18

So the equation becomes..
=cos 18*sin 18*(-cos 36*cos 36)
=0.5*(sin 36 + sin 0 )*(-cos^2 36)
=0.5*(sin 36)*(sin^2 36 - 1)

Ab iske aage nahi aata bhai..:P
1503
@soumitrabengeri
@Messy_19
@sauravd2001
multiply numerator and denominator by 2 sin 18
2sin18 cos18 cos36 cos72 cos144 / 2 sin 18
sin 36 cos 36 cos 72 cos 144/ 2 sin 18
2sin 36 cos 36 cos 72 cos 144/ 4sin 18
sin 72 cos 72 cos 144/ 4 sin 18
2 sin 72 cos 72 cos 144 / 8 sin 18
sin 144 cos 144 / 8 sin 18
2 sin 144 cos 144/ 16 sin 18
sin 288/ 16 sin 18
-sin72 / 16 sin 18
now simply put value of sin18 and sin 72

p.s. - i believe most of you have done dis thing if u prepared for JEE
1504
@Messy_19 said:
The chance of India winning a cricket match against Australia is 1/6. What is the minimum number of matches India should play against Australia so that there is a fair chance of winning at least one match?
1 - (5/6)^n > 1/2
n comes out to be 4..is it correct?

P.S Could you please change the question to Australia's probability of winning against India is 1/6? :P
1505
@Messy_19 said:
The chance of India winning a cricket match against Australia is 1/6. What is the minimum number of matches India should play against Australia so that there is a fair chance of winning at least one match?
6 matches?
1506
@Messy_19 4??

1507
4 is the OA
1508
@soumitrabengeri said:
1 - (5/6)^n > 1/2n comes out to be 4..is it correct? P.S Could you please change the question to Australia's probability of winning against India is 1/6?
y did u make such eqn ?

directly out of 6 matches 1 match will go to india. so 6 is the answer ?

am i interpreting wrng anywer ?
pls help
1509
@rkshtsurana sorry bhai late reply ke liye kuch kar raha tha
dekh maine jo kiya hai woh aise
cos18cos36cos72cos144
cos18cos36sin18cos144
1/2(sin36cos36cos144)
1/4(sin72cos144)
1/8(sin216-sin72)
1/8(-sin36-sin72)
-1/8(sin36+sin72)
aur mujhe yaad thi toh usmein put kardi aur nikal liya answere waise bhi direct ho jata uske baad kyunki sin72 hota hai root(10+2root5)/4
aur option mein dekh a pahle rejetc ho gaya jismein 2root 5 hai aur baki c or d mein toh yeh hai ni toh option b hi bacha
1510
@soumitrabengeri bhai samjhaiyo yeh kya kiya hai mere dimag ke toh paar gay ahai yeh main toh bas 5/6 or 1/6 mein hi ghumne ja rah ahun jabse
1511

hey anyways happy dhanteras to all of u pagal's 😛

1512

see the attached file i have drawn a diagram

expalination of diagram
ab is chord of 21 cm divided into two parts of 4 and 21
and cd is line drawn on ab which is of 6 cm which divides ab into 2 parts of 4 and 21
what is the radius of circle answere hai 65/6 appraoch btao
1513
@catter2011 said:
y did u make such eqn ?directly out of 6 matches 1 match will go to india. so 6 is the answer ?am i interpreting wrng anywer ?pls help
@sauravd2001 said:
@soumitrabengeri bhai samjhaiyo yeh kya kiya hai mere dimag ke toh paar gay ahai yeh main toh bas 5/6 or 1/6 mein hi ghumne ja rah ahun jabse
Fair chance of winning atleast one match= fair chance of winning no match = 1/2

So probability of losing match= 5/6

So probability of losing n matches = (5/6)^n

so (5/6)^n =1/2 .. so for n=3 it will give 125/216>1/2.. and for n=4 it will give 625/1296
As we have to consider the "lesser-than" part because we need the probability of winning atleast one match to be greater than or equal to 1/2. So 4 will be the answer.
1514
@catter2011 said:
y did u make such eqn ?directly out of 6 matches 1 match will go to india. so 6 is the answer ?am i interpreting wrng anywer ?pls help
@sauravd2001 said:
@soumitrabengeri bhai samjhaiyo yeh kya kiya hai mere dimag ke toh paar gay ahai yeh main toh bas 5/6 or 1/6 mein hi ghumne ja rah ahun jabse
fair chance means 50-50 chance, hence that equation
1515
@soumitrabengeri @krum hmm aa gaya samjh yeh inhone ne language mein twist de rakha hai
1516
@krum @rkshtsurana @soumitrabengeri bhai woh radius wala question btana kaise hoga maine tukke bazi nikala hai lekin bahut jyada tym le gaya almost 10 minute 😞 koi simple method ho toh btao
1517
@soumitrabengeri said:
Fair chance of winning atleast one match= fair chance of winning no match = 1/2So probability of losing match= 5/6So probability of losing n matches = (5/6)^nso (5/6)^n =1/2 .. so for n=3 it will give 125/216>1/2.. and for n=4 it will give 625/1296 As we have to consider the "lesser-than" part because we need the probability of winning atleast one match to be greater than or equal to 1/2. So 4 will be the answer.
means probability of loosing 4 matches continuously dropped below 1/2, hence in those four matches ther's a fair chance of winning atleast one . p(w) >= 1/2 , but if u take number of matches as 6, u will have pakka chance i.e. p(w)=1... got it.
1518
@soumitrabengeri yaar obviously..

6 matches mein pakka chance hein tho

1/2 chance(fair chance) keliye >=3 i.e 4 match ki jaroorath hein.. itna calc bhi ni chahiye.. common sense is enough if u get the question crctly

and 1/6 chance keliye >=1 match.
1519
@sauravd2001 said:
@krum@rkshtsurana@soumitrabengeri bhai woh radius wala question btana kaise hoga maine tukke bazi nikala hai lekin bahut jyada tym le gaya almost 10 minute koi simple method ho toh btao
kaunsa ques..
1520
@rkshtsurana bhai 76 pe dekh maine ke diagram ke sath post kiya hai