Official Quant thread for CAT 2013

@Torque024 said:
Have a worksheet in my lapy, don't know the answers. You may discuss.1. A hexagon with sides of length 2, 7, 2, 11, 7, 11 is inscribed in a circle. Find the radius of the circle?
r=7

2. A triangle ABC has positive integer sides, angle A = 2 angle B and angle C > 90. Find the minimum length of the perimeter of ABC.



3. Given a certain hospital is opened only in last week. If 10 people travel through bus to hospital then what is the probability at least two people travel on the same day?

1


@ScareCrow28 said:
We have k identical mugs. In an n-storey building, we have to determine the highest floor from which, when a mug is dropped, it still does not break. The experiment we are allowed to do is to drop a mug from a floor of our choice. How many experiments are necessary to solve the problem in any case, for sure? P.S. I just know the answer..so i won't give any options
A classical interview question asked for programming profile :D
@mathaddict

Why it shouldn't be this :

2 heads and one tails = [(1/3)*(1/2)] + [(2/3)*(1/2)*(1/2)] = 1/3
all three heads = (1/2)*(1/2)*(1/2) = 1/8

1/3 + 1/8 = 11/24

@kinkong said:
10% of salty sea water contained in a flask was poured out in a beaker.After this a part of water contained in beaker was vaporized by heating and due to this,the percentage of salt in beaker increased "M" times.If it is known that after the content of beaker was poured into the flask,the percentage of salt in the flask increased by x%.Find the original quantityof sea water in the flask. plz guys help karo...arun sharma ka hai ye ..plz.....
plz check question, kuch missing hai, what is x% here, not clear.

lol its 1/3 finally .. to this qn


@gnehagarg said:
suppose three coins are lying on a table ,two of them with head facing up and one with tails lying up.One coin is chossen at random and flipped.What is probability that after flip the majority of the coins (at least 2 of them will have haeds facing up)
@grkkrg I read it first time correctly but seeing ur solution I thought I misread it.. lol. If it is flipped it is 1/3 .. if it is tossed it is 2/3
@gautam22 said:
approx 7 hoga sir ke aapka pura 7 aa raha hai
cosine rule laga kar cos63, cos18 aise kia kya?
@mohnish_khiani sorry i couldnt get wat u meant to say

@krum said:
r=72. A triangle ABC has positive integer sides, angle A = 2 angle B and angle C > 90. Find the minimum length of the perimeter of ABC.3. Given a certain hospital is opened only in last week. If 10 people travel through bus to hospital then what is the probability at least two people travel on the same day?1
http://www.qbyte.org/puzzles/p063s.html
yes it is. :)
@mathaddict said:
@mohnish_khiani sorry i couldnt get wat u meant to say


Why it shouldn't be this :

case 1. 2 heads and one tails show up = [(1/3)*(1/2)] + [(2/3)*(1/2)*(1/2)] = 1/3
case 2. all three heads show up = (1/2)*(1/2)*(1/2) = 1/8

1/3 + 1/8 = 11/24



What i meant was the case 1 is when 2 heads show up and case 2 is when all 3 heads are shown up.Then add the probablity.Is this a wrong method??


@mohnish_khiani dude.. u have 1/3 rd chance of tossing tail coin and irrespective of its result u get majority heads

To toss other two u have prob of 2/3 but u have 1/2 chance of getting heads and end it as a 2 heads scenario.

so it is simple 1/3*1+ 2/3*1/2 = 2/3
you are confused whether to flip one or two coins at a time i guess
You flip only one coin and u r done after that
@gautam22 said:
sir pura 7 kaise aa sakta hai jab side 7 ko consider karenge tab beech mein 63 aur side 58.5 aur 58.5 ho jayenge to approx 7 hona chahiye
yaar cosine lagane se alag alag values aa rahe the, sare approx 7 the, par same nai the, isliye perpedicular dal kar kia, process kafi lamba hai, rat ko post karta hun, abhi i'm busy
@mathaddict said:
@mohnish_khiani dude.. u have 1/3 rd chance of tossing tail coin and irrespective of its result u get majority headsTo toss other two u have prob of 2/3 but u have 1/2 chance of getting heads and end it as a 2 heads scenario.so it is simple 1/3*1+ 2/3*1/2 = 2/3you are confused whether to flip one or two coins at a time i guessYou flip only one coin and u r done after that


No what i meant was first out of 3 select 2 and those 2 are heads and the next case will be all three are heads.

Even the tail coin when flipped can have head and the head coin when flipped can have tails.

dude @mohnish_khiani the qn said only 1 coin is flipped ..



@krum said:
H H Twhen H is flipped - 2/3*1/2when T is flipped - 1/3*1so 1/3+1/3=2/3


In question it is asked about at least 2 heads after flips.
When H is flipped there are 2T and 1 H after flips
When H is flipped i am thinking that this is not possible.1/2 is possible if question is about atleast two flips but here question is about after flips atleast two heads.

@mathaddict said:
dude @mohnish_khiani the qn said only 1 coin is flipped ..
Oops,sorry read the question wrong.Thanks dude
@gnehagarg what was the answer given according to your source?
@mohnish_khiani it happens.. :D
Due to the recent global financial crisis, many companies in the field of IT Services offer jobs on contractual basis with a clause of fine for the leave taken by the employee. An ITS company employs an engineer for 290 days on a salary of Rs. 500 for eight hours work per day, and the engineer has to pay a fine of Rs.50 for each hour of his absence. The engineer may compensate his one-day absence by working 4 hours extra for two days. If the engineer receives Rs.1,32,400 at the end of the contract, how many hours was he absent from his job?(1) 110 hours(2) 112 hours(3) 114 hours(4) 118 hours
OA is 112hrs......share ur approach.........

the max amount he recieves if he works all the time is 145000

But he recieved 12600 less.

If he misses 1 day he looses 500 + 50*8 - 900 rs per day

so he missed 12600/900 - 14 days = 112 hours

@19rsb said:
Due to the recent global financial crisis, many companies in the field of IT Services offer jobs on contractual basis with a clause of fine for the leave taken by the employee. An ITS company employs an engineer for 290 days on a salary of Rs. 500 for eight hours work per day, and the engineer has to pay a fine of Rs.50 for each hour of his absence. The engineer may compensate his one-day absence by working 4 hours extra for two days. If the engineer receives Rs.1,32,400 at the end of the contract, how many hours was he absent from his job?(1) 110 hours(2) 112 hours(3) 114 hours(4) 118 hoursOA is 112hrs......share ur approach.........
2) 112 hai kya?