Official Quant thread for CAT 2013

@sauravd2001 said:
sum of first n natural numbers whose sum contain three digits n all 3 digits are same...find the number n
let the digit of the sum be a..so the no. is aaa.
now a+10a+100a=n(n+1)/2

hence 222a=n(n+1)
2*3*37*a=n(n+1)

this means we have to find a value of a for which the LHS reduces to product of two consecutive intergers.
now since the value of a lies between 1

for a=6, we get LHS as 36*37

hence n=36

@vijay_chandola said:
What is the approximate area of a hexagon with side lengths (in order) 5cm, 2cm, 3cm, 6cm, 1cm and 4 cm and all interior angles equal to 120 degrees ?
approx 415.4 ??

It correct will post the approach with diagram.
@htomar said:
approx 415.4 ??It correct will post the approach with diagram.
65_/3/4 square unit is the OA.
@vijay_chandola said:
What is the approximate area of a hexagon with side lengths (in order) 5cm, 2cm, 3cm, 6cm, 1cm and 4 cm and all interior angles equal to 120 degrees ?
edited..65 sqrt3/4...took 121-56 as 55 earlier

You are sitting in a large waiting room, waiting for a final job interview with a reputed software giant. In the room with you are a large number of other candidates from all over India. The interviewer says that the first person to be interviewed, who's birthday is today, will be guaranteed a job. But only the first person. It is your birthday today! If it is your father's birthday in one week's time, how many people can be interviewed before you, before your probability of getting the job falls below 90%?

@anytomdickandhary @naga25french @deedeedudu @krum @vijay_chandola @ScareCrow28
@Zedai @scrabbler @techsurge @chillfactor @Brooklyn @sujamait @soumitrabengeri @rkshtsurana @Estallar12

P.S: I don't have an OA to this..so do post your answers with approaches.
@nick_baba
so people interviewed b4 me shudnt have their b'days 2day ryt .
prob.for each --> 364/365
so v have to find (364/365)^n >= .90 ; n is maximum . ryt ??
here n comes around 38
@rubikmath said:
@nick_babaso people interviewed b4 me shudnt have their b'days 2day ryt .prob.for each --> 364/365so v have to find (364/365)^n >= .90 ; n is maximum . ryt ??here n comes around 38
" so people interviewed b4 me shudnt have their b'days 2day"..but this condition is valid even if the first person is not having b'day but each and every one who follows, has.!!.

lets wait what others have to say.
@rubikmath said:
@nick_babaso people interviewed b4 me shudnt have their b'days 2day ryt .prob.for each --> 364/365so v have to find (364/365)^n >= .90 ; n is maximum . ryt ??here n comes around 38
If there is no person before him having b'day today, then his probabilty is 1 na.
@ScareCrow28 said:
If there is no person before him having b'day today, then his probabilty is 1 na.
yup. but the question is how many people can be interviewed before probability falls below .9 .
as you said if he is first -->1 ; if second then probability decreases .and goes on decreasin as no.of people before him increases.

@nick_baba said:
You are sitting in a large waiting room,......
@rubikmath said:
@nick_babaso people interviewed b4 me shudnt have their b'days 2day ryt .prob.for each --> 364/365so v have to find (364/365)^n >= .90 ; n is maximum . ryt ??here n comes around 38
this makes perfect sense


@nick_baba said:
" so people interviewed b4 me shudnt have their b'days 2day"..but this condition is valid even if the first person is not having b'day but each and every one who follows, has.!!.lets wait what others have to say.
I don't understand your argument here


@ScareCrow28 said:
If there is no person before him having b'day today, then his probabilty is 1 na.
but you don't know whether the person before you has his birthday today

PS: I don't know the significance of my father's birthday here :P
@nick_baba said:
You are sitting in a large waiting room, waiting for a final job interview with a reputed software giant. In the room with you are a large number of other candidates from all over India. The interviewer says that the first person to be interviewed, who's birthday is today, will be guaranteed a job. But only the first person. It is your birthday today! If it is your father's birthday in one week's time, how many people can be interviewed before you, before your probability of getting the job falls below 90%?@anytomdickandhary @naga25french @deedeedudu @krum @vijay_chandola @ScareCrow28@Zedai @scrabbler @techsurge @chillfactor @Brooklyn @sujamait @soumitrabengeri @rkshtsurana @Estallar12 P.S: I don't have an OA to this..so do post your answers with approaches.
What is the significance of the father's birthday here?

@rubikmath said:
@nick_babaso people interviewed b4 me shudnt have their b'days 2day ryt .prob.for each --> 364/365so v have to find (364/365)^n >= .90 ; n is maximum . ryt ??here n comes around 38
Agree with this explanation..
@soumitrabengeri said:
What is the significance of the father's birthday here?Agree with this explanation..
even i dunno this...but it is as it is..
@nick_baba said:
even i dunno this...but it is as it is..

Tag me if someone tries to make some sense of that given information..:P
@grkkrg said:
this makes perfect sense I don't understand your argument here but you don't know whether the person before you has his birthday todayPS: I don't know the significance of my father's birthday here
what i'm saying is that even if the candidates before you, except the first one, have b'day but are not the first ones to be interviewed, what change would it make..???..i mean then in that case the prob of 364/365 may or may not hold.!!

which is more likely ? i)atleast 1 six when 6 dice are rolled ii)atleast 2 sixes when 12 dice are rolled iii)atleast 3 sixes when 18 dice are rolled ?
@nick_baba said:
what i'm saying is that even if the candidates before you, except the first one, have b'day but are not the first ones to be interviewed, what change would it make..???..i mean then in that case the prob of 364/365 may or may not hold.!!
no . i think , what the question means is that whoever has their b'day today and the first one to be interviewed(among people having b'day today) will get hired .
if this is not the case , the problem is pretty weird as we dont have the probability of others getting hired when its not their b'day .
@soumitrabengeri said:
Tag me if someone tries to make some sense of that given information..
yup..but m waiting for the GODS to come up with a satisfactory solution...this question bothered me all night after i faced it..
@nick_baba said:
what i'm saying is that even if the candidates before you, except the first one, have b'day but are not the first ones to be interviewed, what change would it make..???..i mean then in that case the prob of 364/365 may or may not hold.!!
See here we are banking on the fact that no candidate before me has his birthday today.
If any one candidate who goes before me has his birthday today then that case is not in my favour.
So that case is not considered.
For me to be the first candidate who has his birthday today, ALL the candidates who go before me should have their birthdays on other days.
@grkkrg what if some people have birthdays on same day and he didnot tell how many people are there ?
@sauravd2001 said:
@grkkrg what if some people have birthdays on same day and he didnot tell how many people are there ?
doesn't matter
as long as it's not today, any of the other 364 days are in my favour