Official Quant thread for CAT 2013

MBA CAT 2024
10841

@mbajamesbond said:
There are two boxes – I and II. Each contains balls of two colours – White and Black. A ball is selected at random. It is known that P(W ∩ I) = 0.3 and P(B'|II) = 0.8, where W, B, I and II represent the events White ball selected, Black ball selected, ball selected from Box I and ball selected from Box II respectively. Find P(I|B).
soln agar ho tho, post kar lena...
10842
@tmohan02 said:
A test has 80 questions. There is one mark for a correct answer, while there is a negativepenalityof -1/2 for a wrong answer and -1/4 for anunattemptedquestion. It is known that he has left 10 questions unanswered and scored 34.5 marks.The number of correct answers are????Plz explain???
answered correctly-->x
answered wrongly -->y
x+y=70-->(1)
and x-y/2-(10/4) = 34.5 ==>x - (y/2) = 37-->(2)
==> 3y/2 = 33 ==> y =22 ==>x=48

so 48 is the ans.......?

10843
@tarun.g
Each employee of a certain company is in either Department X or Department Y, and there are more than twice as many employees in Department X as in Department Y. The average (arithmetic mean) salary is $25,000 for the employees in Department X and $35,000 for the employees in Department Y. Which of the following amounts could be the average salary for all of the employees of the company?Indicate all such amounts.$26,000$28,000$29,000$30,000$31,000$32,000$34,000

in dept y, assume p people
so in dept x, no.of people = 2p+q

(2p+q)*25K + p*35 = (3p+q)*s
==>85*p + 25*q = 3s*p + s*q
==>(25-s)*q = (3s-85)*p
so i will go with 26K and 28K.....only these will make both of the same sign


is this correct....?
10844
In the image below: - AB and AD are tangent to the circle - BC and AD are parallel.
What is the length of AC?
10845
@tmohan02 said:
A test has 80 questions. There is one mark for a correct answer, while there is a negativepenalityof -1/2 for a wrong answer and -1/4 for anunattemptedquestion. It is known that he has left 10 questions unanswered and scored 34.5 marks.The number of correct answers are????Plz explain???
48?

C + W = 70
C - 0.5W = 34.5 + 2.5
C - 0.5W = 37
2C - W = 74

3C = 144
C = 48
10846
@manasvr said:
Please stop spamming this thread with empty posts sir.
10847
@tarun.g said:
Each employee of a certain company is in either Department X or Department Y, and there are more than twice as many employees in Department X as in Department Y. The average (arithmetic mean) salary is $25,000 for the employees in Department X and $35,000 for the employees in Department Y. Which of the following amounts could be the average salary for all of the employees of the company?Indicate all such amounts.$26,000$28,000$29,000$30,000$31,000$32,000$34,000
Maximum value equation can assume is when number of emp in X = 2x number of employees in y.
= 28333.333, if you take any higher multiplier of Y, the denominator increases at a much greater rate than the numerator, hence the overall value will only decrease.

26,000 and 28,000 fit the criteria as they are
In order to prove solve the two equations:
Let x= number of employees in Y
N= the multiplier for department X where N>=2

(25,000xN+ 35,000x)/ (xN+x)= 26,000 we get N = 9, so when number of employees in x= 9x the no. in Y we get 26,000

similarly
(25,000xN+ 35,000x)/ (xN+x)= 28,000 N= 7/3 = 2.33 when number of employees in X is 2.33 the no. on Y we get 28,000



Hence proven
eDIT:
Range of average will be (25000,28.3333]




10848
@mbajamesbond said:
There are two boxes – I and II. Each contains balls of two colours – White and Black. A ball is selected at random. It is known that P(W ∩ I) = 0.3 and P(B'|II) = 0.8, where W, B, I and II represent the events White ball selected, Black ball selected, ball selected from Box I and ball selected from Box II respectively. Find P(I|B).
@shadowwarrior

OA




10849
@mbajamesbond said:
@pyashraj @19rsb

Here is the OA
10850

Sambhu beats kalu by 30 metres or 10 seconds.How much time was taken by sambhu to complete a race 1200 metres ?

"30 metres or 10 seconds is confusing"
How to solve this ?

10851
@nole said:
Sambhu beats kalu by 30 metres or 10 seconds.How much time was taken by sambhu to complete a race 1200 metres ?How to solve this ?
Kalu takes 10 secs for 30 ms
For 1200 ms he'll take 1200*10/30=400 secs
Sambhu takes 10 secs less i.e. 390 secs
10852
@nole said:
Sambhu beats kalu by 30 metres or 10 seconds.How much time was taken by sambhu to complete a race 1200 metres ?How to solve this ?
is ans 400 sec?
10853
@nole said:
Sambhu beats kalu by 30 metres or 10 seconds.How much time was taken by sambhu to complete a race 1200 metres ?"30 metres or 10 seconds is confusing"How to solve this ?
390?
10854
@19rsb yeah(6min 30sec ) kaise kara ? :)
10855
@nole said:
Sambhu beats kalu by 30 metres or 10 seconds.How much time was taken by sambhu to complete a race 1200 metres ?

"30 metres or 10 seconds is confusing"
How to solve this ?
to travel 30m kalu requires 10 seconds. so for 1170 kalu takes 390 secs by which time sambhu finishes the race
10856
@nole said:
Sambhu beats kalu by 30 metres or 10 seconds.How much time was taken by sambhu to complete a race 1200 metres ?"30 metres or 10 seconds is confusing"How to solve this ?
Sambhu speed=Ss, Kalu speed=Sk
30/Sk=10, Sk=3;
1200/Sk-(1200/Ss)=10
390=1200/Ss
10857
@nole said:
Sambhu beats kalu by 30 metres or 10 seconds.How much time was taken by sambhu to complete a race 1200 metres ?"30 metres or 10 seconds is confusing"How to solve this ?
First we must know about the length of the first race to solve this na? or are we considering it to be a 100m race?
10858
@nole said:
Sambhu beats kalu by 30 metres or 10 seconds.How much time was taken by sambhu to complete a race 1200 metres ?"30 metres or 10 seconds is confusing"How to solve this ?
Kalu will take 10s to cover 30 mtrs. So speed of kalu = 3m/s
Time for covering 1200 mtrs = 1200/3 = 400

Sambhu is faster so he will take 10 sec less = 390
10859
@ScareCrow28 How do we know kalu will take 10s to cover 30 mtrs? can u please explain the line "sambhu beats kalu by 30 metres or 10 seconds" . I am not able to create a equation out of that line.
10860
@nole said:
@ScareCrow28 How do we know kalu will take 10s to cover 30 mtrs? can u please explain the line "sambhu beats kalu by 30 metres or 10 seconds" . I am not able to create a equation out of that line.
Its given that Kalu is beaten by 10 secs i.e. he reached the finish line 10 secs after Sambhu
When Sambhu reached finish line Kalu had 30 ms more to go which he covered in 10 sec