Official Quant thread for CAT 2013

MBA CAT 2024
10681
Six persons try to swim across a wide river.Its known that on an average only three persons out of 10 are successful in crossing the river.Whats the probability that at most four of the 6 persons will cross the river safely?

What @ScareCrow28 had calculated is correct. Just to emphasize his point and to clarify the idea, read on.

The probability distribution of the random variable X is called a binomial distribution, and is given by the formula:
P(X)= nCr * p^r * q^(n-r)
where
n = the number of trials
r = 0, 1, 2, ... n
p = the probability of success in a single trial
q = the probability of failure in a single trial
(i.e. q = 1 창ˆ' p)

Keeping the above mentioned idea in mind,
p is given to us as 3/10 or 0.3
=> q = 1 - 0.3 = 0.7
Also, n = 6 {There are 6 people trying to cross the river}

P(0) = 6C0 * (0.3)^0 * (0.7)^6 = 1 * 1 * 0.117649 = 0.117649
P(1) = 6C1 * (0.3)^1 * (0.7)^5 = 6 * 0.3 * 0.16807 = 0.302526
P(2) = 6C2 * (0.3)^2 * (0.7)^4 = 15 * 0.09 * 0.2401 = 0.324135
P(3) = 6C3 * (0.3)^3 * (0.7)^3 = 20 * 0.027 * 0.343 = 0.18522
P(4) = 6C4 * (0.3)^4 * (0.7)^2 = 15 * 0.0081 * 0.49 = 0.059535
P(5) = 6C5 * (0.3)^5 * (0.7)^1 = 6 * 0.00243 * 0.7 = 0.010206
P(6) = 6C6 * (0.3)^6 * (0.7)^0 = 1 * 0.000729 * 1 = 0.000729

As you can see from above, total is = 0.117649 + 0.302526 + 0.324135 + 0.18522 + 0.059535 + 0.010206 + 0.000729 = 1 {Add it up in calculator if you don't believe me :)}

The question is asking us for at most 4 crosses, so that would be
P(0) + P(1) + P(2) + P(3) + P(4) = 1 - P(5) + P(6)
=> 0.117649 + 0.302526 + 0.324135 + 0.18522 + 0.059535 = 1 - (0.010206 + 0.000729)
=> 0.989065 = 1 - 0.010935
=> Ans is ~ 0.99

I agree that the above method is too long for an exam but I have elaborated it for clarity sake.

Shortcut for exam:

1 - [ P(5) + P(6) ] = 1 - [ 6*0.3^5*0.7 + 0.3^6] = 1 - 0.01 = 0.99

6*0.7 is 0.42 and 0.3^5 is 0.00243. Take 0.42 as ~0.4 & 0.00243 as ~0.0025. The product would be 0.01
0.3^6 is a very small value when compared to 1, so neglect it.
Both these approximations, you should be able to do in your head and get the answer.
10682
@YouMadFellow said:
Oh God, don't trust for calculations for me .. I have made mistakes as silly as 4*2 = 6 !Find the value of C0 - C2 + C4 - C6 + C8................ using binomial theoremC0,C2........ represents nC0, nC2........ (No OA, so show approach, well, you know what, one who is confident should always show approach no matter what )
In terms of "i" ho sakta hai kya? :P
10683
From one of the walls of a square room of side length 1 unit, Maradona kicks a frictionless, perfectly elastic ball which bounces of the three other walls once each and returns to him. What is the distance traveled by the ball?ďťż
10684
@ravihanda Sir \\___o// Good Afternoon :)
10685
@ScareCrow28 said:
In terms of "i" ho sakta hai kya?
Well, The answer should be real. Even I found it in terms of 'i', but it turns out that it is not the answer 😐 . I don't know what is the type of OA 😞
10686

A team of minner planned to mine 1800 tonnes in a certain number of days.Due to some difficulties in one third of the planned days, the team was able to achieve an output of 20 tons of ore less than the planned output.To make up for this, the team overachieved for the rest of the days by 20 tons.The end result for this that they completed the one day ahead of time.How many tone of ore did the team initially plan to ore per day.

A 50
B 100
C 150
D 200
E 250


Correct Answer : 100

Can someone please tell me the procedure for this.

10687
@YouMadFellow said:
Well, The answer should be real. Even I found it in terms of 'i', but it turns out that it is not the answer . I don't know what is the type of OA
Ans 0 hai kya??
I think symmetry hai C0 - C2 + C4 - C6 +..me (If no of terms are even) ..
10688
@hiteshkhurana82 said:
From one of the walls of a square room of side length 1 unit, Maradona kicks a frictionless, perfectly elastic ball which bounces of the three other walls once each and returns to him. What is the distance traveled by the ball?
2rt(2) ?
10689
@ScareCrow28 said:
Ans 0 hai kya?? I think symmetry hai C0 - C2 + C4 - C6 +..me (If no of terms are even) ..
No, answer is not fixed 😃

n = 1 => 1C0 = 1
n = 2 => 2C0 - 2C2 = 0
n = 3 => 3C0 - 3C2 = 1 - 3 = -2

EDIT: I have the OA now. :)
10690
@YouMadFellow said:
No, answer is not fixed n = 1 => 1C0 = 1n = 2 => 2C0 - 2C2 = 0n = 3 => 3C0 - 3C2 = 1 - 3 = -2 EDIT: I have the OA now.
What's the OA ??
10691
@ScareCrow28 said:
What's the OA ??
Well, let others try it out too, but I will tell you that go ahead with the 'i' thing, but then go few steps further if you remember/know the types of representations of complex numbers 😃
10692
@grkkrg said:
2rt(2) ?
sar btado kya kiya hai, dn knw d OA.
10693
@hiteshkhurana82 said:
From one of the walls of a square room of side length 1 unit, Maradona kicks a frictionless, perfectly elastic ball which bounces of the three other walls once each and returns to him. What is the distance traveled by the ball?
I made the diagram, and marked the starting point as distance x, and angle A

After this, I kept on using tanA formula in each right triangle at the corners, and finally I got this:

tanA*( 2- (1/tanA) ) = 1 => tanA = 1 => A = 45 degrees

=> 2*(x*root(2) +(1 - x)*(root(2)) = 2root(2)
10694
A team of minner planned to mine 1800 tonnes in a certain number of days.Due to some difficulties in one third of the planned days, the team was able to achieve an output of 20 tons of ore less than the planned output.To make up for this, the team overachieved for the rest of the days by 20 tons.The end result for this that they completed the one day ahead of time.How many tone of ore did the team initially plan to ore per day.

A 50 B 100 C 150 D 200 E 250

cc: @mohnish_khiani

Let us assume the no. of days as '3d' and the output per day as 'x'
Then, 3d*x = 1800 ---(1)

For the first 'd' days, the output was (x-20).
For the next '2d-1' days, the output was (x+20).
=> d(x-20) + (2d-1)(x+20) = 1800
=> dx - 20d + 2dx + 40d - x - 20 = 3dx {Replacing 1800 with 3dx from equation (1)}
=> 20d = x + 20
=> d = (x+20)/20 ---(2)
=> 3 [(x+20)/20] x = 1800
=> x^2 + 20x = (1800/3)*20
=> x^2 + 20x - 12000 = 0
=> (x+120)(x-100) = 0
=> x = -120 or 100

Since x is the output it cannot be negative.
So, the initial planned output is 100 tonnes. Option B

Shortcut for exam
Go by options.
Option A: 50 per day would mean a total of 36 days.
12*30 + 23*60 Look at second last digit. It will not add up to be 1800

Option B: 100 per day would mean a total of 18 days.
6*80 + 11*120 = 480 + 1320 = 1800. So the answer is Option B
10695
How many distinct right triangles with integer side lengths are there one of whose sides is of length 60?
10696

Following is a question from prev. year's CL Sectional Test:
I just want to check whether the answer given is wrong or there is an error in my calculations
It is pretty easy...Just want to chek as I am at office..Post solution!!!!!!

100 million bacteria can completely decompose a garbage dump in 15 days and 60 million can do so in 30 days. If same quantity of garbage is added to the initial quantity of the dump everyday , how many bacteria will be required to completely decompose the dump in 10 days????????
10697
@YouMadFellow OA log series hai kya??
10698
@sahil.oberoi said:
Following is a question from prev. year's CL Sectional Test:I just want to check whether the answer given is wrong or there is an error in my calculationsIt is pretty easy...Just want to chek as I am at office..Post solution!!!!!!100 million bacteria can completely decompose a garbage dump in 15 days and 60 million can do so in 30 days. If same quantity of garbage is added to the initial quantity of the dump everyday , how many bacteria will be required to completely decompose the dump in 10 days????????
Pehle btao Ans 140 Mn hai kya?
Let, v= variable dump/day and f = fixed dump ..
100 * 15 = 14v + f
60 * 30 = 29v + f
From here, v = 20 and, f = 1220

Therefore, in 10 days

n*10 = 9v + f = 1400
Hence, n= 140 mn ..

10699
@ScareCrow28 sahi hai bhai..approach btaiyo???
10700
@sahil.oberoi said:
Following is a question from prev. year's CL Sectional Test:I just want to check whether the answer given is wrong or there is an error in my calculationsIt is pretty easy...Just want to chek as I am at office..Post solution!!!!!!100 million bacteria can completely decompose a garbage dump in 15 days and 60 million can do so in 30 days. If same quantity of garbage is added to the initial quantity of the dump everyday , how many bacteria will be required to completely decompose the dump in 10 days????????
a - rate of decomposition
b - initial quantity of dump
c - garbage added per day

100*a*15=b+15c
60*a*30=b+30c

300a=15c
==> c=20a,b=1200a

say x bacteria needed

x*a*10=b+10c

==> x=(1200+200)/10=140