Official Quant thread for CAT 2013

@jain4444 said:
bhai hum toh khud hee bachte hue ghum rahe hai chalo sitter karo ke a cloth merchant professes to sell cloth at 4%loss. But using a false meter he gains 20%. What is the actual length of the metr used by him...?...60 cm 70 cm 80 cm 110 cm
80cm?
@ScareCrow28 said:
Expected value of a continuous random variable E(x) with probability distribution function f(x) is given byE(x) = Integration x*f(x)dxSo, E(w) = Integration 1/(b-a) * w dw = (b^2-a^2)/2(b-a) (limits -infinity to +infinity)Hence E(w) = (b+a)/2 ....
Nice solution :thumbsup:
constraint is given, a ‰¤ w ‰¤ b and zero for otherwise.

So, would there be no use of this info at all?
@jain4444 said:
approach daloo bhai log yahan boht ajeeb sa aa raha hai @chillfactor sir jii madad
Since dimensions are a, b, c, a, b, c, there are two identical parts. So 12!/2! cases.

Had it been regular hexagon, answer will be 12!/6

@19rsb said:The following probability distribution can be used to represent the waiting time of the customer in a bank (w):f(w)= 1/(b-a) for a ‰¤ w ‰¤ b = 0 otherwiseWhat will be the expected waiting time E (w) of the customer in the bank ?

Expected waiting time = Integral xf(x) from x = 0 to inf
= P + Q + R

P = Integral xf(x) from x = 0 to a
= 0

Q = Integral xf(x) from x = a to b
= Integral x/(b - a) from x = a to b
= (a + b)/2

R = Integral xf(x) from x = b to inf
= 0

So, expected waiting time = P + Q + R = (a+ b)/2
@vijay_chandola said:
Nice solution constraint is given, a ‰¤ w ‰¤ b and zero for otherwise.So, would there be no use of this info at all?
Yes there would be bhai..
That E(x) has its limits from -infinity to +infinity.. So, from only a to b would come in the picture :)
@chillfactor said:
Since dimensions are a, b, c, a, b, c, there are two identical parts. So 12!/2! cases.Had it been regular hexagon, answer will be 12!/6
This seals it! I was wrong
@19rsb said:
The following probability distribution can be used to represent the waiting time of the customer in a bank (w):f(w)= 1/(b-a) for a ‰¤ w ‰¤ b = 0 otherwiseWhat will be the expected waiting time E (w) of the customer in the bank ?
b+a/2

Uniform PRobab Distribution !! 1st tym i love i had Maths in Engg 😁
@jain4444 said:
leyo sood sir xat question From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Thenthey will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would bethe contender numbered 2.23. Which position should a contender choose if he has to be the leader? (5 marks)(1) 3 (2) 67 (3) 195 (4) 323 (5) 451
67.

There is a nice pattern in these kind of questions....we can observe by trying for a smaller number of people.
No Survivor
1 1
2 1
3 3
4 1
5 3
6 5
7 7
8 1
9 3
10 5
11 7
12 9
13 11
14 13
15 15
16 1

In other words, if number of people is a power of 2, then "winner" resets to person 1, for each extra person add 2 more.

So now if there are 70 people, take nearest power of 2 below it i.e. 64, that will give person 1, and for the extra (70-64) = 6 people add 2 x 6 = 122 hence the 13th person will win.

If there are 150 people, 1 + (150-128)*2 = 45th person will win.

Here there are 545 people so 1 + (545-512)*2 = 67th person will win.

regards
scrabbler

@jain4444 said:

From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Thenthey will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would bethe contender numbered 2.23. Which position should a contender choose if he has to be the leader? (5 marks)(1) 3 (2) 67 (3) 195 (4) 323 (5) 451
We can easily notice that in case of 2 ż persons, person standing at the first position will be the last man standing.

So, in case of 2 ż + k, after removing k persons we are left with 2 ż persons. Now whoever is standing next to this kth person will be the last man standing.

545 = 512 + 33

Now, 33rd person who is eliminated is standing at 66th position. So, contestant no 67 will be the leader.
@chillfactor said:
We can easily notice that in case of 2ⁿ persons, person standing at the first position will be the last man standing.So, in case of 2ⁿ + k, after removing k persons we are left with 2ⁿ persons. Now whoever is standing next to this kth person will be the last man standing.545 = 512 + 33Now, 33rd person who is eliminated is standing at 66th position. So, contestant no 67 will be the leader.
can u explain a lil more sir?
@jain4444 said:
leyo sood sir xat question From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Thenthey will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would bethe contender numbered 2.23. Which position should a contender choose if he has to be the leader? (5 marks)(1) 3 (2) 67 (3) 195 (4) 323 (5) 451
545 = 2^9 + 33
so 2(33) + 1 = 67
option 2

@chillfactor ___/\___ sir , how v ll proceed if instead of alternate..every 3rd contestant is asked to step up...there was a method that we convert in base 3 and then ve do right shift..can u explain ?
@Brooklyn said:
can u explain a lil more sir?
Lets say that 1st person kills the 2nd and then the 3rd persons gets the sword and he will kill 4th person and so on.

In case there are 2ⁿ persons, whoever has the sword in the starting will be the only survivor. Suppose there are 2ⁿ + 1 persons. So, first person will kill 2nd person, now we are left with exactly 2ⁿ persons and sword is with 3rd person and we know that when 2ⁿ persons are there then the person having sword will be the only survivor in the end.

Similarly, when there are 2ⁿ + k persons we just have to find the who will be having the sword once k persons are dead.

Person standing at '2k'th position is the kth person to die and "2k + 1'th person will get tge sword. So,he will be the last man standing
Q: I travel three distances in the ration of 1:2:3 at speeds of 20 m/s, 30 m/s amd 40 m/s. If the total time taken is 23 minutes, find the total distance covered.
@veertamizhan said:
Q: I travel three distances in the ration of 1:2:3 at speeds of 20 m/s, 30 m/s amd 40 m/s. If the total time taken is 23 minutes, find the total distance covered.
43.2 kms
@veertamizhan said:
Q: I travel three distances in the ration of 1:2:3 at speeds of 20 m/s, 30 m/s amd 40 m/s. If the total time taken is 23 minutes, find the total distance covered.
7.2km x 6 = 43.2km (edited for the 3rd time :/)
@deedeedudu my kitab says total distance covered - 360 meters.
@jain4444 said:
leyo sood sir xat question From a group of 545 contenders, a party has to select a leader. Even after holding a series of meetings, the politicians and the general body failed to reach a consensus. It was then proposed that all 545 contenders be given a number from 1 to 545. Thenthey will be asked to stand on a podium in a circular arrangement, and counting would start from the contender numbered 1. The counting would be done in a clockwise fashion. The rule is that every alternate contender would be asked to step down as the counting continued, with the circle getting smaller and smaller, till only one person remains standing. Therefore the first person to be eliminated would bethe contender numbered 2.23. Which position should a contender choose if he has to be the leader? (5 marks)(1) 3 (2) 67 (3) 195 (4) 323 (5) 451
1000011th position in binary i.e. 67th position
@veertamizhan said:
Q: I travel three distances in the ration of 1:2:3 at speeds of 20 m/s, 30 m/s amd 40 m/s. If the total time taken is 23 minutes, find the total distance covered.
Average speed = 6 / (1/20 + 2/30 + 3/40) = 720/23 m/s
So in 23 min I will cover 720 x 60 = 43200m.

regards
scrabbler

@veertamizhan said:
Q: I travel three distances in the ration of 1:2:3 at speeds of 20 m/s, 30 m/s amd 40 m/s. If the total time taken is 23 minutes, find the total distance covered.
x/20+2x/30+3x/40=1380

==>x=1380*120/23=7200m=7.2km

total=6x=43.2km
@veertamizhan said:
@deedeedudu my kitab says total distance covered - 360 meters.
Not possible even at the lowest speed 20 ms will b travelled in 1 sec
23 mins means 23*60 sec in that time he'll travel more than 360 ms thats evident ain't it?
@veertamizhan said:
Q: I travel three distances in the ration of 1:2:3 at speeds of 20 m/s, 30 m/s amd 40 m/s. If the total time taken is 23 minutes, find the total distance covered.
43.2 km

7.2km @ 20m/s
14.4km @ 30m/s
21.6km @ 40m/s