Official Quant thread for CAT 2013

@nole said:
@scrabbler Though it won't have any effect on answer but i think 10! * (1 + E+E+E....) there all numbers won't be E right ? they should be different even numbers. right ?10 ! * (E+1) (odd number) even number * odd number = even number ( i think so) so how do we know in final term there are only 8 2's ? I may be horribly wrong here,but this is what i understood.
E refers to a generic even number. I intended it as a variable... I am using the property that sum of any number of evens is even only....and if I add 1 to a bunch of evens, we will get odd...

regards
scrabbler

@maroof10 said:
Climbing up on a moving escalator,Ram can reach the first floor frm ground floor in 30 sec.If he climbs up on stationary stairs,he takes 20 secs to reach first floor.How many secs will he take for the same trip if he climbs up with his standard pace in the direction of an escalator going up?
10 seconds?

@scrabbler said:
Tricky...? Try karte hue....10! * (1 + 11 + 11*12+ 11*12*13...)= 10! * (12 + 12*odd + 12*odd + 12*Even + 12 *Even all the way aage...)=10! * (12) * (Odd)= 2^8 * 2^2 * odd = 2^10 highest....I guess 10. Please double-check logic though, not sure.regardsscrabbler
Purrrfect !!

@scrabbler yes we got odd number but 10 ! *( odd number) is again even number isn't it ?
@maroof10 said:
Climbing up on a moving escalator,Ram can reach the first floor frm ground floor in 30 sec.If he climbs up on stationary stairs,he takes 20 secs to reach first floor.How many secs will he take for the same trip if he climbs up with his standard pace in the direction of an escalator going up?
Is it 10
@iLoveTorres said:
like i meant if i take say he doesnt score 20 runs and scores 56 runs so effectively he is scoring 36 runs. if you relate it to the original problem this has to align somewhere right?
No, he doesn't score 20 in one innings less than current OR he scored 56 in one more than current. n changes.

Had it said, instead of scoring 20 in his last innings he scored 56, then n would remain same but total n*a would increase by 36, so average would increase by 36/n

regards
scrabbler

N= 123456789123456789...92 digits Find the remainder when N is divided by 38
@nole said:
@scrabbler yes we got odd number but 10 ! *( odd number) is again even number isn't it ?
Yes. But consider a * b . If a has m powers of 2 and b has n, then a*b will have m+n powers of 2 right?

So if 10! has 8 powers of 2 and (OddNumber) has none, then totally 10*OddNumber will have 8...

regards
scrabbler

@scrabbler oh 😃 thanks a lot 😃 this was my main concern. got it 😃
@pavimai said:
N= 123456789123456789...92 digits Find the remainder when N is divided by 38
is the answer 12?

i have posted this 4-5 times before in pg,m posting again coz m not getting it.i hope it doesn't amount to spamming,

A teacher wanted to adminster a multiple choice(each question having six choices) based quiz of high difficulty level to a class of sixty students.The quiz had sixty questions.The probability of selecting the correct answer for a good and brilliant student was 0.2 and 0.25 respectively.All the students were seated serially in 10 rows and 6 columns.

q) three good students were seated next to each other.What is the probability of them having the same incorrect choice for four consecutive questions ?

i did it like

to get one incorrect answer, probabilty is 1/5

so all INCORRECT for one student is 1/5*1/5*1/5*1/5

so overall for 3 students (1/5*1/5*1/5*1/5)^3 but it is not in options.where did i go wrong ?

answer is 4/3125

@ChirpiBird no its 15 secs
@maroof10 said:
Climbing up on a moving escalator,Ram can reach the first floor frm ground floor in 30 sec.If he climbs up on stationary stairs,he takes 20 secs to reach first floor.How many secs will he take for the same trip if he climbs up with his standard pace in the direction of an escalator going up?

His speeds (Upstream, stationary and downstream) will be in AP. So U - S = S - D

If n is number of steps, we can say n/30 - n/20 = n/20 - n/t where t is the time "downstream".

Solving t = 15.

regards
scrabbler

@maroof10 said:
@ChirpiBird no its 15 secs
Let speed of man be x and escalator be n m/s
30x - 30n = 20x
Hence x = 3n

So, time taken will be = 20x/3n+n = 60n/4n = 15 sec..
@maroof10 said:
@ChirpiBird no its 15 secs
this is how i did..

let number of stairs on escalator and normal stairs be N
v= persons speed. u= escalator speed
N/v=20
or N=20v

now (N+(N/v)u)/v=30
where (N+(N/v)u) is the length of the escalator

solving we get.. 2u=v
now to get if he's going along the escalator.. he'll travel less distance/climb less stairs.

(N-(N/v)u)/v=t
20-20*u/v=t
20-20*(1/2)=t
t=10sec

tell me where i am going wrong.
@ChirpiBird said:
10 seconds?
let ram take 1 step/sec and escalator take n steps/sec
therefore
30-30n=20 ==> n=1/3
now when the escalator is moving up by the time ram takes 3 steps escalator takes one step
so he has to take 20 steps i.e 20/4=5 such cycles
but for 3 steps ram takes 3 sec so totally 15 sec
@ScareCrow28 thanks
@ScareCrow28 thanks
@nole said:
@Estallar12 If you don't mind can you explain me how to proceed from thisA=10! + 12 ! + 14 !...... 100 !A= 10 ! (1 + 12*11 + 14*13*12*11 + ...... 100!/10!))Is the answer possible if we proceed from this angle ?
Oh Damn!
A = 10! + 12! + 14! and so on.

I took it as A = 10! + 11! + 12! ... + 100! 😲 :splat:

See, if A = 10! + 12! + 14! + ... + 100!
Then, A = 10! ( 1 + 12*11 + 14*13*12*11 + ... + 100!/10! )
The term is the bracket will be an odd number because 1 is added to the rest terms which are even so it won't contribute to powers of 2.

Thus, only powers of 2 in 10! will be our answer which is 8.

@sbharadwaj
@ChirpiBird said:
this is how i did..let number of stairs on escalator and normal stairs be Nv= persons speed. u= escalator speedN/v=20or N=20vnow (N+(N/v)u)/v=30where (N+(N/v)u) is the length of the escalator

Where did this come from?

Too many variables....core dump ho raha hai...sorry! :)

regards
scrabbler