Good Question :
Ashish, Bimal and Chatur are three friends who come to visit an amusement park. Each of the three is accompanied by his father and his grandfather to the park. In how many ways can these nine people stand in the queue at the entry gate if no father wants to stand ahead of his son in the queue?

@RTP: Dude, I didn't quite get what you meant by shuffling.. Should the families be in defined order? son-father-grandfather.. Could you explain your method?
According to me it is 9C3 * 6C3
Though 9C3 * 6C3 = 9!/(3!*3!*3!), I am a bit curious about what you meant!

el3meNt Says

The arrangement you considered isn't possible because g1 is the father of f1, because "No father stands ahead of his son"..

i have a small doubt here
lets say the three are A,B and C their fathers f1 f2 and f3
grandfathers g1 g2 and g3

cant this be possible g1 f1 A g2 g3 f2 f3 B C.....? surely it can right? it satisfies the given conditions ....did u ppl consider these sort of arrangements in ur solution ? cud u ppl elaborate on this pls ?

i have a small doubt here
lets say the three are A,B and C their fathers f1 f2 and f3
grandfathers g1 g2 and g3

cant this be possible g1 f1 A g2 g3 f2 f3 B C.....? surely it can right? it satisfies the given conditions ....did u ppl consider these sort of arrangements in ur solution ? cud u ppl elaborate on this pls ?

arranging 9 people in a line -9!

shuffling 3 people around 3!

3 different families 3!x3!x3! no shuffling i.e 1 way

implies 9!/3!x3!x3!

9C3 * 6C3

family of A,B,C make 1 possible sequence each....

select 3 out of 9 for family A
select 3 out of remaining 6 for family B

Good Question :
Ashish, Bimal and Chatur are three friends who come to visit an amusement park. Each of the three is accompanied by his father and his grandfather to the park. In how many ways can these nine people stand in the queue at the entry gate if no father wants to stand ahead of his son in the queue?

Good Question :
Ashish, Bimal and Chatur are three friends who come to visit an amusement park. Each of the three is accompanied by his father and his grandfather to the park. In how many ways can these nine people stand in the queue at the entry gate if no father wants to stand ahead of his son in the queue?

Good Question :
Ashish, Bimal and Chatur are three friends who come to visit an amusement park. Each of the three is accompanied by his father and his grandfather to the park. In how many ways can these nine people stand in the queue at the entry gate if no father wants to stand ahead of his son in the queue?

Thanks Dude. It was 24-2 even though I had attempted 29 questions out of which 3 have been ignored for marking coz they required certain assumptions to be taken.
Though after interacting with some ppl who gave CAT last yr I realised that certain assumptions need to be taken if CBD and NOTA are not there in the options and TIME should prepare us for this eventuality as well.

Jhaji and TnT saar could advise us better on this I think.

@Rooney awesome sec 1 score !! just for the sake of curiosity, was it 24-2 or 25-5 ?

Mine changed to 99.77

Coaching classes are preparing us for surprises; let the surprises be pleasant.

kill4iim Says

Check it now...I think your percentile should have changed...mine has changed to 99.92.....

yeah... "one that shouldn't be named"...
But really surprising how AIR4 could fetch you only 99.71??

OA (112) 99.71
QADI (62) 99.96
VALR(50) 99.68

keeler.drummer Says

What is sectional cutoff for time? 80%ile?

Didn't miss the sectional.
Sec-1 : 83.03
Sec-2 : 99.58
OA : 98.49
AIR: 331

Nothing to be proud of but a reason to smile.

Funny thing.. I can't stop laughing after seeing my scorecard of 1207

Sec-1 : 76.59 :splat:
Sec-2 : 99.46 :shocked:

Missed a sectional for the first time in the new format.. And now I am getting desperate... ;)

Rooney \m/

No surprises from my side...Its disastrous as usual :splat:

OA: 99.34 %ile... :splat:

AIR: 144
CR: 22 :splat:

of course cleared cutoff's .... I never miss that..

not so good as above bt theek thaak scores for me

sec-1_____97.02%le
sec-2_____99.64%le;)
OA_______99.70%le:D(back to 99s after a disastrous 1209)


rooney575....evrytime i post my score be it on any PG thread...i do it...nd i'm doing it once again

\\__-___0/

congrats to all the toppers...

Dude let us always refer to 1207 as 'What must not be named'. :splat:

Congos for AIR-4 in Simcat-7

I got AIR-26. OA of 99.32

Simcat's quailty is too good but very few test-takers, which would be around 5000.
They don't allow to save the question paper in any format, else I would have shared the question papers with all of you. After that you all would start abhoring Aimcat's VA.

Ten books are arranged in a row on a bookshelf. A student has to select three out of these ten books in such a way that no two books selected by him must have been lying adjacently. In how many ways can he make the selection.

I generally use the following method which i have learnt during JEE days.
Now i have to select three books, so first let those be marked bookS1, book S2 and book S3.
let there be x1 number of books before S1 in the shelf. x2 number of books between S1 and S2, x3 number of books between S2 and S3 and x4 number of books after S3
x1<----(S1)-----> x2<-------(S2)----->x3<--------(S3)------->x4
x1+x2+x3+x4 = 7 as three books are already marked.
now the minimum possible value for x2 and x3 is '1' but for x1 and x4 it is '0'.
maximum possible value for x2 is 6 i.e., when x3=1;x1=x4=0
similarly for x3 it is 6, for x1 and x4 it is 5.

the number of possible ways = number of integral solutions for x1+x2+x3+x4=7 with the following conditions
1<=x2,x3<=6; 0<=x1,x4<=5
= coefficient of t^7 in (1+t+t^2+t^3+t^4+t^5)(t+t^2+t^3+t^4+t^5+t^6)(t+t^2+t^3+t^4+t^5+t^6)(1+t+t^2+t^3+t^4+t^5)
the terms in the first parantheses are the possible values of x1, similarly for the remaining.
= coefficient of t^7 in t^2
= coefficient of t^5 in

(1+t+t^2+t^3+t^4+t^5) =

So, number of ways = coeff. of t^5 in *
= coeff of t^5 in (1-t)^(-4)
coeff of t^r in (1-t)^(-n) = (n+r-1)Cr
So here, 8c5 = 56

This method might be better when qs related to the no 2 of things should be together...

Dude let us always refer to 1207 as 'What must not be named'. :splat:

Congos for AIR-4 in Simcat-7

I got AIR-26. OA of 99.32

Simcat's quailty is too good but very few test-takers, which would be around 5000.
They don't allow to save the question paper in any format, else I would have shared the question papers with all of you. After that you all would start abhoring Aimcat's VA.

Ohh... that was a mistake?
I thought the first statement was about aimcat 1207 and the percentile was for 1208..

we can have only these possible combination of numbers of according to the conditions
257,235,237,357
but we can't take 237 and 357 as whatever number is formed by them will be divisible by 3

now we have only two choices 257 and 235 and in these also we have to place 7 and 3 as unit digit for keeping them prime,
so check for only four numbers
257,527,253,523 out of which 257 and 523 are prime...(naive approach, not too good in quant )

keeler.drummer Says

Right answer, could you please post the process too

getting 15 as my ans.
numbers are 257 and 523

getting 15 as my ans.
numbers are 257 and 523

253---11 is a factor
527---17 is a factor

253,257,523,527,
1560=13

Let X be the set of three digit prime numbers with the following properties:

1) Each digit of the elements of X are distinct.

2) Each digit of the elements of X are prime.

Let K be the sum of all the elements of X. Find the sum of the digits of K?

kill4iim Says

Guys has anyone checked the 1208 solutions....the first 3 questions that are being displayed on the website for section 2 are not from 1208 .. they are from a previous mock....

abhishek_sharma Says

It is 1208. Rooney did the same mistake. Wish I could also not make the same mistakes which rooney doesn't.

srikvarmap Says

abhishek bhai , aimcat 1207 test window is from 12th to 14th of september and how you got your percentile even before many of the test takers didn't completed their test ? that may be your 1208 score card :)

Funny thing.. I can't stop laughing after seeing my scorecard of 1207

Sec-1 : 76.59 :splat:
Sec-2 : 99.46 :shocked:

Missed a sectional for the first time in the new format.. And now I am getting desperate... ;)

Rooney \m/

arey vo tumhare comment kee wajah se nai likha tha....tht was meant to show my respect for ur scores....evry time i do.. \\__-__0/ for ur score nd once again i did \\__-__0/...

spectacular performance