The Official CAT 2007 Quant Thread

[sachin2807]

Originally Posted by esh.nil

the question is a+b+c = 4
so isnt the ans 6C2 = 15 ways??
out of this one is not possible... 004
so totally 14 ways..

they have given a totally diff solution.They divided it into four cases
CASE 1: All fruits are the same.
CASE 2: Three fruits same and fourth one is different.
CASE 3: Two fruits same while other two are different.
CASE 4: Two fruits are of one type while the other two are of another type

Totally,
2+6+3+3=14

[sharang]

In triangle ABC,A(-8,5) B(-15,-19) C(1,-7).Then slope of angle bisector of angle A is ?
1) -12/7
2) 6/5
3) -11/2
4) 7/3

[esh.nil]

Originally Posted by sachin2807

they have given a totally diff solution.They divided it into four cases
CASE 1: All fruits are the same.
CASE 2: Three fruits same and fourth one is different.
CASE 3: Two fruits same while other two are different.
CASE 4: Two fruits are of one type while the other two are of another type

Totally,
2+6+3+3=14

@sachin.. my soln is also the same...
I used the formula isntead of using all the cases..
a+b+c = 4
(n+r-1)C(R-1) = (4+3-1)C2 = 6C2
in this one variety can be selected utmost 3,
so answer will be 6c2-1 =14

the usual way,
112--- 3 ways(3!/2!)
202--- 3 ways
301--- 6 ways
400 --- 2 ways(there is only 3 fruits of one type)..

@monil bhai.... why did u stop after finding the 755^1, why dint u proceed further to find the remainder?? I am not very clear with ur method, can u pls explain???

[sharang]

Consider the fn f : Z+ --> Z+, where Z+ is the set of all positive integers.
If f satisfies
t^2 *f(s)=s{f(t)}^2,
find ratio of f(kx)/f(x)

[esh.nil]

Originally Posted by sharang

In triangle ABC,A(-8,5) B(-15,-19) C(1,-7).Then slope of angle bisector of angle A is ?
1) -12/7
2) 6/5
3) -11/2
4) 7/3

I got the answer as (a) -12/7
but my approach is not the best one.... I am waiting for a better appraoch from puys..

What I did was to find the eqn of line BC and find a tentative point for the D(where ang bisector meets BC) from the ans and select it..

[reachmonil]

Originally Posted by esh.nil

@monil bhai.... why did u stop after finding the 755^1, why dint u proceed further to find the remainder?? I am not very clear with ur method, can u pls explain???

Originally Posted by reachmonil

Expressing in base 3 means mod 3. By Euler's theorem, we have E(3)=2. So, what we have to find now is 755^1 in base 3 = 222. Hence the last 3 digits. Correct?

755^555 mod 3 would give the same remainder as 755^1 in base 10. So... I directly just convert 755^1 into base 3 and got the last 3 digits. Luckily, this answer is correct for the specific example. Though I need to standardise it for general approach, which I don't have enought time to do today. Maybe you can try it using 3-4 examples.

[shyam_146]

hey hi.
this is shyam here from mumbai . have just joined in pagal guy and cant get the head or the tail of it. so if u can just help me out to get started with it . would highly appreciate a reply very soon as would not be interested in wasting time in looking for so as to get started it. thanakx man CHEERS!!!!!!!!!!!!!

[sharang]

Originally Posted by esh.nil

I got the answer as (a) -12/7
but my approach is not the best one.... I am waiting for a better appraoch from puys..

What I did was to find the eqn of line BC and find a tentative point for the D(where ang bisector meets BC) from the ans and select it..

The ans is -11/2...anyways post ur approach

[sachin2807]

Originally Posted by esh.nil

I got the answer as (a) -12/7
but my approach is not the best one.... I am waiting for a better appraoch from puys..

What I did was to find the eqn of line BC and find a tentative point for the D(where ang bisector meets BC) from the ans and select it..

i m getting -11/2 as the answer.
fst i used angle bisector theorem,
AB/AC=BD/DC
AB=25 and AC=15
so,BD/DC=5/3
so,corresponding point D will be (-5,-23/2)
nd then directly find the slope of the line joining pts A and D.

[esh.nil]

Originally Posted by reachmonil

755^555 mod 3 would give the same remainder as 755^1 in base 10. So... I directly just convert 755^1 into base 3 and got the last 3 digits. Luckily, this answer is correct for the specific example. Though I need to standardise it for general approach, which I don't have enought time to do today. Maybe you can try it using 3-4 examples.

Monil bhai...The first example I took, there is a difference between ur ans and mine.
ur approach: consider (623)^7 so the remainder is same as 623,
calculating the last 3 digits
3|623
3|207--2
3|69--0
3|23--0
last 3 digits = 002
but acc to my method, the remainder of 623^7%27 = 2^7%27 = 20
20 in base 3 = 202...

So where is the mistake??