PG Premier League - Chennai Dream Team

[ramaan]

Originally Posted by maverick_srikan

There is just 1 solution to this, and i guess TIME also gave the solution as 1. Can you pls check and confirm?

x^2/y+y^3*x=66

let the two terms be a and b.

Now a*b=864 and a+b=66. We get just 1 solution, if I am correct!

Maverick,Jst nw i checked..time gave the solution as 2..their method is completely different..they are telling 2 solution will come and not telling what is that 2 solutions..

and what i posted as qn was correct..

its x/y(x+y^4)=66...jst check for (6,2)=>6/2(6+2^4)=66
3(6+16)=3(22)=66..

first one is x^3*y^2=864..
6^3*2^2=216*4=864...

[exile]

Yelloz!!

I'm planning to collect a few questions concept wise and post it. Lets see how far it materializes..

To begin with, min-max problems.

1) if | 2x +1 | <=3 and |3y -2|<=5, find the maximum value of |x| + (|x| + |y|)

2) if p^3*q^4*r^6*s=216, find the minimum value of 2p^3+3q^4+r^6+s

3)Let a =3-5x, b=2x-4, c=1-4x and y = min(a,b,c) for different values of x. Find the maximum value of x

4)If 2x + 3y + 4z =100 and x,y,z are natural numbers..
a) Find the maximum value of x^2 + y^2 + z^2
b) Find the maximum value of 2x^2 + 5y^2 + 8z^2

This is one of the my weakest area in quants. I would love to see various approaches for all these problems...

Happy solving!!

[naga25french]

Originally Posted by exile

Yelloz!!



4)If 2x + 3y + 4z =100 and x,y,z are natural numbers..

a) Find the maximum value of x^2 + y^2 + z^2


Happy solving!!

is the answer 2030 ?

[naga25french]

Originally Posted by exile

Yelloz!!


4)If 2x + 3y + 4z =100 and x,y,z are natural numbers..

b) Find the maximum value of 2x^2 + 5y^2 + 8z^2



Happy solving!!

is the answer 4078 ?

[naga25french]

Originally Posted by exile

4)If 2x + 3y + 4z =100 and x,y,z are natural numbers..
a) Find the maximum value of x^2 + y^2 + z^2
b) Find the maximum value of 2x^2 + 5y^2 + 8z^2
Happy solving!!

ma solutions:

a)co eff of x < coeff of y < coeff of z

so x should take maximum possible value to get maximised x^2 +y^2 + z^2

x = 45

y = 2

z = 1


so now 45^2 + 2^2 + 1^2 = 2030

so answer is 2030...

b)

2x^2 +5y^2 + 8z^2...

now coefficient of x^2 < coeeff of y^2 < coeff of z^2

so again we can use same values

x= 45 , y = 2 , z = 1


so maximised value (2 * 2025) + (5 * 4) + (1*8 ) = 4078


so the answer is 4078..

[maverick_srikan]

1) if | 2x +1 | <=3 and |3y -2|<=5, find the maximum value of |x| + (|x| + |y|)

-2=<x<=1

and y=> -1 and y<=7/3 (2.33 approx)

max value will be |-2|+(|-2|+|2.33|)

2+4.33 => 6.33

2) if p^3*q^4*r^6*s=216, find the minimum value of 2p^3+3q^4+r^6+s

AM>=GM

2p^3+3q^4+r^6+s/4>= (2p^3*3q^4*r^6*s)^1/4

2p^3+3q^4+r^6+s/4>= (6*(p^3*3q^4*r^6*s))^1/4

==>(6*216)^1/4 =>6*4=24

3)Let a =3-5x, b=2x-4, c=1-4x and y = min(a,b,c) for different values of x. Find the maximum value of x

Minumum value would be where a=b=c

4)If 2x + 3y + 4z =100 and x,y,z are natural numbers..
a) Find the maximum value of x^2 + y^2 + z^2
b) Find the maximum value of 2x^2 + 5y^2 + 8z^2

a and b) would go with naga's answer!, though i think the method can be more foolproof. Satan bhai?

[naga25french]

Originally Posted by exile

Yelloz!!


1) if | 2x +1 | <=3 and |3y -2|<=5, find the maximum value of |x| + (|x| + |y|)


Happy solving!!

ma take :

maximum value of x is -2 .. so l x is 2

maximum value of y is 7/3.. so l y l is 7/3

now the value of |x| + (|x| + |y|) = 2 + (2 + 7/3) = 19/3

not sure of the answer ...

correct me if i am wrong...

[nishant_rungta]

Hi guys,

Sorry to say but we do not have a CL expert session tomorrow

The schedule seems really tight for them.

Will keep u all informed about this in a day's time or so...

All the best for the mocks tomo.


Nishant

[naga25french]

ma scores in this week mocks:

pathetic simcat score :

verbal ---------- 9.5

quants --------- 12.75

di -------------- 8.5


overall ---------- 30.75

it was very a much decent paper.. di back fired me to the core... wasted a lot of time in that cricket tournament di.. unfortunately after lot of reasoning answers are all given , cannot be determined........
hmmm its all in the game.........



ma scores in cl mock cat 6 :

verbal ------------ 27.5

di ---------------- 36.5

quants ----------- 42.5

overall ------------106.5

pathetic accuracy in di ....

cl mock cat 6 is a very different paper.... quants question were all real gems... superb question paper..

all the best for puys who r gonna take it on saturday........

[guhan135]

Originally Posted by krsh.vik

Look at this
Single-elimination tournament - Wikipedia, the free encyclopedia

This should clear all doubts if at all there are any

The logical way to solve these kinda questions-

1. Each match = 1 player eliminated.
2. This means, for "N" players, "N-1" need to be eliminated => N-1 matches...
3. The question is solved in the previous step itself


Guys, our End terms start tomo. Will contribute more to this thread from Friday!

Till then continue the good discussions and keep preparing.

I see most determined ppl lose their cool/ get fed up at this point in time. (2-3 months b4 CAT) and stop preparing.

Just a fact- Everyone will feel this way @ some point or other. Jus relax for a couple of days, dont give up.

"Most people give up when victory was juat an inch away from them"