Maximum value of an expression

[winnerhere]

Given x + y + z = 12

find the maximum value of (x^2)(y^3)(z)

a)6291

b)6912

c)2691

d)9612

[madhukumar_v]

IMO 6912.

X can be -ve, since it has a square.

so lets say X and Y are equal, and Y=12;

So, Y^3= 1728

Look at answers which one is divisible by 1728, its 6912. hence B.

[barcebal]

this question is missing something...

Because you could have x=-100,000 y=100,000 and z=12 which is way bigger than any choice there.

Need more info (are they all positive; are they all distinct; are they all integers?)

[winnerhere]

hi people,

x,y,z > 0

[indiantiger]

Where is the choice E?

[nithi_mystics]

Is the answer B?

[winnerhere]

Is the answer B?

yes..could you please explain how u got this answer?

[nithi_mystics]

It was trial and error method.

Since we want the max value, I did not chose 1 for x,y or z. Similarly no 0.
So we are left with the numbers, 2,3,4,5,6,7,8

If we take 3 numbers that add up to 12 (say 4,6,2), we would assign the highest value to y(since the term has y^3), the second highest value to x (since it has a square) and the least value to z.

So I tried the following,

x y z x+y+z (x^2)(y^3)(z)
2 8 2 12 4096
4 6 2 12 6912
3 7 2 12 6174
5 5 2 12 6250

Hope this helps! But I am sure that should be some other easy way of doing it.

Is the answer B?

yes..could you please explain how u got this answer?