Cheeky approach to few tricky problems-1

[Shalabh's Quants]

Sometime we are caught up with easy but lengthy problems. In the series of Cheeky approach to few lengthy problems, I am recommnding few common sense approaches.

Enjoy!

Q. What is the value of x^3+y^3+z^3 ? if x+y+z = 6 and xy+yz+zx = 11.

A.24
B.36
C.54
D.121
E.25
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Just analyse x+y+z = 6 and xy+yz+zx = 11. Try to fit in few small +ive integers for x, y & z .

Say... x=y=z=2. But this does not satisfy xy+yz+zx = 11. Hence rejected.

Just by hit & trial, lets see x=1, y=2 & x=3 satisfies xy+yz+zx = 11. Hence solution is B.

[AbhiJ]

Can you solve it algebraically ?

[Shalabh's Quants]

Can you solve it algebraically ?

Not possible due to lack of data.

Since (x+y+z)^3 = x^3+y^3+z^3 +3(x+y+z)(xy+yz+zx) - 3xyx;

We are not given the value of xyz.

[AbhiJ]

Then the question has more than one solution, unless you add another constraint like x,y,z are positive integers.