Volume of C1 = pi * r^ 2 * h
Volume of C2 = a^3

Is pi * r ^ 2 * h > a ^ 3 ?

(1)
r = a

Is pi * a ^ 2 * h > a ^ 3

Is pi * h > a

Not enough ifo to answer the question

(2)
Going by the same logic above, question reduces to asking:
Is 2 * pi * r ^ 2 > a ^ 2

Again, not enough to answer the question

Combining 1 and 2

Is pi * a ^ 2 * 2 a > a ^ 3

Is 2 * pi * a ^ 3 > a ^ 3

This is certainly true, hence sufficient, so both statements combined are sufficient

(C)

People easily say 50-50 from 5 options,but i guess it is easier said than done
Even in this question ,
from the moment we read the question we feel it should be C or E
50-50 yet GMAT dont give us 80% marks for choosing second best option ...lol

any way
volume of cylinder=pi x r^2 x h
volum of cube=edge^3

so first doesnt give h so we cannot conclude things

2 doesnt give any thing about r

so not sufficient

with c we have every thing.
and we can compare
so C

Hi there!

No calculations are needed here! Have a look:

(1) From this sttm we are sure we are able to draw the base of the cube (a square) INSIDE the base of the cilinder (a circle) but we know nothing on the height of the cilinder, so that it can be positive but near zero (volume of cilinder is therefore arbitrarily near zero) or it can be really huge (to guarantee its volume is greater than the volume of the cube).

Important: think about R compared to L*sqrt(2)/2 where R is the radius of the circular base of the cilinder and L is the edge of the cube.

(2) We know nothing on the base of the cilinder, it can be with radius positive but near zero (volume of cilinder is arbitrarily near zero) or it can be huge (to guarantee its volume is greater than the volume of the cube).

(1+2) We are sure the cilinder "eats" the cube, therefore the volume of the cilinder is greater, for sure.

Regards,
Fabio.