Target question: What is the volume of the right circular cylinder X ?
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Aside: A right circular cylinder is a cylinder whose bases are aligned directly above the other.
So, the cylinder on the left (below) is a right cylinder, and the one on the right is an oblique cylinder

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Key property: Area of cylinder \(= \pi r^2 h\)

Statement 1: The height of X is 20
Since we still don't know the radius of the cylinder, statement 1 is NOT SUFFICIENT

Statement 2: The base of X has area 25π.
Area of a circle \(= \pi r^2\)
So statement 2 is telling us that: \( \pi r^2 = 25 \pi\)
Since we still don't know the height of the cylinder, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that \(h = 20\)
Statement 2 tells us that \( \pi r^2 = 25 \pi\)
So the volume of the cylinder \(= \pi r^2 h = (25 \pi)(20) = 500 \pi\)
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent
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Volume of cylinder pi*r^2*h
#1 height -20
Radius not know Insufficient
#2
Area of base 25 pi
Pi*r^2=25pi
r=5
Height not know Insufficient
From 1&2
Area of cylinder
Pi*25*20
500pi
Option C



Posted from my mobile device

Solution:

A new og 2021 question

Volume of X (V)= ∏r^2 h where r is the radius of X and h is the height of X.

St(1):- The height of X is 20.

The statement does not provide us with any data on the value of "r" that is essential to calculate V. (Insufficient)

St(2):- The base of X has area 25π.

The statement does not provide us with any data on the value of "h" that is essential to calculate V. (Insufficient)

Combining both we have

h = 20 (from st(1) )

∏r^2 = 25 ∏

=> r = 5 units.

V = ∏r^2h and can be computed. (Sufficient) option(C)

Hope this helps
Devmitra Sen (GMAT Quant Expert)

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Answer: Option C

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