What is The Volume of the Right Circular Cylinder X ? GMAT Data Sufficiency

Question: What is the volume of the right circular cylinder X ?

(1) The height of X is 20.
(2) The base of X has area 25\(\pi\).

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“What is the volume of the right circular cylinder X?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide 2021". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:
The below image shows a right circular cylinder. A right circular cylinder is the one whose bases aligned directly above the other.

As per the formula, the volume of a cylinder is πr²h.
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 25\(\pi\).
Area of a circle= \(\pi\)r²
So statement 2 is telling us that: \(\pi\)r² = 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 height (h) = 20
Statement 2 tells us that \(\pi\)r² = 25\(\pi\)
So the volume of the cylinder \(\pi\)r²h
=>(25\(\pi\))(20)
=>500\(\pi\)

Correct Answer: C

Approach Solution 2:
Volume of X (V)= \(\pi\)r^2 h where r is the radius of X and h is the height of X.
Statement (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 Volume. (Insufficient)
Statement (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 Volume. (Insufficient)
Combining both we have
h = 20 (from st(1) )
\(\pi\)r^2 = 25 \(\pi\)
=> r = 5 units.
Volume = \(\pi\)r^2h and can be computed.

Correct Answer: C

Approach Solution 3:

Volume of cylinder \(\pi\)*r^2*h

#1 height -20

Radius not know Insufficient

#2Area of base 25 \(\pi\)

\(\pi\)*r^2= 25\(\pi\)

r=5

Height not know Insufficient

From 1&2

Area of cylinder

\(\pi\)*25*20

500\(\pi\)

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Correct Answer: C

Some suggested GMAT Data Sufficiency Questions

• In the Figure Above, What is the Area of Semicircle DPA? GMAT Data Sufficiency 
• Is |x-10| > |x-30|GMAT Data Sufficiency 
• What is The Value of (a!+b!)(c!+d!)? GMAT Data Sufficiency 
• If xy = - 6, What is the Value of xy(x + y)? GMAT Data Sufficiency 
• A Drawer Contains 8 Socks, and 2 Socks are Selected at Random Without Replacement GMAT Data Sufficiency 
• The Average Price of Three Stocks is $25 per Shar GMAT Data Sufficiency 
• Given k is a Nonzero Integer, is k>0? GMAT Data Sufficiency 
• If J≠0, What Is The Value Of J? GMAT Data Sufficiency
• Paint X Costs $15 per Gallon, and Paint Y Costs $20 per Gallon GMAT Data Sufficiency
• What is the total value of Company H's stock? GMAT Data Sufficiency
• Is PQ > 1? GMAT Data Sufficiency
• How Many of the Students in a Certain Class are Taking Both a History and a Science Course? GMAT Data Sufficiency
• The Set S of Numbers has the following Properties GMAT Data Sufficiency
• A Contractor Combined x Tons of a Gravel Mixture that Contained 10 percent Gravel G GMAT Data Sufficiency
• If Jeff has four movies, and must choose to watch either 1, 2, or 3 different movies GMAT Data Sufficiency
• From a Group of M Employees, N Will be Selected, at Random, GMAT Data Sufficiency
• Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)? GMAT Data Sufficiency 
• Juan Bought Some Paperback Books That Cost $8 GMAT Data Sufficiency GMAT Data Sufficiency 
• The symbol ∆ Denotes One of The Four Arithmetic Operations GMAT DATA Sufficiency GMAT Data Sufficiency 
• X is Older Than Y, Z Is Younger Than W And V is Older Than Y. Is Z Younger Than X? GMAT Data Sufficiency