If right circular cylinders A and B have the same radius : height ratio, what is the ratio of the curved surface area of cylinder A to the curved surface area of cylinder B?(1) The ratio of the radius of cylinder A to the radius of cylinder B is 2:1(2) The ratio of the volume of cylinder A to the volume of cylinder B is 8:1a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer?

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If right circular cylinders A and B have the same radius : height ratio, what is the ratio of the curved surface area of cylinder A to the curved surface area of cylinder B?

(1) The ratio of the radius of cylinder A to the radius of cylinder B is 2:1

(2) The ratio of the volume of cylinder A to the volume of cylinder B is 8:1

a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
c)
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
d)
EACH statement ALONE is sufficient.
e)
Statements (1) and (2) TOGETHER are NOT sufficient.

Correct answer is option 'D'. Can you explain this answer?

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If right circular cylinders A and B have the same radius : height rati...

Steps 1 & 2: Understand Question and Draw Inferences

Let the radius and height of Cylinder A be R_Aand H_A respectively, and

The radius and height of Cylinder B be R_B and H_Brespectively.

Given:

R_A: H_A = R_B: H_B

This equation can also be written as:

R_A: R_B= H_A : H_B . . . (1)

We know that the curved surface area of a right circular cylinder, CSA = 2πRH, where R and H are the radius and height of the cylinder respectively.

So, CSA_A : CSA_B = 2πR_AH_A: 2πR_BH_B

CSA_A : CSA_B = R_AH_A: R_BH_B . . . (2)

Substituting (1) in (2), we get:

CSA_A : CSA_B = R_A²: R_B² = H_A²: H_B² . . . (3)

From Equation (3) it is clear that we will be able to determine the ratio of CSA_A : CSA_Bif we know the ratio R_A: R_B or the ratio H_A: H_B

Step 3: Analyze Statement 1

(1) The ratio of the radius of cylinder A to the radius of cylinder B is 2:1

Since the ratio R_A: R_B is given, we will be able to determine the ratio CSA_A : CSA_B

Statement 1 is sufficient.

Step 4: Analyze Statement 2

(2) The ratio of the volume of cylinder A to the volume of cylinder B is 8:1

We know that volume of a right circular cylinder, V = πR² H, where R and H are the radius and height of the cylinder respectively.

So,

V_A : V_B = πR_A²H_A: πR_B²H_B

V_A : V_B = R_A²H_A: R_B²H_B . . . (4)

Substituting (1) in (4), we get:

V_A : V_B = R_A³: R_B³ . . . (5)

We are given that V_A : V_B = 8:1

So, from Equation (5), we get:

R_A³: R_B³ = 8:1

This means that,

R_A: R_B = 2:1

Since we have been able to determine the ratio R_A: R_B is given, we will be able to determine the ratio CSA_A : CSA_B

Statement 2 is sufficient.

Step 5: Analyze Both Statements Together (if needed)

You get a unique answers in steps 3 and 4, so this step is not required

Answer: Option (D)

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If right circular cylinders A and B have the same radius : height ratio, what is the ratio of the curved surface area of cylinder A to the curved surface area of cylinder B?(1) The ratio of the radius of cylinder A to the radius of cylinder B is 2:1(2) The ratio of the volume of cylinder A to the volume of cylinder B is 8:1a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer?

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If right circular cylinders A and B have the same radius : height ratio, what is the ratio of the curved surface area of cylinder A to the curved surface area of cylinder B?(1) The ratio of the radius of cylinder A to the radius of cylinder B is 2:1(2) The ratio of the volume of cylinder A to the volume of cylinder B is 8:1a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about If right circular cylinders A and B have the same radius : height ratio, what is the ratio of the curved surface area of cylinder A to the curved surface area of cylinder B?(1) The ratio of the radius of cylinder A to the radius of cylinder B is 2:1(2) The ratio of the volume of cylinder A to the volume of cylinder B is 8:1a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If right circular cylinders A and B have the same radius : height ratio, what is the ratio of the curved surface area of cylinder A to the curved surface area of cylinder B?(1) The ratio of the radius of cylinder A to the radius of cylinder B is 2:1(2) The ratio of the volume of cylinder A to the volume of cylinder B is 8:1a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'D'. Can you explain this answer?.

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