The surface area of cylinder A is how many times the surface : GMAT Data Sufficiency (DS)
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# The surface area of cylinder A is how many times the surface

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The surface area of cylinder A is how many times the surface [#permalink]

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02 Nov 2012, 17:09
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The surface area of cylinder A is how many times the surface area of cylinder B?

(1) The diameter of A is twice the diameter of B.
(2) The height of A is equal to the height of B.

[Reveal] Spoiler:
This is a "what is the value of..." DS question. In this type of question, a statement will be sufficient only if it leads to a single value of the variable (or expression) you're asked about.

Remember, surface area of a cylinder = 2 π r² + 2 π r h where r is the radius of the cylinder, h is its height and π is a constant. The ratio between the surface areas of the two cylinders can be determined either by calculating the two surface areas or by identifying relationships between r and h of the two.

Stat. (1) + (2) Combined, you get the relationship between the radii as well as heights of the two cylinders. Let 2r be the radius of cylinder A and r be the radius of cylinder B as per Stat. (1), and let h be the height of both cylinders as the height of cylinder A is equal to that of cylinder B. By plugging in these in the formula of the surface area of a cylinder, you find that the surface area of cylinder A = 8 π r² + 4 π r h and that of cylinder B = 2 π r² + 2π r h. It is not possible to determine the ratio between the surface areas of cylinder A and B without knowing the specific values of r and h.

Stat.(1) + (2)->IS->E.

So I understand the math and was able to get to the point of cylinder A = 8 π r² + 4 π r h and that of cylinder B = 2 π r² + 2π r h.

But the provided solution only says that "It is not possible to determine the ratio between the surface areas of cylinder A and B without knowing the specific values of r and h."

I don't understand why. I chose C because we're given the relationship between the two diameters, in addition to H.

Could someone help me to understand?
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 May 2015, 03:49, edited 1 time in total.
Edited the question.
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Re: The surface area of cylinder A is how many times the surface [#permalink]

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02 Nov 2012, 21:23
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anon1 wrote:
The surface area of cylinder A is how many times the surface area of cylinder B?
(1) The diameter of A is twice the diameter of B.

(2) The height of A is equal to the height of B.

[Reveal] Spoiler:
This is a "what is the value of..." DS question. In this type of question, a statement will be sufficient only if it leads to a single value of the variable (or expression) you're asked about.

Remember, surface area of a cylinder = 2 π r² + 2 π r h where r is the radius of the cylinder, h is its height and π is a constant. The ratio between the surface areas of the two cylinders can be determined either by calculating the two surface areas or by identifying relationships between r and h of the two.

Stat. (1) + (2) Combined, you get the relationship between the radii as well as heights of the two cylinders. Let 2r be the radius of cylinder A and r be the radius of cylinder B as per Stat. (1), and let h be the height of both cylinders as the height of cylinder A is equal to that of cylinder B. By plugging in these in the formula of the surface area of a cylinder, you find that the surface area of cylinder A = 8 π r² + 4 π r h and that of cylinder B = 2 π r² + 2π r h. It is not possible to determine the ratio between the surface areas of cylinder A and B without knowing the specific values of r and h.

Stat.(1) + (2)->IS->E.

So I understand the math and was able to get to the point of cylinder A = 8 π r² + 4 π r h and that of cylinder B = 2 π r² + 2π r h.

But the provided solution only says that "It is not possible to determine the ratio between the surface areas of cylinder A and B without knowing the specific values of r and h."

I don't understand why. I chose C because we're given the relationship between the two diameters, in addition to H.

Could someone help me to understand?

$$Surface area of A = 2*pi*2r*(2r+h)$$

$$Surface area of B = 2*pi*r*(r+h)$$

$$\frac{Area_A}{Area_B} = \frac{2*pi*2r*(2r+h)}{2*pi*r*(r+h)}$$

$$= \frac{2*(2r+h)}{(r+h)}$$

So to know the ratio, we need atleast r in terms of h. What makes a hemisphere,cylinder, cone, and cuboid different from a sphere and square is the presence of a "+" in the calculation of the total surface area.

While the given data would have been sufficient had the cylinders been open at the top and bottom, it is not sufficient in the case of normal cylinders.

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Re: The surface area of cylinder A is how many times the surface [#permalink]

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30 May 2015, 03:22
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The surface area of cylinder A is how many times the surface area of [#permalink]

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02 Jun 2015, 10:27
The surface area of cylinder A is how many times the surface area of cylinder B?

(1) The diameter of A is twice the diameter of B.
(2) The height of A is equal to the height of B.

[Reveal] Spoiler:
Remember, surface area of a cylinder = 2 π r² + 2 π r h where r is the radius of the cylinder, h is its height and π is a constant. The ratio between the surface areas of the two cylinders can be determined either by calculating the two surface areas or by identifying relationships between r and h of the two.

Stat. (1) + (2) Combined, you get the relationship between the radii as well as heights of the two cylinders. Let 2r be the radius of cylinder A and r be the radius of cylinder B as per Stat. (1), and let h be the height of both cylinders as the height of cylinder A is equal to that of cylinder B. By plugging in these in the formula of the surface area of a cylinder, you find that the surface area of cylinder A = 8 π r² + 4 π r h and that of cylinder B = 2 π r² + 2π r h. It is not possible to determine the ratio between the surface areas of cylinder A and B without knowing the specific values of r and h.

Stat.(1) + (2)->IS->E.

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Re: The surface area of cylinder A is how many times the surface [#permalink]

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09 Jul 2016, 12:33
Hello from the GMAT Club BumpBot!

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Re: The surface area of cylinder A is how many times the surface [#permalink]

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13 Jul 2016, 20:13
Wording of Question is ambiguous... It is not clear if it is asking total surface area or just lateral/ curved surface area...could someone clarify ???

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Re: The surface area of cylinder A is how many times the surface [#permalink]

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13 Jul 2016, 23:58
smashbiker84 wrote:
Wording of Question is ambiguous... It is not clear if it is asking total surface area or just lateral/ curved surface area...could someone clarify ???

Posted from my mobile device

It's total area. If it were otherwise it would have been explicitly mentioned.
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Re: The surface area of cylinder A is how many times the surface [#permalink]

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14 Jul 2016, 13:57
Hi Bunuel,

I can´t understand why is E, with the proportion of diameter and the same height is just not Cylinder A two times Cylinder B?

Or I should analyse something else?

Regards
Omar M
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Re: The surface area of cylinder A is how many times the surface [#permalink]

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14 Jul 2016, 16:07
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If you find this question on the real GMAT, you should first be very wary because each statement alone is quite obviously insufficient. Even if you didn't know the surface area formula, it should be clear looking at each statement that you need both pieces of info. This is a very clear C trap question and I think the best bet would be to just try plugging in easy numbers to see both statements fall short.

Make the height equal to 1
Try radius 2 for bigger cylinder, radius 1 for smaller, then try radius 4 for bigger, 2 for smaller. Quick calculations and it becomes clear answer is E

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Re: The surface area of cylinder A is how many times the surface [#permalink]

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18 Jul 2016, 12:57
LXVE wrote:
If you find this question on the real GMAT, you should first be very wary because each statement alone is quite obviously insufficient. Even if you didn't know the surface area formula, it should be clear looking at each statement that you need both pieces of info. This is a very clear C trap question and I think the best bet would be to just try plugging in easy numbers to see both statements fall short.

Make the height equal to 1
Try radius 2 for bigger cylinder, radius 1 for smaller, then try radius 4 for bigger, 2 for smaller. Quick calculations and it becomes clear answer is E

Sent from my SM-G928T using GMAT Club Forum mobile app

Thanks LXVE , Now it´s clear.
Re: The surface area of cylinder A is how many times the surface   [#permalink] 18 Jul 2016, 12:57
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