GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 12 Dec 2019, 02:11

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Between a cube and a right circular cylinder, does the cube have a

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59685
Between a cube and a right circular cylinder, does the cube have a  [#permalink]

Show Tags

23 Jul 2017, 23:26
00:00

Difficulty:

45% (medium)

Question Stats:

66% (02:11) correct 34% (02:40) wrong based on 68 sessions

HideShow timer Statistics

Between a cube and a right circular cylinder, does the cube have a higher lateral surface area? Lateral surface area refers to the area of the sides (the two base areas, one on top and one on bottom, are not taken into account). Assume π = (3/2)^3

(1) The height of the cylinder is twice its radius.
(2) Both the cube and the cylinder have the same volume.

_________________
Retired Moderator
Status: Long way to go!
Joined: 10 Oct 2016
Posts: 1323
Location: Viet Nam
Re: Between a cube and a right circular cylinder, does the cube have a  [#permalink]

Show Tags

24 Jul 2017, 02:11
1
Bunuel wrote:
Between a cube and a right circular cylinder, does the cube have a higher lateral surface area? Lateral surface area refers to the area of the sides (the two base areas, one on top and one on bottom, are not taken into account). Assume π = (3/2)^3

(1) The height of the cylinder is twice its radius.
(2) Both the cube and the cylinder have the same volume.

Call the side of the cube is $$a$$, the volume of the cube is $$a^3$$ and the lateral surface area of the cube is $$4a^2$$

Call the height and the radius of the cylinder are $$h$$ and $$b$$. The volume of the cylinder is $$\pi hb^2$$ and the lateral surface area of the cylinder is $$2\pi bh$$

(1) Since we could know $$h=2b$$, however we can't know the value of $$a$$. Insufficient.

(2) We have $$a^3 = \pi hb^2$$. We have to compare $$4a^2$$ and $$2\pi bh$$

Since $$a^3 = \pi hb^2 \implies 2 \pi bh = \frac{2a^3}{b}$$ . We now have to compare $$\frac{2a^3}{b}$$ and $$4a^2$$ or we have to compare $$\frac{a}{b}$$ and 2. However, we have no information about $$\frac{a}{b}$$, insufficient.

Combine (1) and (2):

From (1) have $$h=2b$$.

From (2) have $$a^3 = \pi hb^2 = 2\pi b^3 \implies \frac{a}{b} = \sqrt[3]{2\pi}$$

Now, from given condition we have $$\pi = (\frac{3}{2})^3 \\ \implies 2\pi = 2 * \frac{27}{8} = \frac{27}{4} < 8 \\ \implies \sqrt[3]{2\pi} < 2$$

From this, we could compare $$\frac{a}{b}$$ and 2 or we could compare $$\frac{2a^3}{b}$$ and $$4a^2$$. Sufficient.

_________________
Intern
Status: Prepping for GMAT
Joined: 06 Nov 2017
Posts: 23
Location: France
GPA: 4
Re: Between a cube and a right circular cylinder, does the cube have a  [#permalink]

Show Tags

30 Oct 2018, 03:55
Bunuel wrote:
Between a cube and a right circular cylinder, does the cube have a higher lateral surface area? Lateral surface area refers to the area of the sides (the two base areas, one on top and one on bottom, are not taken into account). Assume π = (3/2)^3

(1) The height of the cylinder is twice its radius.
(2) Both the cube and the cylinder have the same volume.

Let's formalize the surface area for both the cube and the cylinder:

- A cube has 4 side faces with each face having an area of $$a^2$$ (assuming that a cube's side's length is "a"). Thus: $$CubeLatArea = 4*a^2$$
- For the cylinder, its lateral area is that of a rectangle with a length equal to the height of the cylinder and a width equal to the circumference of its base. Thus: $$CylinderLatArea = 2*π*r*h$$

Therefore, the question asks us if $$4*a^2 - 2*π*r*h > 0$$ (Eq)

(1) The height of the cylinder is twice its radius.

This statement does not provide any data regarding the cube itself. Therefore, by itself, it's insufficient (cross off A and D).

(2) Both the cube and the cylinder have the same volume.

Translated, this statement means that: $$a^3 = π*r^2*h$$. This does not help us in answering the question stated by the problem. Therefore, by itself, this statement is insufficient (cross off B).

(1)+(2) The height of the cylinder is twice its radius and both the cube and the cylinder have the same volume

In this case, we have:
- $$h = 2*r$$
- $$a^3 = π*r^2*h$$

Thus: $$a^3 = 2*π*r^3$$ meaning that $$a = (2*π)^(\frac{1}{3})*r$$

Injecting the above in (Eq) and keeping in mind that $$h = 2*r$$ yields:

$$4*(2*π)^(\frac{2}{3})*r^2 - 4*π*r^2$$

After simplifying it, we get: $$4*r^2*π*(\frac{2}{π^(1/3)}-1)$$ which is negative. Thus, both statements together are sufficient.

Director
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: Between a cube and a right circular cylinder, does the cube have a  [#permalink]

Show Tags

05 Feb 2019, 04:37
Bunuel wrote:
Between a cube and a right circular cylinder, does the cube have a higher lateral surface area? Lateral surface area refers to the area of the sides (the two base areas, one on top and one on bottom, are not taken into account). Assume π = (3/2)^3

(1) The height of the cylinder is twice its radius.
(2) Both the cube and the cylinder have the same volume.

As per the question

lateral surface area of cube = 4a^2

from 1 h = 2 r
Cannot do anything from this

from 2 Both the cube and the cylinder have the same volume.
Cube and the cylinder have same volume

a^3 = 4/3 π r^2 * h

Again we dont have anything from this, 3 unknown variables

Combine both the statements

We can get a relationship between a and r

From which we can calculate the lateral surface area of both the figures Since this is a DS question one need not solve everything

C
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Re: Between a cube and a right circular cylinder, does the cube have a   [#permalink] 05 Feb 2019, 04:37
Display posts from previous: Sort by