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

 It is currently 13 Nov 2018, 17:16

### 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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### Essential GMAT Time-Management Hacks

November 14, 2018

November 14, 2018

07:00 PM PST

08:00 PM PST

Join the webinar and learn time-management tactics that will guarantee you answer all questions, in all sections, on time. Save your spot today! Nov. 14th at 7 PM PST

# A solid cube is placed in a cylindrical container. Which of the follow

Author Message
TAGS:

### Hide Tags

Intern
Joined: 29 Aug 2010
Posts: 14
A solid cube is placed in a cylindrical container. Which of the follow  [#permalink]

### Show Tags

29 Oct 2017, 21:47
3
00:00

Difficulty:

85% (hard)

Question Stats:

48% (02:59) correct 52% (03:26) wrong based on 49 sessions

### HideShow timer Statistics

A solid cube is placed in a cylindrical container. Which of the following percent values COULD possibly represent the ratio of the volume of the cylinder not occupied by the cube to the volume of the cylinder? (Assume the value of $$\pi$$ to be 3)

(A) 16%
(B) 25%
(C) 28%
(D) 32%
(E) 36%
Manager
Joined: 05 Dec 2016
Posts: 244
Concentration: Strategy, Finance
GMAT 1: 620 Q46 V29
Re: A solid cube is placed in a cylindrical container. Which of the follow  [#permalink]

### Show Tags

29 Oct 2017, 23:37
Let's consider extreme situation:
Assume that cube is inscribed into the cylinder, then the ratio of its sides to radius of cylinder would be 2^1/2 to 1.
Volume of cube=(2^1/2)^3=2^3/2=2*2^1/2
Volume of cylinder=3*1^2*2^1/2=3*2^1/2
Volume of space in cylinder not occupied by cube=3*2^1/2-2*2^1/2=2^1/2
Ratio of volume not occupied by cube to volume of cylinder= 2^1/2 : 3*2^1/2=1/3

(a) 16%
Means that remaining 84% is occupied by cube, which cannot be true because maximum possible occupied space for cube would be 66,66%
(b) 25%
Means that remaining 75% is occupied by cube, which cannot be true because maximum possible occupied space for cube would be 66,66%
(c) 28%
Means that remaining 72% is occupied by cube, which cannot be true because maximum possible occupied space for cube would be 66,66%
(d) 32%
Means that remaining 68% is occupied by cube, which cannot be true because maximum possible occupied space for cube would be 66,66%
(e) 36%
Means that remaining 64% is occupied by cube, which CAN be true because maximum possible occupied space for cube would be 66,66%
Hence we can infer that cube is not inscribed in the cylinder.

Intern
Joined: 29 Aug 2010
Posts: 14
Re: A solid cube is placed in a cylindrical container. Which of the follow  [#permalink]

### Show Tags

30 Oct 2017, 22:25
1
1
Let us consider the situation where the largest possible cube (shaded in grey) fits perfectly in a particular cylinder as shown in the diagram below; however, the question does not state that we must fit in a largest possible cube into the cylinder.

Let the edge of the cube be $$a$$.
Since the cube has to have a perfect fit (minimum non-utilization of cylinder space),
we must have:
Height of the cylinder = edge of the cube = $$a$$

In right angled triangle CAB:
$$CB^2$$ $$=$$ $$CA^2$$+$$AB^2$$ $$=$$ $$a^2$$ + $$a^2$$ $$=$$ $$2a^2$$
$$=> CB =a\sqrt{2}$$
Thus, the diameter of the cylinder $$= a\sqrt{2}$$

=> Radius of the cylinder $$=$$$$\frac{a}{\sqrt{2}}$$

Thus, volume of the cylinder
$$=$$ $$\pi$$ X $$radius^2$$ X $$height$$
$$=$$ $$\pi$$ X $$(\frac{a}{\sqrt{2}})^2$$ X $$a$$
$$= \frac{3}{2}a^3$$

Volume of the Cube $$= a^3$$
Thus, volume of the cylinder not occupied by the cube
$$=$$ $$\frac{3}{2}$$$$a^3$$$$-$$$$a^3$$
$$= \frac{a^3}{2}$$

Thus, the required percent

$$= (\frac{a^3}{2})/(\frac{3}{2}a^3) X 100$$
$$=$$ 33.3 %

The above situation depicts the case where minimum volume of the cylinder as a percent of the
total volume of the cylinder is unutilized, i.e. not covered by the cube.
Thus, in any other scenario, the required percent value would be either greater than or equal to
33.3%

The only possible value from the answer options is 36%

The correct answer is option E.
Attachments

Cylinder.PNG [ 9.5 KiB | Viewed 620 times ]

Re: A solid cube is placed in a cylindrical container. Which of the follow &nbs [#permalink] 30 Oct 2017, 22:25
Display posts from previous: Sort by