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

 It is currently 15 Aug 2018, 02:07

### 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
Your Progress

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

# If cylinder P has a height twice that of cylinder Q and a radius half

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47918
If cylinder P has a height twice that of cylinder Q and a radius half  [#permalink]

### Show Tags

04 Feb 2018, 21:46
00:00

Difficulty:

25% (medium)

Question Stats:

69% (00:45) correct 31% (00:41) wrong based on 35 sessions

### HideShow timer Statistics

If cylinder P has a height twice that of cylinder Q and a radius half that of cylinder Q, what is the ratio between the volume of cylinder P and the volume of cylinder Q ?

(A) 1:8

(B) 1:4

(C) 1:2

(D) 1

(E) 2:1

_________________
examPAL Representative
Joined: 07 Dec 2017
Posts: 546
Re: If cylinder P has a height twice that of cylinder Q and a radius half  [#permalink]

### Show Tags

05 Feb 2018, 00:29
Bunuel wrote:
If cylinder P has a height twice that of cylinder Q and a radius half that of cylinder Q, what is the ratio between the volume of cylinder P and the volume of cylinder Q ?

(A) 1:8

(B) 1:4

(C) 1:2

(D) 1

(E) 2:1

There are two ways to approach this, we'll show both.

As the calculation looks straightforward, we'll just do it.
This is a Precise approach.

Writing H,R for P and h,r for Q we have H = 2h and 2R = r
Since volume is h*pi*r^2 then the volume of P is (2h)(pi)(r^2)/4 and that of Q is (h)(pi)(r^2)
Dividing the two gives 1:2, answer (C).

As the question asks for relations between sides and areas/volumes, we'll look for a Logical approach.

In a cylinder, the area is proportional to the height and proportional to twice the radius.
So, increasing the height by a factor of 2 would increase the volume by a factor of 2.
Decreasing the radius by a factor of 2 decreases the volume by a factor of 4.
Then the volume of P was muliplied by 2 and then divided by 4 relative to Q meaning that P:Q is 1:2
(C) is our answer.
_________________

David
Senior tutor at examPAL
Signup for a free GMAT course

We won some awards:

Save up to \$250 on examPAL packages (special for GMAT Club members)

SC Moderator
Joined: 22 May 2016
Posts: 1902
If cylinder P has a height twice that of cylinder Q and a radius half  [#permalink]

### Show Tags

05 Feb 2018, 10:04
Bunuel wrote:
If cylinder P has a height twice that of cylinder Q and a radius half that of cylinder Q, what is the ratio between the volume of cylinder P and the volume of cylinder Q ?

(A) 1:8

(B) 1:4

(C) 1:2

(D) 1

(E) 2:1

Another approach: assign values.

Height of P = 4. Q's height is half that of P
Height of Q = 2

Radius of Q = 4. P's radius is half that of Q
Radius of P = 2

Volume of P:
$$\pi r^2h =\pi(2^2)(4)= 16\pi$$

Volume of Q:
$$\pi r^2h = \pi(4^2)(2)= 32\pi$$

Ratio between volume of P and volume of Q?
$$\frac{16\pi}{32\pi}=\frac{1}{2}= 1:2$$

Answer C
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

If cylinder P has a height twice that of cylinder Q and a radius half &nbs [#permalink] 05 Feb 2018, 10:04
Display posts from previous: Sort by

# If cylinder P has a height twice that of cylinder Q and a radius half

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.