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

 It is currently 21 Feb 2019, 04:33

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Online GMAT boot camp for FREE

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

# The stiffness of a diving board is proportional to the cube of its thi

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

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 53061
The stiffness of a diving board is proportional to the cube of its thi  [#permalink]

### Show Tags

06 Dec 2018, 04:28
00:00

Difficulty:

85% (hard)

Question Stats:

47% (02:22) correct 53% (02:55) wrong based on 61 sessions

### HideShow timer Statistics

The stiffness of a diving board is proportional to the cube of its thickness and inversely proportional to the cube of its length. If diving board A is twice as long as diving board B and has 8 times the stiffness of diving board B, what is the ratio of the thickness of diving board A to that of diving board B? (Assume that the diving boards are equal in all respects other than thickness and length.)

A. 2
B. 4
C. 8
D. 16
E. 64

_________________
SVP
Joined: 18 Aug 2017
Posts: 1887
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
The stiffness of a diving board is proportional to the cube of its thi  [#permalink]

### Show Tags

06 Dec 2018, 06:03
Bunuel wrote:
The stiffness of a diving board is proportional to the cube of its thickness and inversely proportional to the cube of its length. If diving board A is twice as long as diving board B and has 8 times the stiffness of diving board B, what is the ratio of the thickness of diving board A to that of diving board B? (Assume that the diving boards are equal in all respects other than thickness and length.)

A. 2
B. 4
C. 8
D. 16
E. 64

stiffness = thickness^3/ length ^3

given length of A= 2 * length of B
and stiffness of A = 8 * stiffness of B

t hickness^3= stiffness* length ^3

find for both a and b

A thickness^3= stiffness* length ^3/ B thickness^3= stiffness* length ^3
or say thickness (A/B) ^3= 8 SB* 2^3* Lb/ sb* lb
so thickness (A/B)^3= 64
or thickness ( A/B) = 4 IMO B
_________________

If you liked my solution then please give Kudos. Kudos encourage active discussions.

Intern
Joined: 02 Feb 2019
Posts: 1
Re: The stiffness of a diving board is proportional to the cube of its thi  [#permalink]

### Show Tags

02 Feb 2019, 11:39
I found Archit3110's answer very difficult to comprehend so here's another way to think about this problem that might help:

Ultimately we need to express the stiffness of diving board A in terms of board B

The first step is to derive the formula for stiffness. We know that the stiffness (S) of a diving board is proportional to the cube of its thickness (T); so $$S=T^3$$. We also know that the stiffness of a diving board is inversely proportional to the cube of its length (L); so $$S=1/L^3$$.

Putting these together you get: $$S=\frac{T^3}{L^3}$$.

Now if we go back and re-read the question, we know that diving board A is twice as long as diving board B and has 8 times the stiffness of diving board B. To make things simple, let's say that the stiffness of diving board A is 8, and the length of diving board A is 2. This means that the stiffness of diving board B is 1 and its length is also 1.

Next, we need to determine the ratio of the thickness of diving board A to the thickness of diving board B. Keep in mind that the formula you created for stiffness needs to be re-written so that it solves for thickness cubed. So we change $$S=\frac{T^3}{L^3}$$ to $$T^3=S*L^3$$.

Now that we have the formula for thickness (really, thickness cubed), we can start solving for the ratio of the thickness of A to the thickness of B. Start with the thickness of diving board B which is: $$T^3=S*L^3$$.

Given that diving board A is twice as long and 8 times as stiff as diving board B, we know that the formula for A is: $$T^3=8S*(2L)^3$$.

Next divide the thickness (cubed) of diving board A by the thickness (cubed) of diving board B: $$\frac{8S*(2L)^3}{S*L^3}$$ = $$\frac{8S*8L^3}{S*L^3}$$ = $$\frac{64SL^3}{SL^3}$$ = $$64$$

This tells us that the ratio of diving board A's thickness (cubed) to diving board B's thickness (cubed). The final step is to take the cube root of 64, which is 4. The answer.
Re: The stiffness of a diving board is proportional to the cube of its thi   [#permalink] 02 Feb 2019, 11:39
Display posts from previous: Sort by

# The stiffness of a diving board is proportional to the cube of its thi

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

 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®.