It is currently 20 Feb 2019, 12:25

### 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

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

Author Message
TAGS:
Moderator
Joined: 18 Apr 2015
Posts: 5572
Followers: 89

Kudos [?]: 1117 [0], given: 5159

The stiffness of a diving board is proportional to the cube [#permalink]  21 Jun 2017, 13:06
Expert's post
00:00

Question Stats:

71% (03:22) correct 28% (01:49) wrong based on 14 sessions

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.)

[Reveal] Spoiler: OA
4

_________________
Director
Joined: 03 Sep 2017
Posts: 521
Followers: 1

Kudos [?]: 343 [1] , given: 66

Re: The stiffness of a diving board is proportional to the cube [#permalink]  25 Sep 2017, 07:37
1
KUDOS
We can translate what is written in formulas as $$s=\frac{t^3}{l^3}$$ where s is stiffness, t is thickness and l is length. Then, if board A has 3 times the length and 8 times the stiffness of table B, the formula is rewritten as $$8s=\frac{t^3}{8*l^3}$$ so that $$t^3=8s*8l^3$$. Thus the ratio between the cubic thickness of the two tables is $$\frac{64sl^3}{sl^3}=64$$ but since this is the cubic ratio we have to compute the cubic root to find the ratio between thickness, i.e. $$64^{\frac{1}{3}}=4$$
Intern
Joined: 23 Nov 2017
Posts: 45
Followers: 0

Kudos [?]: 45 [0], given: 0

Re: The stiffness of a diving board is proportional to the cube [#permalink]  29 Nov 2017, 07:45
IlCreatore wrote:
We can translate what is written in formulas as $$s=\frac{t^3}{l^3}$$ where s is stiffness, t is thickness and l is length. Then, if board A has 3 times the length and 8 times the stiffness of table B, the formula is rewritten as $$8s=\frac{t^3}{8*l^3}$$ so that $$t^3=8s*8l^3$$. Thus the ratio between the cubic thickness of the two tables is $$\frac{64sl^3}{sl^3}=64$$ but since this is the cubic ratio we have to compute the cubic root to find the ratio between thickness, i.e. $$64^{\frac{1}{3}}=4$$

Can someone explain this to me? I am really struggling with this problem. I understand how you got to S = t^3/l*3, but I don't understand how you got to the next step. How did you end up with 8*l^3 in the denominator?

Intern
Joined: 27 Jul 2017
Posts: 4
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: The stiffness of a diving board is proportional to the cube [#permalink]  29 Nov 2017, 10:01
I believe 6 would be the right answer.
Moderator
Joined: 18 Apr 2015
Posts: 5572
Followers: 89

Kudos [?]: 1117 [0], given: 5159

Re: The stiffness of a diving board is proportional to the cube [#permalink]  29 Nov 2017, 12:49
Expert's post
Please, Guys, refering to the explanation provided by @ilcreatore. it is perfect.

The OA is 4.

Regards
_________________
Intern
Joined: 29 Nov 2017
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: The stiffness of a diving board is proportional to the cube [#permalink]  29 Nov 2017, 13:44
The error is the incorrect transcription of the question. The initial question and math is done with the length being twice as great while the forum explanation is 3 times.
Re: The stiffness of a diving board is proportional to the cube   [#permalink] 29 Nov 2017, 13:44
Display posts from previous: Sort by