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# The cost of a square slab is proportional to its thickness and also pr

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The cost of a square slab is proportional to its thickness and also pr [#permalink]

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21 Jul 2009, 15:28
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65% (hard)

Question Stats:

59% (01:33) correct 41% (01:20) wrong based on 44 sessions

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The cost of a square slab is proportional to its thickness and also proportional to the square of its length. What is the cost of a square slab that is 3 meters long and 0.1m thick.

(1) The cost of a square slab that is 2 meters long and 0.2 m thick is $160 more than the cost of a slab that is 2m long and 0.1 m thick (2) The cost of a square slab that is 3 meters long and 0.1 m thick is 200 more than the cost of a square slab that is 2m long and 0.1 m thick OPEN DISCUSSION OF THIS QUESTION IS HERE: the-cost-of-a-square-slab-is-proportional-to-its-thickness-a-83652.html [Reveal] Spoiler: OA Current Student Joined: 18 Jun 2009 Posts: 358 Location: San Francisco Schools: Duke,Oxford,IMD,INSEAD Followers: 10 Kudos [?]: 72 [0], given: 15 Re: The cost of a square slab is proportional to its thickness and also pr [#permalink] ### Show Tags 21 Jul 2009, 15:59 1 This post was BOOKMARKED Stmt1 - 2m long by 0.2m thick is$160 more than 2m long by 0.1m thick

Now since the cost is directly porportional to the thickness. Lets imagine the "2m long by 0.2m thick" slab as two "2m long by 0.1m thick" slabs

we have "2m long by 0.2m thick" = 160 + "2m long by 0.1m thick"

"2m long by 0.2m thick" can be written as "2m long by 0.1m thick" + "2m long by 0.1m thick"

therefore "2m long by 0.1m thick" + "2m long by 0.1m thick" = 160 + "2m long by 0.1m thick"

therefore "2m long by 0.1m thick" = $160 .... 1 We cant deduce from stmt 1 ... insuff Stmt 2) 3m long by 0.1m thick is$200 more than 2m long by 0.1m thick

3m long by 0.1m thick = $200 + 2m long by 0.1m thick .... 2 stmt2 insuffecient combing 1 and 2 we have 3m long by 0.1m thick =$200 + $160(from 1) =$360 ...

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Re: The cost of a square slab is proportional to its thickness and also pr [#permalink]

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21 Jul 2009, 16:02
3
KUDOS
Thickness = t
Length = l
$$c = 9*0.1*k = ?$$

"and also proportional" means that we can put both in the same formula:

$$Cost = k*t*l^2$$, where k is a constant

1)
$$k*2^2*0.1$$ costs x
$$k*2^2*0.2$$ costs x + 160
Using rule of three (cross-multiplication): $$(k*2^2*0.1)/(k*2^2*0.2)= x/( x + 160 )$$, you can find x, and then do the same with 9*0.1*k
SUFFICIENT

2)
Using the same reasoning of 1)
SUFFICIENT

PS.: It was worth? Consider a kudo...
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Re: The cost of a square slab is proportional to its thickness and also pr [#permalink]

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20 Dec 2009, 13:46
please check if this method would work as well since I didn't relaly get coelholds answer (and i get a negative solution for (b) with his method...)

the cost is proportional to the area and the thickness

The cost: C
We're looking for (3^2*0,1) C = ?

(a) (2^2*0,2)*C = (2^2*0,1)*C + 160
0,8*C = 0,4*C + 160
0,4C = 160
C = 400

(b) (3^2*0,1)*C = (2^2*0,1)C + 200
0,9C = 0,4C + 200
0,5C = 200
C = 400

Hence, D.
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Re: The cost of a square slab is proportional to its thickness and also pr [#permalink]

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20 Dec 2009, 22:32
The key with such questions is to set up the formula based on the proportionality.

Cost = K*(L^2)*T
Where K is a constant
L is the length
T is the thickness
Solving we get D

Note is something is inversely proportional, divide instead of multiply. For example if the cost is inversely proportional to the square root of slab impurity then the above formula will become
Cost = K*(L^2)*T/sqrt(I)
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Re: The cost of a square slab is proportional to its thickness and also pr [#permalink]

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20 Dec 2009, 22:53
really a tricky one! i initially thought it to be C but then checked the formula and found it to be D.
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Re: The cost of a square slab is proportional to its thickness and also pr [#permalink]

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15 Oct 2011, 14:17
I wrote the formula as Cost = aL^2 + bT, so I got D.
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Re: The cost of a square slab is proportional to its thickness and also pr [#permalink]

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16 Oct 2011, 10:41
seofah wrote:
The cost of a square slab of concrete is proportional to the thickness and also proportional to the square of the length. What is the cost of square slab that is 3 meters long and 0.1 meters thick?
a. 2m long by 0.2m thick is $160 more than 2m long by 0.1m thick b. 3m long by 0.1m thick is$200 more than 2m long by 0.1m thick

Got D but worked as following:

a. 2^2L + .2W = 2^2L + .1W + 160 => SUFFICIENT (Solve for W and L)
b. 3^2L + .1W = 2^2L + .1W + 200 => SUFFICIENT (Solve for W and L)

Wonder if this a right approach to attack such question.
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Re: The cost of a square slab is proportional to its thickness and also pr [#permalink]

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15 Dec 2014, 07:31
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Re: The cost of a square slab is proportional to its thickness and also pr [#permalink]

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15 Dec 2014, 07:54
Expert's post
OPEN DISCUSSION OF THIS QUESTION IS HERE: the-cost-of-a-square-slab-is-proportional-to-its-thickness-a-83652.html
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Re: The cost of a square slab is proportional to its thickness and also pr   [#permalink] 15 Dec 2014, 07:54
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