Cost is expressed by the formula tb^4 : GMAT Problem Solving (PS)
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# Cost is expressed by the formula tb^4

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Manager
Joined: 13 Jul 2013
Posts: 75
GMAT 1: 570 Q46 V24
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Kudos [?]: 9 [0], given: 21

Cost is expressed by the formula tb^4 [#permalink]

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07 Sep 2013, 21:24
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Question Stats:

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Cost is expressed by the formula tb^4. If b is doubled, the new cost is what percent of the original cost?

(A) 200
(B) 600
(C) 800
(D) 1600
(E) 50

I read the explanation in Manhattan but cant relate to it.

I worked it out this way

Assume,
t=1
b=2

Original = (1*2)^4= 16
New= (1*2*2)^4 = 256

% change= (change/Original)*100
=(240/16)*100
=1500

Where am I going wrong?

Thanks
[Reveal] Spoiler: OA
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Joined: 10 Oct 2012
Posts: 630
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Re: Cost is expressed by the formula tb^4 [#permalink]

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07 Sep 2013, 21:30
1
KUDOS
theGame001 wrote:
Cost is expressed by the formula tb^4. If b is doubled, the new cost is what percent
of the original cost?

(A) 200
(B) 600
(C)800
(D) 1600
(E) 50

I read the explanation in Manhattan but cant relate to it.

I worked it out this way

Assume,
t=1
b=2

Original = (1*2)^4= 16
New= (1*2*2)^4 = 256

% change= (change/Original)*100
=(240/16)*100
=1500

Where am I going wrong?

Thanks

The question asks for the relative percent b/w the new cost and the final cost, that is $$\frac{256}{16}*100$$ and NOT the precent increase/decrease.

For example, initial cost=1 , final cost = 2, and the question asks what percent of the original cost is the final cost : $$\frac{2}{1}*100$$ = 200%

Again, if the question asks, what is the percent increase between the final and the initial cost : $$\frac{2-1}{1}*100$$ = 100%
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Joined: 14 Aug 2013
Posts: 35
Location: United States
Concentration: Finance, Strategy
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Re: Cost is expressed by the formula tb^4 [#permalink]

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07 Sep 2013, 21:56
1
KUDOS
theGame001 wrote:
Cost is expressed by the formula tb^4. If b is doubled, the new cost is what percent
of the original cost?

(A) 200
(B) 600
(C)800
(D) 1600
(E) 50

I read the explanation in Manhattan but cant relate to it.

I worked it out this way

Assume,
t=1
b=2

Original = (1*2)^4= 16
New= (1*2*2)^4 = 256

% change= (change/Original)*100
=(240/16)*100
=1500

Where am I going wrong?

Thanks

Original Cost C1=t1*b1^4
New Cost C2=t2*b2^4....only b is doubled so t2=t1 and b2=2b1
C2=t2*(2b1)^4
=16(t1*b1^4)
=16C1
16 times C1=>1600% of C1
Ans D=1600
Manager
Joined: 26 Feb 2013
Posts: 184
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Kudos [?]: 40 [0], given: 25

Re: Cost is expressed by the formula tb^4 [#permalink]

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07 Sep 2013, 23:23
I thought we need to multiply b^4 and did 2(b^4) and answered wrong.
Manager
Joined: 13 Jul 2013
Posts: 75
GMAT 1: 570 Q46 V24
Followers: 0

Kudos [?]: 9 [0], given: 21

Re: Cost is expressed by the formula tb^4 [#permalink]

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08 Sep 2013, 01:15
mau5 wrote:
theGame001 wrote:
Cost is expressed by the formula tb^4. If b is doubled, the new cost is what percent
of the original cost?

(A) 200
(B) 600
(C)800
(D) 1600
(E) 50

I read the explanation in Manhattan but cant relate to it.

I worked it out this way

Assume,
t=1
b=2

Original = (1*2)^4= 16
New= (1*2*2)^4 = 256

% change= (change/Original)*100
=(240/16)*100
=1500

Where am I going wrong?

Thanks

The question asks for the relative percent b/w the new cost and the final cost, that is $$\frac{256}{16}*100$$ and NOT the precent increase/decrease.

For example, initial cost=1 , final cost = 2, and the question asks what percent of the original cost is the final cost : $$\frac{2}{1}*100$$ = 200%

Again, if the question asks, what is the percent increase between the final and the initial cost : $$\frac{2-1}{1}*100$$ = 100%

Ahhhh, okay. Thanks, I clearly misinterpreted the question.
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Re: Cost is expressed by the formula tb^4 [#permalink]

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08 Sep 2013, 03:45
theGame001 wrote:
Cost is expressed by the formula tb^4. If b is doubled, the new cost is what percent of the original cost?

(A) 200
(B) 600
(C) 800
(D) 1600
(E) 50

I read the explanation in Manhattan but cant relate to it.

I worked it out this way

Assume,
t=1
b=2

Original = (1*2)^4= 16
New= (1*2*2)^4 = 256

% change= (change/Original)*100
=(240/16)*100
=1500

Where am I going wrong?

Thanks

The point is that 16tb^4 is 1600% of tb^4 but 16tb^4 is 1500% greater than tb^4.
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Re: Cost is expressed by the formula tb^4   [#permalink] 08 Sep 2013, 03:45
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