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If the price of coffee, p, doubles every week for 4 weeks, triples a

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If the price of coffee, p, doubles every week for 4 weeks, triples a [#permalink]

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New post 05 Apr 2017, 03:56
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E

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  45% (medium)

Question Stats:

76% (01:26) correct 24% (01:25) wrong based on 55 sessions

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If the price of coffee, p, doubles every week for 4 weeks, triples a week later, and finally quadruples a week after that, which of the following represents the price of coffee at the end of period, in terms of p?

A. 15p
B. 7*8*p
C. 7*2^4*p
D. 3*4*8*p
E. 12*2^4*p
[Reveal] Spoiler: OA

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Re: If the price of coffee, p, doubles every week for 4 weeks, triples a [#permalink]

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New post 05 Apr 2017, 04:50
Initial Price = p
First Week Price = 2p.
Sec Week Price = 4p
Third week Price = 8p
Fourth week = 16p
Fifth week = 3X16 p= 3* 16 p
Sixth week = 4*3*16p = E

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Re: If the price of coffee, p, doubles every week for 4 weeks, triples a [#permalink]

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New post 05 Apr 2017, 09:18
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Since the price doubles every week, it means it gets multiplied by 2 every week.

Price after 4 weeks = 2 * 2 * 2 * 2 * p = 16p
Price after 5 weeks = 3 * 16p
Price after 6 weeks = 4 * 3 * 16p = 12 * 16p

Answer (E)
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Re: If the price of coffee, p, doubles every week for 4 weeks, triples a [#permalink]

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New post 05 Apr 2017, 11:55
Bunuel wrote:
If the price of coffee, p, doubles every week for 4 weeks, triples a week later, and finally quadruples a week after that, which of the following represents the price of coffee at the end of period, in terms of p?

A. 15p
B. 7*8*p
C. 7*2^4*p
D. 3*4*8*p
E. 12*2^4*p


If you are bad at creating equations just pick an easy number to work with.

let P = $1

Week 1 = $2
Week 2 = $4
Week 3 = $8
Week 4 = $16
Week 5 = $48
Week 6 = $192

Testing equations you will find that E fits this.

12*2^4*p
12*2^4*1
12*16*1
192
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Re: If the price of coffee, p, doubles every week for 4 weeks, triples a [#permalink]

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New post 11 Apr 2017, 11:45
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Bunuel wrote:
If the price of coffee, p, doubles every week for 4 weeks, triples a week later, and finally quadruples a week after that, which of the following represents the price of coffee at the end of period, in terms of p?

A. 15p
B. 7*8*p
C. 7*2^4*p
D. 3*4*8*p
E. 12*2^4*p


If the initial price of coffee is p, after week one it's 2p, after week two it’s 4p, after week 3 it’s 8p, and after week 4 it’s 16p.

Since the price triples a week later, the new price is (3)(16p), and since it quadruples the following week, it's (4)(3)(16p) = 12*2^4*p .

Answer: E
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Re: If the price of coffee, p, doubles every week for 4 weeks, triples a [#permalink]

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New post 11 Apr 2017, 17:18
The price of coffee, p doubles every week for 4 weeks
2 x 2 x 2 x 2 = 16
Triples a week later
16 x 3
Quadruples a week later
16 x 3 x 4 = 192

Now do process elimination
Only E works out to 192
Proof:

12 x 2^4 = 12 x 16
= 192

Therefore, the answer is E
Re: If the price of coffee, p, doubles every week for 4 weeks, triples a   [#permalink] 11 Apr 2017, 17:18
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