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12 Jan 2019, 13:36
3
4
00:00

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(N/A)

Question Stats:

54% (02:21) correct 46% (02:39) wrong based on 80 sessions

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The price of a pastry at 10 AM was $p. Each hour after 11 AM, the price decreases by 20%. If Julie bought the pastry at 11:15 AM whereas her sister bought the same 3 hours later, then the price paid by Julie's sister was what percent less than that paid by Julie?(There is no price change apart from those mentioned above) A. 33.33% B. 37.5% C. 48.8% D. 51.2% E. None of these Director Status: Manager Joined: 27 Oct 2018 Posts: 746 Location: Egypt Concentration: Strategy, International Business GPA: 3.67 WE: Pharmaceuticals (Health Care) Re: The price of a pastry at 10AM was$p. Each hour after 11AM, the price  [#permalink]

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12 Jan 2019, 15:34
1
visualizing the time line:

10:00 <---(p)---> 11:00 <---(p)---> 12:00 <---($$\frac{4}{5}$$p)---> 13:00 <---($$(\frac{4}{5})^2$$p)---> 14:00 <---($$(\frac{4}{5})^3$$p)---> 15:00

Julie's price = p
sister's price = $$(\frac{4}{5})^3$$p

$$(\frac{4}{5})^3$$p = p(1- $$\frac{x}{100}$$)

$$(\frac{4}{5})^3$$ = 1- $$\frac{x}{100}$$

$$\frac{x}{100}$$ = 1 - $$\frac{64}{125}$$

x = $$\frac{61}{125} * 100$$ = $$\frac{488}{1000} * 100$$ = 48.8 %

So C IMO
Director
Joined: 28 Jul 2016
Posts: 670
Location: India
Concentration: Finance, Human Resources
GPA: 3.97
WE: Project Management (Investment Banking)

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27 Nov 2019, 21:12
can be done by assuming the initial price i.e. price of the pastry 10 AM - > 10

10 AM - > $10 (price paid by Julie) 11 - >$10 *.8 -> $8 (price paid by Julie) 12 - >$8 * .8 - > $6.4 1 ->$6.4 * .8 -> $5.12 @ 2 ->$5.12*.8 -> 4.096

price paid of Julie's sis - > 4.096

% difference= > (4.096/8) -> here numerator is greater than 50% of 8, thus the %value will be slightly lower than 50%.

from the given choices - > only C works out as an option. thus ANS - > C
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9850
Location: Pune, India
Re: The price of a pastry at 10AM was $p. Each hour after 11AM, the price [#permalink] ### Show Tags 27 Nov 2019, 22:30 akurathi12 wrote: The price of a pastry at 10 AM was$p. Each hour after 11 AM, the price decreases by 20%. If Julie bought the pastry at 11:15 AM whereas her sister bought the same 3 hours later, then the price paid by Julie's sister was what percent less than that paid by Julie?(There is no price change apart from those mentioned above)

A. 33.33%
B. 37.5%
C. 48.8%
D. 51.2%
E. None of these

There is a reduction of 20% every hour so the price becomes (4/5) of what it was in the previous hour.

At 11:15, Julie bought the pastry for p*(4/5)
3 hrs later, at 2:15, her sister bought the pastry for p*(4/5)*(4/5)^3 = p*(4/5)^4 = p*(256/625)

% Diff = [p*(4/5) - p*(256/625)] / p*(4/5) = 1 - (256 * 5)/(625 * 4) = 61/125 = 48.8% ( because 61 is a bit less than 62.5 which is half of 125)

_________________
Karishma
Veritas Prep GMAT Instructor