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Manager  Joined: 12 Oct 2011
Posts: 105
GMAT 1: 700 Q48 V37
GMAT 2: 720 Q48 V40
A certain bakery ran a promotion code: a customer can buy x  [#permalink]

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4
8 00:00

Difficulty:   65% (hard)

Question Stats: 64% (02:58) correct 36% (02:51) wrong based on 203 sessions

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A certain bakery ran a promotion code: a customer can buy x donuts for the regular price of $15 total and get 3 donuts free. If the donut price per dozen during the promotion is$2 less than the normal donut price per dozen, what is x?

A. 15
B. 18
C. 21
D. 25
E. 30
Math Expert V
Joined: 02 Sep 2009
Posts: 61376
Re: A certain bakery ran a promotion code: a customer can buy x  [#permalink]

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BN1989 wrote:
A certain bakery ran a promotion code: a customer can buy x donuts for the regular price of $15 total and get 3 donuts free. If the donut price per dozen during the promotion is$2 less than the normal donut price per dozen, what is x?

A. 15
B. 18
C. 21
D. 25
E. 30

The promotion price per donut is $$\frac{15}{x+3}$$, thus the promotion price per dozen is $$12*\frac{15}{x+3}$$;

The regular price per donut is $$\frac{15}{x}$$, thus the regular price per dozen is $$12*\frac{15}{x}$$;

We are told that the promotion price per dozen is $2 less than the normal donut price per dozen: $$12*\frac{15}{x+3}+2=12*\frac{15}{x}$$ --> $$\frac{180}{x+3}+2=\frac{180}{x}$$. At this point it's better to substitute the values rather than solve for x. Answer choice A, 15, works. Answer: A. _________________ ##### General Discussion Veritas Prep GMAT Instructor V Joined: 16 Oct 2010 Posts: 10113 Location: Pune, India Re: A certain bakery ran a promotion code: a customer can buy x [#permalink] ### Show Tags 3 BN1989 wrote: A certain bakery ran a promotion code: a customer can buy x donuts for the regular price of$15 total and get 3 donuts free. If the donut price per dozen during the promotion is $2 less than the normal donut price per dozen, what is x? A. 15 B. 18 C. 21 D. 25 E. 30 Responding to a pm: The wording of the question is such that it is normal to read it twice to understand it well. Promotion Code: a customer can buy x donuts for the regular price of$15 total and get 3 donuts free

This tells us two things:

During promotion, 3 donuts are given free for $$x$$ donuts at a price of $15, hence it is cost of $$(x+3)$$ donuts. Cost of dozen donuts during promotion = $$\frac{(15*12)}{(x+3)}$$ Given that $$\frac{(15*12)}{(x+3)}$$ = $$\frac{(15 *12)}{x}$$ $$- 2$$ Solving or plugging the answer choices, above we get, $$x = 15$$ Answer A. Thanks, GyM _________________ Target Test Prep Representative V Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 9426 Location: United States (CA) Re: A certain bakery ran a promotion code: a customer can buy x [#permalink] ### Show Tags BN1989 wrote: A certain bakery ran a promotion code: a customer can buy x donuts for the regular price of$15 total and get 3 donuts free. If the donut price per dozen during the promotion is $2 less than the normal donut price per dozen, what is x? A. 15 B. 18 C. 21 D. 25 E. 30 For the regular price, each donut costs 15/x, and thus a dozen donuts will cost 15/x * 12 = 180/x. For the promotional price, each donut costs 15/(x + 3) and thus a dozen will cost 15/(x + 3) * 12 = 180/(x + 3). Since the promotional price per dozen is$2 less than the regular price per dozen, we have:

180/(x + 3) + 2 = 180/x

Multiplying both sides by x(x + 3), we have:

180x + 2x(x + 3) = 180(x + 3)

180x + 2x^2 + 6x = 180x + 540

2x^2 + 6x - 540 = 0

x^2 + 3x - 270 = 0

(x + 18)(x - 15) = 0

x = -18 or x = 15

Since x can’t be negative, x = 15.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: A certain bakery ran a promotion code: a customer can buy x   [#permalink] 04 Jul 2018, 18:23
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