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21 Apr 2012, 21:18
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Difficulty:

55% (hard)

Question Stats:

74% (02:30) correct 26% (04:34) wrong based on 226 sessions

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A merchant paid $300 for a shipment of x identical calculators. The merchant used 2 of the calculators as demonstrators and sold each of the others for$5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment? A. 24 B. 25 C. 26 D. 28 E. 30 Is this question correct? Shipping cost given but cost of each calculator missing..... [Reveal] Spoiler: OA _________________ Giving +1 kudos is a better way of saying 'Thank You'. Kudos [?]: 320 [0], given: 16 Math Expert Joined: 02 Sep 2009 Posts: 41892 Kudos [?]: 129181 [3], given: 12194 Re: A merchant paid$300 for a shipment of x identical [#permalink]

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21 Apr 2012, 23:03
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boomtangboy wrote:
A merchant paid $300 for a shipment of x identical calculators. The merchant used 2 of the calculators as demonstrators and sold each of the others for$5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment? A. 24 B. 25 C. 26 D. 28 E. 30 Is this question correct? Shipping cost given but cost of each calculator missing..... "A merchant paid$300 for a shipment of x identical calculators" means that there was a shipment of x calculators which cost merchant $300. The average cost of each calculator is $$\frac{300}{x}$$; The average price of each calculator is $$\frac{300}{x}+5$$; Number of calculators sold is $$x-2$$; The total revenue is $$300+120=420$$; So, $$(x-2)*(\frac{300}{x}+5)=420$$. At this point it's better to substitute values. Answer choice E fits: $$(30-2)*(\frac{300}{30}+5)=28*15=420$$. Answer: E. Hope it's clear. _________________ Kudos [?]: 129181 [3], given: 12194 Intern Joined: 01 Oct 2013 Posts: 4 Kudos [?]: 2 [1], given: 4 WE: Manufacturing and Production (Manufacturing) Re: A merchant paid$300 for a shipment of x identical [#permalink]

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04 Oct 2013, 13:21
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1st Try selecting options which are divisible by 300
If you select 30 as x.Therefore avg cost of each calculator 300/30 i.e 10$. Set aside 2 .So we have 28 calc. Each calc sold at 5$ more i.e 10+5=15$& 15x28=$420
Difference is $420-$300=120
E) is the answer hope it helps

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Re: A merchant paid $300 for a shipment of x identical [#permalink] ### Show Tags 11 Jan 2014, 08:52 boomtangboy wrote: A merchant paid$300 for a shipment of x identical calculators. The merchant used 2 of the calculators as demonstrators and sold each of the others for $5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was$120 more than the cost of the shipment, how many calculators were in the shipment?

A. 24
B. 25
C. 26
D. 28
E. 30

Is this question correct? Shipping cost given but cost of each calculator missing.....

I'd go with backsolving on this one though I must admit that originally I tried to solve algebraically and was stuck with variables and quadratics

We will have (300/x + 5)(x-2) = 420

Then begin replacing, I started with 25 cause 26 would not yield an integer when divided by 300 but it didn't work, so I realized I needed a bigger number and the only factor of 30 that could work was E

So E

Hope it helps
Cheers!
J

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20 Mar 2014, 14:07

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21 Mar 2014, 02:51
SomIyer wrote:
A merchant paid $300 for a shipment of x identical calculators. The merchant used 2 of the calculators as demonstrators and sold each of the others for$5 more than the average (arithmetic mean) cost of the x calculators. If the total revenue from the sale of the calculators was $120 more than the cost of the shipment, how many calculators were in the shipment? A. 24 B. 25 C. 26 D. 28 E. 30 Merging similar topics. Please refer to the discussion above. P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 3, 5, and 7. Thank you. _________________ Kudos [?]: 129181 [0], given: 12194 GMAT Club Legend Joined: 09 Sep 2013 Posts: 16589 Kudos [?]: 273 [0], given: 0 Re: A merchant paid$300 for a shipment of x identical [#permalink]

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25 Jun 2016, 02:11
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Re: A merchant paid $300 for a shipment of x identical [#permalink] ### Show Tags 15 Sep 2017, 22:48 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Kudos [?]: 273 [0], given: 0 Re: A merchant paid$300 for a shipment of x identical   [#permalink] 15 Sep 2017, 22:48
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