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In the first week of last month, Company X realized an avera [#permalink]
18 Nov 2011, 12:59

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Difficulty:

45% (medium)

Question Stats:

56% (02:17) correct
44% (01:06) wrong based on 42 sessions

In the first week of last month, Company X realized an average wholesale profit of $5304 per day from the sale of q units of Product Y. Which of the following CANNOT be the difference between Product Y’s sale price and cost per unit?

Re: 1st week of last month [#permalink]
18 Nov 2011, 16:03

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The wholesale profit is given to be $5304. The question also defines the number of units sold as q.

Let p represent the difference between Product Y's sale price and the cost per unit (i.e. the profit per unit).

q * p = total profit = 5304

Since we know q has to be a positive integer, and the only options provided for the value of p are integers, we can break the wholesale profit down into its prime factorability (word?) to determine what the possible values of q are.

Re: 1st week of last month [#permalink]
19 Nov 2011, 10:30

q*(s-c) = 5304 q = 5304/(s-c)

Since q must be integer, 5304 must be divisible by (s-c). Plug in answer choices. 5304 is not divisible by 7 and 11. Therefore, neither 7 nor 11 can be s-c.

Re: 1st week of last month [#permalink]
22 Feb 2013, 16:15

enigma123 wrote:

Thanks AKProdigy87 and I agree not a very good question Kostyan.

I respectfully disagree. It's a great question.

The key operator that everyone seems to have missed is the "average". The average profit of $5304 per day is equivalent to a total profit of $37128 for the whole week. Therefore, the difference between sale price and cost per unit is equal to $37128, which is divisible by all of the answer choices, except for 11.

Re: In the first week of last month, Company X realized an avera [#permalink]
23 Feb 2013, 04:51

Expert's post

enigma123 wrote:

In the first week of last month, Company X realized an average wholesale profit of $5304 per day from the sale of q units of Product Y. Which of the following CANNOT be the difference between Product Y’s sale price and cost per unit?

(A) $3 (B) $4 (C) $7 (D) $11 (E) $51

Notice that the difference between sale price and cost per unit is the profit per unit. So, we are asked to find which of the options cannot be the profit per unit.

Now, since the average daily profit was $5304, then the profit per week was $7*5304=7*(2^3*3*13*17).

We also know that these profit was generated from the sale of q units, thus q=(profit per week)/(profit per unit)=7*(2^3*3*13*17)/(profit per unit).

q=(# of units sold)=integer, thus from the options presented profit per unit cannot be 11 because in this case q won't be an integer.

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