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# In the first week of last month, Company X realized an avera

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Senior Manager
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In the first week of last month, Company X realized an avera  [#permalink]

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Updated on: 23 Feb 2013, 04:30
1
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75% (hard)

Question Stats:

60% (02:37) correct 40% (02:31) wrong based on 179 sessions

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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

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Originally posted by enigma123 on 18 Nov 2011, 12:59.
Last edited by Bunuel on 23 Feb 2013, 04:30, edited 1 time in total.
Edited the question and added OA.
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Re: In the first week of last month, Company X realized an avera  [#permalink]

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23 Feb 2013, 04:51
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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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Re: 1st week of last month  [#permalink]

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18 Nov 2011, 16:03
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1
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.

5304 = 3 * 1768 = 3 * 4 * 442 = 3 * 4 * 2 * 221
= 2 * 3 * 4 * 13 * 17

Any product of the combination of the integers {2,3,4,13,17} are possibly values for p.

Therefore, C: 7 and D: 11 are both not possible differences between Product Y's sale price and cost of unit.
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Re: 1st week of last month  [#permalink]

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19 Nov 2011, 10:30
1
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.

This is not a quality question.
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Re: 1st week of last month  [#permalink]

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20 Nov 2011, 20:22
Thanks AKProdigy87 and I agree not a very good question Kostyan.
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Re: 1st week of last month  [#permalink]

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22 Feb 2013, 16:15
4
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.

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Re: In the first week of last month, Company X realized an avera  [#permalink]

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19 Aug 2017, 11:58
Bunuel wrote:
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.

Wait!
The question says "in the 1st week of the last month". Does that really mean "end of the 1st week"? "in the 1st week" could also mean someday within the 1st week. Also, how and why should I assume that the company did its business on all 7 days of the week? A company making \$5k per day profit need not really be a company which must be running its business all days of the week.
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Re: In the first week of last month, Company X realized an avera  [#permalink]

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13 Feb 2020, 05:23
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

The difference between Product Y’s sale price and cost per unit is the profit per unit. Notice that the profit for the first week of last month, in dollars, is 5304 x 7. Assuming each unit has a profit of a whole number of dollars, we see that q must be a factor of 5304 x 7. So let’s prime factorize 5304 x 7:

5304 x 7 = 4 x 1326 x 7 = 2^2 x 2 x 663 x 7 = 2^3 x 3 x 221 x 7 = 2^3 x 3 x 13 x 17 x 7

Looking at the answer choices, we see that A) 3, B) 7, C) 4 = 2^2, and E) 3 x 17 = 51 are factors of 5304 x 7. However, D) 11 is not. Therefore, 11 is the correct answer.

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Re: In the first week of last month, Company X realized an avera   [#permalink] 13 Feb 2020, 05:23