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

Question

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

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

Bunuel · Accepted Answer

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.

Answer: D.

daedalus1989 · Answer

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.

So, D is the answer.

AKProdigy87 · Answer

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.

kostyan5 · Answer

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.

enigma123 · Answer

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

chaudhurysr · Answer

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.

ScottTargetTestPrep · Answer

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.

Answer: D

KarishmaB · Answer

Simply use the divisibility rules to check whether 5304 * 7 is divisible by each option. (A) $3 --> 5 + 3 + 4 = 12 so it is divisible by 3 (B) $4 --> 5304 ends with 04 so it is divisible by 4 (C) $7 --> 5304 * 7 is obviously divisible by 7 (D) $11 --> Diff between 5 and 3+4 is 2, not a multiple of 11 hence this is not divisible by 11 (E) $51 Answer (D) Check this post for divisibility rules of all powers of 4: https://anaprep.com/number-properties-d ... wers-of-2/

bumpbot · Answer

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

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