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

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.

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.

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

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.

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

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/