In the first week of last month, Company . . .

[Vincen]

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

D is the OA.

I am confused. I got and answer which is not in the list. I need help.

[Jay@ManhattanReview]

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

D is the OA.

I am confused. I got and answer which is not in the list. I need help.

Profit per day = $5304, thus, profit per week = $7*5304

We know that the difference between Product Y's sale price and cost per unit is profit per unit

This, Profit per unit = profit per week / number of units sold = (7*5304) / q

=> q = (7*5304) / Profit per unit

Since q is a positive integer, (7*5304) must be divisible by 'Profit per unit'.

One of the ways is to factorise 7*5304 and see which integers (Profit per unit) divide it completely. The option value, not a factor of 7*5304, is the correct answer.

7*5304 = 7*2^3*3*13*17

We see that option D (11) is not a factor of (7*5304) -- the correct answer.

The correct answer: D

Hope this helps!

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-Jay
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[Scott@TargetTestPrep]

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

D is the OA.

I am confused. I got and answer which is not in the list. I need help.

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