profit & loss

rahul.s 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

OA: D
Source: MGMAT
Level: 700 - 800

Here, q y = 7 × $5304, where y is the average wholesale profit made on each unit of Product Y. Take a careful look and find the question written as:

If q y = 7 × 5304, where q is a positive integer, which of the following CANNOT be y?
(A) $3
(B) $4
(C) $7
(D) $11
(E) $51

We realize that y is a certain factor of 7 × 5304. Quick check through the choices with divisibility rules in mind: A yes, B yes, C yes, [spoiler]D NO [/spoiler][(3 + 4) – (5 + 0) = 2]

[spoiler]D[/spoiler]

rahul.s 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

Profit = No of units*(Sale Price - Cost Per Unit) = q*d

Now q is an integer
All the answer choices for d is also an integer

5304 = 2^3*3*13*17

Now a factor of since q and d are integers they cannot be a multiple of 11 since 5304 is not a multiple of 11
Hence D

I understand till the part where (Selling price - cost) = 5304 * Quantity, where Q must be an integer, therefore difference between SP and Cost must be integer as well.

I test divisibility rules, and I get that choice A, B and E are possible choices, hence I'm left with choices C and D as they both give non integers when I put them in the equation.

My question is, does the wording "week...per day" matter here? ie: should the equation be
Quantity * difference = 5304 * 7 (for 7 days a week)? If it is so, I expected that the question should be rephrased to clarify what is really being asked here.

SaraLotfy, the answer to your question lies in the answer of Average in the Series = 1, 2, 3, 4, 5,6, 9; The mean here is 30/7 = 4.28

Notice that 4.28 is not present in any of the value.

Hence, we cannot assume that 5304 would be an integer value for any of the day.

So, you need to multiple 5304*7. below is the solution to the problem


ANSWER [D]

5304*7 = q ( SP per unit - CP per unit)
( SP per unit - CP per unit) = 5304*7/q

(A) 3 is a factor of 5304; POSSIBLE
(B) 4 is a factor of 5304; POSSIBLE
(C) 7 is present in Numerator; POSSIBLE
(D) 11 is not a factor of 5304
(E) 51 is a factor of 5304; POSSIBLE

SaraLotfy wrote:I understand till the part where (Selling price - cost) = 5304 * Quantity, where Q must be an integer, therefore difference between SP and Cost must be integer as well.

I test divisibility rules, and I get that choice A, B and E are possible choices, hence I'm left with choices C and D as they both give non integers when I put them in the equation.

My question is, does the wording "week...per day" matter here? ie: should the equation be
Quantity * difference = 5304 * 7 (for 7 days a week)? If it is so, I expected that the question should be rephrased to clarify what is really being asked here.

Thank you rahulmittal

I understand the process of solving: once 5304 is multiplied by 7, therefore clearly 7 can be a factor.

Please bear with me here
Could you please clarify what do you mean by "the answer to your question lies in the answer of Average in the Series = 1, 2, 3, 4, 5,6, 9; The mean here is 30/7 = 4.28"

How did you reach this?

SaraLotfy wrote:Thank you rahulmittal

I understand the process of solving: once 5304 is multiplied by 7, therefore clearly 7 can be a factor.

Please bear with me here
Could you please clarify what do you mean by "the answer to your question lies in the answer of Average in the Series = 1, 2, 3, 4, 5,6, 9; The mean here is 30/7 = 4.28"

How did you reach this?

Sara, I was trying to show you the need of phrase "week...per day"; this question can seem to be tricky if the person tries to work on the problem taking only a single day and solving
5304 = q ( SP - CP)
Doing so will leave options with answer 7 & 11; i think you were also stuck in the same phase?

You need to consider 5304 * 7 (yes 7 days a week)

The series example which i gave was just to show that you cannot assume that 5304 can be a perfect figure at any specific day; It's a mean. And, the mean may or may not be present in the Series.
For instance,
the Series = 1, 2, 3, 4, 5,6, 9; The mean here is 30/7 = 4.28" & 4.28 is not present in the series