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Profit / Loss

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Profit / Loss

by MI3 » Sat Jul 16, 2011 7:38 am
Experts out there, please advise on how to resolve the below problem (I don't have the solution handy)

Q. 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

Thank you.
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by jainnikhil02 » Sat Jul 16, 2011 8:21 am
IMO D

Because : profit = sale Price - cost price.

and it is assumed that the profit from the all unit is same.

then Q*(profit per unit )= 5304

ans Q is a integer because it is a quantity.

so only D is the option which didnt give the product equal to the $5304.
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by goalevan » Sat Jul 16, 2011 4:57 pm
The difference between a unit's sale price and cost is the unit profit. The unit profit must be a factor of the total weekly profit. In other words, the weekly profit must be a multiple of the unit profit.

The question can be rephrased:

"5,304 * 7 is NOT a multiple of which of the following integers?"

It would be time consuming to calculate the prime factorization of 5304, so we can start by attacking the answer choices.

C) This answer choice is already out because 7 was a factor of the weekly profit from the beginning.

A) 5 + 3 + 0 + 4 = 12, which is a multiple of 3, so we can take 5304 / 3 = 1768.

B) We know that 100 is divisible by 4, so we know that 5304 is divisible by 4 since 5304 = 53 * 100 + 4.

D) 5304 / 11 = 482 2/11, which is not an integer. This is the correct answer.

E) Note that 51 is NOT prime because 3 * 17 = 51. We have already established that 3 is part of the prime factorization, so we could test 17 by long division to confirm. At this point it's unnecessary since we've already established that 11 is not a factor.

Note that C) 7 is a trap answer, because 5304 is not divisible by 7. E is also a trap because 51 is not a prime factor of 5304, but it is a factor nonetheless.
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