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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

Word Problems

by swerve » Mon Feb 22, 2021 2:55 pm

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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

The OA is D

Source: Manhattan Prep

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Source: Beat The GMAT — Problem Solving | Mon Feb 22, 2021 2:55 pm

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8088; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Word Problems

by Scott@TargetTestPrep » Sun Mar 07, 2021 7:59 am

swerve wrote: ↑
Mon Feb 22, 2021 2:55 pm
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

The OA is D

Solution:

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

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