A manager wants to assign each of his $e$ employees to one

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BTGmoderatorLU: Moderator; Posts: 2547; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Wed Oct 23, 2019 1:42 pm

Source: Princeton Review

A manager wants to assign each of his $e$ employees to one of $p$ projects. If $3 < p < 11 < e$, then can the manager assign the employees to the projects such that each project has the same number of employees?

1) It is possible for the manager to assign 11$e$ employees to one of $p$ projects such that there is an equal number of employees in each project.
2) It is possible for the manager to assign 6$e$ employees to one of $p$ projects such that there is an equal number of employees in each project.

The OA is D

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Source: Beat The GMAT — Data Sufficiency | Wed Oct 23, 2019 1:42 pm

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Wed Oct 23, 2019 10:39 pm

BTGmoderatorLU wrote:Source: Princeton Review

A manager wants to assign each of his $e$ employees to one of $p$ projects. If $3 < p < 11 < e$, then can the manager assign the employees to the projects such that each project has the same number of employees?

1) It is possible for the manager to assign 11$e$ employees to one of $p$ projects such that there is an equal number of employees in each project.
2) It is possible for the manager to assign 6$e$ employees to one of $p$ projects such that there is an equal number of employees in each project.

The OA is D

For each project to have the same number of employees, e/p must be an integer.

Question rephrased: Is e/p an integer?

1) It is possible for the manager to assign 11$e$ employees to one of $p$ projects such that there is an equal number of employees in each project.

=> 11e/p is an integer. Since p < 11 and 11 is a prime, for 11e/p to be an integer, e/p must be an integer. Sufficient.

2) It is possible for the manager to assign 6$e$ employees to one of $p$ projects such that there is an equal number of employees in each project.

So, we have 6e/p an integer.

Case 1: Say p = 6 and p = 12, then 6*12/6 = 12, an integer. We see that e/p = 12/6 = 2, an integer.
Case 2: Say p = 8 and p = 12, then 6*12/8 = 9, an integer. We see that e/p = 12/8 = 1.5, not an integer.

No unique answer. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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