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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