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26 Apr 2022, 22:48

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Sajjad1994

Project IR Butler 2019-20 - Get one IR Question Everyday
Question # 143, Date : 20-Feb-2020
This post is a part of Project IR Butler 2019-20. Click here for Details

Alvin (President), Brad (Vice President), Chad (Vice President), Dan (senior analyst), Ellinor (analyst), and Farsad (analyst) work at Goldly & Morgman, a corporate firm that works with consultants. The president supervises the vice president, who in turn supervises the senior analyst, who in turn supervises the analysts. There is one exception, which is that Brad does not supervise anyone. These are the only supervisory relationships involving these 6 employees.

Each proposal it receives from its consultants must be initially reviewed by exactly one employee. Each proposal reviewed by an employee must then be reviewed by that person’s supervisor. No other rules require anyone else to review the proposal. Anyone not required to review a given proposal will not review it.

Select Dan among reviewers for the maximum number of employees that could have reviewed a single proposal if Dan were among the reviewers. Select Alvin among reviewers for the maximum number of employees that could have reviewed a single proposal if Alvin were among the reviewers. Make only two selections, one in each column.

Dan among reviewers	Alvin among reviewers
		1
		2
		3
		4
		5
		6

A -> Analyst, SA -> Sr. Analyst, VP -> Vice Prez, P -> Prez

By charting out the hierarchy, we can make this easy.

Brad <- Alvin -> Chad -> Dan -> Ellinor & Farsad

If Dan is among the reviewers, then the proposal can either be shared with him or with Ellinor/Farsad. As we have to find the maximum number of reviewers, we start at the A level and go up to the P level.
Total -> A + SA + VP + P = 4

If Alvin is among the reviewers, then the proposal can either be shared with him (least reviews) or with Ellinor/Farsad (max reviews). As we have to find the maximum number of reviewers, we start at the A level and go up to the P level.
Total -> A + SA + VP + P = 4

Both selections will be 4.

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16 Sep 2025, 11:30

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Sajjad1994

Dan among reviewers: To maximize the number of reviewers, Dan must be at the top of a long review chain. This happens when an analyst initially reviews the proposal, which leads to Dan, then Chad, and finally Alvin. The maximum number of employees that could have reviewed a single proposal with Dan among them is 4 (Ellinor/Farsad, Dan, Chad, Alvin).

Alvin among reviewers: For Alvin to be among the reviewers, a proposal must be reviewed by anyone other than Alvin himself. The maximum number of employees that could have reviewed a single proposal if Alvin were among the reviewers is 4 (Ellinor/Farsad, Dan, Chad, Alvin). This occurs when an analyst initially reviews the proposal. The other options lead to shorter chains (Dan's chain is 3, Chad's/Brad's is 2), so the maximum is 4.