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A sales manager must select a team of either three or of fou

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A sales manager must select a team of either three or of four salespeople to deliver a presentation to a prospective client. How many different teams can she select?

(1) The team will comprise either 1/8 or 1/6 of the total number of salespeople, depending on the size of the team.
(2) It is suspected that 20 salespeople will NOT be selected to be part of this team.
[Reveal] Spoiler: OA

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Re: A sales manager must select a team of either three or of fou [#permalink]

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A sales manager must select a team of either three or of four salespeople to deliver a presentation to a prospective client. How many different teams can she select?

(1) The team will comprise either 1/8 or 1/6 of the total number of salespeople, depending on the size of the team.
If the team has 4 salespeople, it will comprise 1/6 of the total.
If the team has 3 salespeople, it will comprise 1/8 of the total. It cannot be the other way round.
So we conclude that there are 4*6 or 3*8 = 24 people. Now we can determine how many different teams he can select.

(2) It is suspected that 20 salespeople will NOT be selected to be part of this team.
If the team has 4 salespeople, the total number is 4+20=24.
If the team has 3 salespeople, the total number is 3+20=23.
Since the total number varies, we CANNOT determine how many different teams he can select.

A
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Re: A sales manager must select a team of either three or of fou [#permalink]

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A sales manager must select a team of either three or of four salespeople to deliver a presentation to a prospective client. How many different teams can she select?

Say there are total of x salespeople, then the # of teams is \(C^3_x+C^4_x\). So, all we need to know is the total # of salespeople (x).

(1) The team will comprise either 1/8 or 1/6 of the total number of salespeople, depending on the size of the team --> x/8=3 --> x=24 (or x/6=4 --> x=24). Sufficient.

(2) It is suspected that 20 salespeople will NOT be selected to be part of this team. This implies that there could be total of 20+3=23 or 20+4=24 salespeople. Not sufficient.

Answer: A.
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Re: A sales manager must select a team of either three or of fou [#permalink]

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Re: A sales manager must select a team of either three or of fou   [#permalink] 06 Jan 2018, 08:39
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