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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 fou [#permalink]

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New post 15 Jun 2013, 05:27
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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.

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

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New post 15 Jun 2013, 05:34
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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.

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

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New post 15 Jun 2013, 05:38
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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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New post 18 Feb 2018, 08:41
I really do not understand why it is clear, that it is x/8=3. It is not mentioned that the given fractions are respectively why couldn't it be x/6=3 ?
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Re: A sales manager must select a team of either three or of fou [#permalink]

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New post 19 Feb 2018, 02:49
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gmatmo wrote:
I really do not understand why it is clear, that it is x/8=3. It is not mentioned that the given fractions are respectively why couldn't it be x/6=3 ?


Hi

This is because 1/8 of a positive number will always be lesser than 1/6 of that number. So if total number of salespeople are n, then n/8 must be < n/6
So here n/8 can only be 3 not 4.
Re: A sales manager must select a team of either three or of fou   [#permalink] 19 Feb 2018, 02:49
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