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

Question

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.

Zarrolou · Accepted Answer

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

Bunuel · Answer

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.

gmatmo · Answer

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 ?

amanvermagmat · Answer

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.

mattisweb · Answer

Could "suspected", in terms of wording, also not imply probability, therefore meaning that (24C4)/(24C4+23C3) > 0.5, which is true? Then II would be sufficient as well.

egmat · Answer

mattisweb  I can see why "suspected" might seem ambiguous, but in GMAT Data Sufficiency, statements are  deterministic facts , not probabilistic scenarios. When GMAT says "It is suspected that 20 salespeople will NOT be selected," they're giving you a  definite condition  that must be true.

While your math is correct ( P(	ext{team of 4}) = \frac{\binom{24}{4}}{\binom{24}{4} + \binom{23}{3}} > 0.5 ), GMAT would never structure a DS statement this way because:

DS statements must be  verifiable facts , not probabilistic assertions 
 If statements could be interpreted probabilistically, DS problems would become unsolvable (infinite interpretations possible) 
 GMAT uses clear probability language when needed (e.g., "the probability that..." or "randomly selected")

You can practice similar DS questions  here  (you'll find a lot of OG questions) - select  Data Sufficiency  under  Quant  and choose  Medium  level questions to challenge yourself with nuanced language patterns.

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

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GMAT Data Sufficiency (DS) Questions

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