In how many ways can a coach select a 4-person university team from a pool of eligible candidates?

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In how many ways can a coach select a 4-person university team from a pool of eligible candidates?

(1) The number of eligible candidates is three times as great as the number of slots on the team.
(2) 60% of the 20 athletes are eligible to play on the four-person university team.


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BTGmoderatorDC wrote:
Thu May 19, 2022 10:23 pm
In how many ways can a coach select a 4-person university team from a pool of eligible candidates?

(1) The number of eligible candidates is three times as great as the number of slots on the team.
(2) 60% of the 20 athletes are eligible to play on the four-person university team.


OA D

Source: Veritas Prep
Target question: In how many ways can a coach select a 4-person university team from a pool of eligible candidates?
This is a great candidate for rephrasing the target question.

In order to determine the number of ways to select a 4-person university team, we need to know the number of eligible candidates.
Let's let n = the number of eligible candidates
Once we know the value of n, then the total number of ways to select a 4 people will equal nC4

So, let's REPHRASE the target question....
REPHRASED target question: What is the value of n?

Aside: Below, you'll find a video with tips on rephrasing the target question

Statement 1: The number of eligible candidates is three times as great as the number of slots on the team.
There are 4 available "slots"
So, we can write: n = (3)(4)
In other words, n = 12 (there are 12 eligible candidates)
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: 60% of the 20 athletes are eligible to play on the four-person university team.
In other words, 60% of 20 = n
Solve, to get n = 12 (there are 12 eligible candidates)
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: D
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