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In how many ways can a coach select a 4-person university te

This topic has 2 expert replies and 0 member replies

In how many ways can a coach select a 4-person university te

Post Tue Mar 06, 2018 7:24 am
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.

What's the best way to determine whether statement 1 is sufficient? Can any experts help?

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Post Tue Mar 06, 2018 8:23 am
ardz24 wrote:
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.
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: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

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

Cheers,
Brent

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Brent Hanneson – Creator of GMATPrepNow.com
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Post Thu Mar 08, 2018 5:02 pm
ardz24 wrote:
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.
To determine the number of ways a coach can select a 4-person university team from a pool of eligible candidates, we need to determine the number of candidates.

Statement One Alone:

The number of eligible candidates is three times as great as the number of slots on the team.

Since the number of slots for the team is 4, the number of eligible candidates is 12. Thus, there are 12C4 ways to select the team. Statement one alone is sufficient to answer the question.

Statement Two Alone:

60% of the 20 athletes are eligible to play on the four-person university team.

The number of eligible athletes is 0.6 x 20 = 12. Thus, there are 12C4 ways to select the team. Statement two alone is sufficient to answer the question.

Answer: D

_________________
Jeffrey Miller Head of GMAT Instruction

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