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In how many ways can a coach select a 4-person university team from a
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24 Aug 2015, 16:49

6

15

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

76% (01:03) correct 24% (01:07) wrong based on 512 sessions

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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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24 Aug 2015, 18:23

6

1

dav90 wrote:

pate13 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 greater than the number of slots on the team. 2) 60% of the 20 athletes are eligible to play on the four-person university team.

Even 1st statement can tell the total eligible candidates, then why answer is not D?

The 1st statement basically only states, eligible candidates > 3*(4). so the value could be greater than 12, so there is no way one can find the # of possibilities if the total eligible candidates list is unknown.

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24 Aug 2015, 18:08

pate13 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 greater than the number of slots on the team. 2) 60% of the 20 athletes are eligible to play on the four-person university team.

Even 1st statement can tell the total eligible candidates, then why answer is not D?
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Re: In how many ways can a coach select a 4-person university team from a
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24 Aug 2015, 18:27

1

kingjamesrules wrote:

dav90 wrote:

pate13 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 greater than the number of slots on the team. 2) 60% of the 20 athletes are eligible to play on the four-person university team.

Even 1st statement can tell the total eligible candidates, then why answer is not D?

The 1st statement basically only states, eligible candidates > 3*(4). so the value could be greater than 12, so there is no way one can find the # of possibilities if the total eligible candidates list is unknown.

hope this answers. Kudos if this helped.

I missed '' Greater than"...
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Re: In how many ways can a coach select a 4-person university team from a
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28 Aug 2015, 06:39

2

kingjamesrules wrote:

dav90 wrote:

pate13 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 greater than the number of slots on the team. 2) 60% of the 20 athletes are eligible to play on the four-person university team.

Even 1st statement can tell the total eligible candidates, then why answer is not D?

The 1st statement basically only states, eligible candidates > 3*(4). so the value could be greater than 12, so there is no way one can find the # of possibilities if the total eligible candidates list is unknown.

hope this answers. Kudos if this helped.

I can understand your argument if the 1st statement said: "The number of eligible candidates is greater than 3 times the number of slots on the team". But it actually says:"The number of eligible candidates IS three times greater than the number of slots on the team. I still think the answer is D. Both these statements give the same information. And that information is enough. Number of ways to choose a 4 person team from 12 candidates = 12Choose4.

Re: In how many ways can a coach select a 4-person university team from a
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28 Aug 2015, 06:54

1

I can understand your argument if the 1st statement said: "The number of eligible candidates is greater than 3 times the number of slots on the team". But it actually says:"The number of eligible candidates IS three times greater than the number of slots on the team. I still think the answer is D. Both these statements give the same information. And that information is enough. Number of ways to choose a 4 person team from 12 candidates = 12Choose4.[/quote]

I completely agree. That's why I posted this question: to see other people's interpretation.

Re: In how many ways can a coach select a 4-person university team from a
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28 Aug 2015, 07:01

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hb4100 wrote:

I can understand your argument if the 1st statement said: "The number of eligible candidates is greater than 3 times the number of slots on the team". But it actually says:"The number of eligible candidates IS three times greater than the number of slots on the team. I still think the answer is D. Both these statements give the same information. And that information is enough. Number of ways to choose a 4 person team from 12 candidates = 12Choose4.

A better way to rephrase statement 1 should be " The number of eligible candidates is greater than three times the number of slots on the team." The only way this statement can be interpreted is Eligible candidates > 3*4

But even without this rephrase, Eligible candidates = 3*4 ONLY if the statement mentioned it this way. But the additional "greater than" will make me suspicious of this equality.

Re: In how many ways can a coach select a 4-person university team from a
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28 Aug 2015, 07:59

pate13 wrote:

I can understand your argument if the 1st statement said: "The number of eligible candidates is greater than 3 times the number of slots on the team". But it actually says:"The number of eligible candidates IS three times greater than the number of slots on the team. I still think the answer is D. Both these statements give the same information. And that information is enough. Number of ways to choose a 4 person team from 12 candidates = 12Choose4.

I completely agree. That's why I posted this question: to see other people's interpretation.[/quote]

I also think it's D if the actual question is written like this. I agree with both of you, it clearly says that it is 3 times greater and therefore the answer is D (both statements provide the same information).

Re: In how many ways can a coach select a 4-person university team from a
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08 Sep 2015, 13:00

1

The answer is clearly D. This is a sub-600 level question that has been categorized as 700+ due to incorrect wording by the source and the confusion it has caused.

Re: In how many ways can a coach select a 4-person university team from a
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08 Sep 2015, 16:56

I also want to point out a flaw in the second statement, which states that 60 % of 20 athletes are eligible.

We should not assume that there are not categories as well, there can be 40 other candidates eligible who are not athletes but fall under any other abc category

Re: In how many ways can a coach select a 4-person university team from a
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19 Jul 2017, 22:26

kingjamesrules wrote:

dav90 wrote:

pate13 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 greater than the number of slots on the team. 2) 60% of the 20 athletes are eligible to play on the four-person university team.

Even 1st statement can tell the total eligible candidates, then why answer is not D?

The 1st statement basically only states, eligible candidates > 3*(4). so the value could be greater than 12, so there is no way one can find the # of possibilities if the total eligible candidates list is unknown.

hope this answers. Kudos if this helped.

That's not correct. "3 times greater than 4" means 4+3*4 =16

What you are saying should have been written as "more than 3 times greater than 4"

Re: In how many ways can a coach select a 4-person university team from a
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25 Oct 2017, 20:05

1

I agree with Rekha

3 times as many as = 3x4 = 12 3 times greater than = 3 + 3 *4 = 16 greater than 3 times >3x =. >12

Statement 1 is definitely not 3 times as many as. but says 3 times greater than = 16, then statement 1 must be sufficient. However then , statement 1 and statement 2 are contradicting to each other, statement1 says 16 and statement2 will say 12.

OR on the whole, i am not understanding meaning of statements properly.

Re: In how many ways can a coach select a 4-person university team from a
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25 Oct 2017, 21:45

I think we need someone from VeritasPrep to comment on this question, because its causing a lot of confusion. A lot of people will benefit if the meaning of '3 times greater than' is made clear.

Re: In how many ways can a coach select a 4-person university team from a
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06 Mar 2018, 03:45

pate13 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 greater than the number of slots on the team. 2) 60% of the 20 athletes are eligible to play on the four-person university team.

The actual question stem is: "In how many ways can a coach select a university team from a pool of eligible candidates?" "4-person" does not appear in the online version.

Some reprinted books left the warehouse before we caught the mistake and hence you might see the question as it appears above.
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Re: In how many ways can a coach select a 4-person university team from a
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06 Mar 2018, 08:27

Top Contributor

pate13 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: 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

Re: In how many ways can a coach select a 4-person university team from a
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08 Mar 2018, 16:50

pate13 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.

Re: In how many ways can a coach select a 4-person university team from a
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02 Jul 2019, 05:18

pate13 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.

Even with the edit suggested above, the wording is still deeply problematic. I have no idea who the "athletes" in Statement 2 are; the question only mentions "candidates". Are we choosing an athletic team, or a debate team? Are the 20 athletes the only candidates? I don't even understand how there can be any ineligible candidates when the question tells us the coach is only selecting people "from a pool of eligible candidates".
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