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Carmelo and LeBron participate in a seven-person footrace on the baske

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Carmelo and LeBron participate in a seven-person footrace on the baske  [#permalink]

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New post 21 Aug 2015, 03:57
2
10
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A
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D
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Difficulty:

  65% (hard)

Question Stats:

55% (01:48) correct 45% (02:04) wrong based on 148 sessions

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Carmelo and LeBron participate in a seven-person footrace on the basketball court during All-Star Weekend. If all seven contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?

(A) 5040
(B) 2520
(C) 720
(D) 120
(E) 42

Kudos for a correct solution.

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Re: Carmelo and LeBron participate in a seven-person footrace on the baske  [#permalink]

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New post 21 Aug 2015, 06:35
7! = 5040
5040/2=2520 half the time carmelo is in front, vice versa

Answer:
(B) 2520
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Re: Carmelo and LeBron participate in a seven-person footrace on the baske  [#permalink]

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New post 21 Aug 2015, 20:49
3
Bunuel wrote:
Carmelo and LeBron participate in a seven-person footrace on the basketball court during All-Star Weekend. If all seven contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?

(A) 5040 (B) 2520 (C) 720 (D) 120 (E) 42


Ans: B
Solution: arranging 7 person on 7 position where specific one person is always ahead of the other specific = 7!/2 = 2520
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Re: Carmelo and LeBron participate in a seven-person footrace on the baske  [#permalink]

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New post 30 Aug 2015, 08:55
1
Bunuel wrote:
Carmelo and LeBron participate in a seven-person footrace on the basketball court during All-Star Weekend. If all seven contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?

(A) 5040
(B) 2520
(C) 720
(D) 120
(E) 42

Kudos for a correct solution.


PRINCETON REVIEW OFFICIAL SOLUTION:

Carmelo beats LeBron? Carmelo beats LeBron? No one said anything about specific results, especially not on a question that includes so many people.

Many questions on the GMAT can be overwhelming in appearance so first thing…Relax. This question looks nasty, but it’s pretty straightforward, requiring two things: the basic first calculation and then some additional work to solve the problem. It would be extremely painful to try to calculate this whole question in one fell swoop. So don’t.

Calculate out all possibilities first to get your bearings. That is, how many different arrangements, period? Since the order of arrangement again matters, this is another permutation. And since we’re placing all seven runners, this calculation is…

7 x 6 x 5 x 4 x 3 x 2 x 1, cash and prizes worth 5040 arrangements.

Now, what to do? Again, some nice deep breathing to control your nerves – relax and think. These 5040 arrangements are a comprehensive list; every possible seven-person order of finish has been counted. So, we have accounted for every time Carmelo beats LeBron AND every time LeBron beats Carmelo. Doesn’t it make sense that, for every time Carmelo beats LeBron, there is exactly one other instance in which LeBron beats Carmelo? Or more simply, doesn’t it make sense that, if these 5040 represents everything, that Carmelo beats LeBron exactly 50% of the time and vice versa?

The thought takes time. You need to have the presence to recognize that grinding your way in, around, and through this question could take roughly forever. Stepping back and recognizing that this is simply a 50/50 proposition and applying that thought to the 5040 you cranked out gives you 2520. The answer is B.

A consistent approach to certain question types can play a major role in earning more points as you build your analytic and math skills as well as your confidence. Coaches in basketball can improve your game just like a GMAT coach can do the same.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: Carmelo and LeBron participate in a seven-person footrace on the baske  [#permalink]

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New post 30 Aug 2015, 08:57
Bunuel wrote:
Bunuel wrote:
Carmelo and LeBron participate in a seven-person footrace on the basketball court during All-Star Weekend. If all seven contestants finish (including Charles Barkley) and there are no ties, how many different arrangements of finishes are there in which Carmelo defeats LeBron?

(A) 5040
(B) 2520
(C) 720
(D) 120
(E) 42

Kudos for a correct solution.


PRINCETON REVIEW OFFICIAL SOLUTION:

Carmelo beats LeBron? Carmelo beats LeBron? No one said anything about specific results, especially not on a question that includes so many people.

Many questions on the GMAT can be overwhelming in appearance so first thing…Relax. This question looks nasty, but it’s pretty straightforward, requiring two things: the basic first calculation and then some additional work to solve the problem. It would be extremely painful to try to calculate this whole question in one fell swoop. So don’t.

Calculate out all possibilities first to get your bearings. That is, how many different arrangements, period? Since the order of arrangement again matters, this is another permutation. And since we’re placing all seven runners, this calculation is…

7 x 6 x 5 x 4 x 3 x 2 x 1, cash and prizes worth 5040 arrangements.

Now, what to do? Again, some nice deep breathing to control your nerves – relax and think. These 5040 arrangements are a comprehensive list; every possible seven-person order of finish has been counted. So, we have accounted for every time Carmelo beats LeBron AND every time LeBron beats Carmelo. Doesn’t it make sense that, for every time Carmelo beats LeBron, there is exactly one other instance in which LeBron beats Carmelo? Or more simply, doesn’t it make sense that, if these 5040 represents everything, that Carmelo beats LeBron exactly 50% of the time and vice versa?

The thought takes time. You need to have the presence to recognize that grinding your way in, around, and through this question could take roughly forever. Stepping back and recognizing that this is simply a 50/50 proposition and applying that thought to the 5040 you cranked out gives you 2520. The answer is B.

A consistent approach to certain question types can play a major role in earning more points as you build your analytic and math skills as well as your confidence. Coaches in basketball can improve your game just like a GMAT coach can do the same.


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_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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Re: Carmelo and LeBron participate in a seven-person footrace on the baske  [#permalink]

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New post 19 Apr 2017, 16:32
the question leaves me stunned with its ambiguous words. I hardly catch the idea that there are 7 runners in a race. I just bother "tie" or "basketball".
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Re: Carmelo and LeBron participate in a seven-person footrace on the baske  [#permalink]

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Re: Carmelo and LeBron participate in a seven-person footrace on the baske &nbs [#permalink] 10 Aug 2018, 01:42
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