GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2018, 21:34

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# A certain football coach allows his quarterback to call thre

Author Message
TAGS:

### Hide Tags

Manager
Joined: 04 Aug 2013
Posts: 97
Location: India
Schools: McCombs '17
GMAT 1: 670 Q47 V35
GPA: 3
WE: Manufacturing and Production (Pharmaceuticals and Biotech)
A certain football coach allows his quarterback to call thre  [#permalink]

### Show Tags

12 Jul 2014, 23:52
3
00:00

Difficulty:

85% (hard)

Question Stats:

46% (02:03) correct 54% (02:11) wrong based on 114 sessions

### HideShow timer Statistics

A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different arrangements of plays can be run, if the same play can’t be run more than once?

A. 24
B. 125
C. 243
D. 504
E. 729
Manager
Joined: 27 May 2014
Posts: 81
Re: A certain football coach allows his quarterback to call thre  [#permalink]

### Show Tags

13 Jul 2014, 07:21
6
1
Bunuel : is this approach correct.

Number of ways to choose the first play: 9
Second play: 8
Third:7

9*8*7= 504
##### General Discussion
Math Expert
Joined: 02 Sep 2009
Posts: 50002
Re: A certain football coach allows his quarterback to call thre  [#permalink]

### Show Tags

13 Jul 2014, 05:18
2
1
anceer wrote:
A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different arrangements of plays can be run, if the same play can’t be run more than once?

A. 24
B. 125
C. 243
D. 504
E. 729

P=3, R=4, and T=2.

There are following cases possible:

1. Different kinf of plays:

PRT (Any combination) = 3*4*2*3!=144.

2. Two same kind of plays and one from other kind of play:

PPR (Any combination. Notice that the two P's here must be different) = $$C^2_3*4*3!=72$$;
PPT = $$C^2_3*2*3!=36$$;

RRP = $$C^2_4*3*3!=108$$;
RRT = $$C^2_4*2*3!=72$$;

TTP = $$C^2_2*3*3!=18$$;
TTR = $$C^2_2*4*3!=24$$;

3. All three plays are of the same kind:

PPP = C^3_3*3!=6
RRR = C^3_4*3!=24
TTT is not possible because we have only two T's.

Total = 144 + 72 + 36 + 108 + 72 + 18 + 24 + 6 + 24 = 504.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 50002
Re: A certain football coach allows his quarterback to call thre  [#permalink]

### Show Tags

13 Jul 2014, 09:28
bankerboy30 wrote:
Bunuel : is this approach correct.

Number of ways to choose the first play: 9
Second play: 8
Third:7

9*8*7= 504

Yes. That's correct.
_________________
Intern
Status: Researching for Schools
Joined: 21 Apr 2013
Posts: 19
Location: United States
GMAT 1: 640 Q45 V34
GMAT 2: 730 Q49 V40
WE: Project Management (Computer Software)
Re: A certain football coach allows his quarterback to call thre  [#permalink]

### Show Tags

23 Jul 2014, 08:52
But the question said 'same play can’t be run more than once'. So I got 144 as my answer. Am I missing something. Please help!!!
Math Expert
Joined: 02 Sep 2009
Posts: 50002
Re: A certain football coach allows his quarterback to call thre  [#permalink]

### Show Tags

23 Jul 2014, 10:57
vivekisthere wrote:
But the question said 'same play can’t be run more than once'. So I got 144 as my answer. Am I missing something. Please help!!!

Yes, the same play can’t be run more than once but the kinds of plays could repeat. For example, PPT is valid because P's there are two different passing plays out of 3.
_________________
Director
Joined: 13 Mar 2017
Posts: 622
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: A certain football coach allows his quarterback to call thre  [#permalink]

### Show Tags

23 Apr 2018, 02:42
anceer wrote:
A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different arrangements of plays can be run, if the same play can’t be run more than once?

A. 24
B. 125
C. 243
D. 504
E. 729

The question has played smartly with the words where it says "Same play can't be run more than once" and not "Same category of play can't be run more than once"..

After understanding this, question becomes really simple as categorization of play as passing play, running play and trick play doesn't have any role in selecting the three plays and the total arrangements will be 9*8*7 = 504..

Though i don't understand such kind of wordings in a quant question of GMAT as QA question is framed to test quantitative skill and not VA skill..
Really a tricky question if one doesn't pay heed to wordings..
_________________

CAT 2017 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".

Re: A certain football coach allows his quarterback to call thre &nbs [#permalink] 23 Apr 2018, 02:42
Display posts from previous: Sort by