|
Author |
Message |
|
TAGS:
|
|
|
Intern
Joined: 19 Nov 2011
Posts: 8
Followers: 0
Kudos [?]:
2
[0], given: 0
|
If a code word is defined to be a sequence of different [#permalink]
 28 Jan 2012, 03:59
Question Stats:
74% (01:43) correct
26% (00:37) wrong based on 50 sessions
If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words? A. 5 to 4 B. 3 to 2 C. 2 to 1 D. 5 to 1 E. 6 to 1
Last edited by Bunuel on 28 Jan 2012, 04:02, edited 1 time in total.
Added the OA
|
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12094
Followers: 1875
Kudos [?]:
10094
[1] , given: 959
|
1
This post received
KUDOS
RadhaKrishnan wrote: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?
A. 5 to 4
B. 3 to 2
C. 2 to 1
D. 5 to 1
E. 6 to 1 Notice that as we are dealing with code words then the order of the letters matters. # of ways to choose 5 different letters out of given 10 letters when the order of chosen letters matters (as for example code word ABCDE is different from BCDEA) is P^5_{10}; # of ways to choose 4 different letters out of given 10 letters when the order of chosen letters matters is P^4_{10}; Ratio=\frac{P^5_{10}}{P^4_{10}}=\frac{10!}{5!}*\frac{6!}{10!}=\frac{6}{1}. Answer: E.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders
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. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
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. NEW!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 24 Mar 2010
Posts: 82
Followers: 0
Kudos [?]:
8
[0], given: 133
|
Re: If a code word is defined to be a sequence of different [#permalink]
23 Dec 2012, 13:29
Numbers of Options applicable for 5 letter digit -> 10 * 9 * 8 * 7 * 6 ( as option pool for first digit is 10, for second 9 because one is removed and so on) Numbers of Options applicable for 5 letter digit -> 10 * 9 * 8 * 7Required Ratio -> (10 * 9 *8 * 7 * 6)/(10 * 9* 8 * 7) = 6:1
_________________
- Stay Hungry, stay Foolish -
|
|
|
|
|
|
Senior Manager
Joined: 13 Aug 2012
Posts: 468
Followers: 13
Kudos [?]:
88
[0], given: 11
|
Re: If a code word is defined to be a sequence of different [#permalink]
28 Dec 2012, 06:43
RadhaKrishnan wrote: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?
A. 5 to 4
B. 3 to 2
C. 2 to 1
D. 5 to 1
E. 6 to 1 Number of 5-letter code formed from 10 letters: =10*9*8*7*6Number of 4-letter code formed from 10 letters: =10*9*8*7Answer: 6 to 1 or E
|
|
|
|
|
|
Director
Joined: 28 Jul 2011
Posts: 593
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 1
Kudos [?]:
26
[0], given: 16
|
Bunuel wrote: RadhaKrishnan wrote: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?
A. 5 to 4
B. 3 to 2
C. 2 to 1
D. 5 to 1
E. 6 to 1 Notice that as we are dealing with code words then the order of the letters matters. # of ways to choose 5 different letters out of given 10 letters when the order of chosen letters matters (as for example code word ABCDE is different from BCDEA) is P^5_{10}; # of ways to choose 4 different letters out of given 10 letters when the order of chosen letters matters is P^4_{10}; Ratio=\frac{P^5_{10}}{P^4_{10}}=\frac{10!}{5!}*\frac{6!}{10!}=\frac{6}{1}. Answer: E. Hi Bunnel, In this problem you have used Permutations, but in the problem you have used combination, which also deals with code a-researcher-plans-to-identify-each-participant-in-a-certain-134584.htmlCan you please when to use permutaions or Combinations in these type of problems?
_________________
+1 Kudos If found helpful..
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 12094
Followers: 1875
Kudos [?]:
10094
[0], given: 959
|
mydreammba wrote: Bunuel wrote: RadhaKrishnan wrote: If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?
A. 5 to 4
B. 3 to 2
C. 2 to 1
D. 5 to 1
E. 6 to 1 Notice that as we are dealing with code words then the order of the letters matters. # of ways to choose 5 different letters out of given 10 letters when the order of chosen letters matters (as for example code word ABCDE is different from BCDEA) is P^5_{10}; # of ways to choose 4 different letters out of given 10 letters when the order of chosen letters matters is P^4_{10}; Ratio=\frac{P^5_{10}}{P^4_{10}}=\frac{10!}{5!}*\frac{6!}{10!}=\frac{6}{1}. Answer: E. Hi Bunnel, In this problem you have used Permutations, but in the problem you have used combination, which also deals with code a-researcher-plans-to-identify-each-participant-in-a-certain-134584.htmlCan you please when to use permutaions or Combinations in these type of problems? In this case the order of the letters matters, but in other question we are only interested in codes which are in alphabetical order (so we are interested in only one particular order). This post might help: a-researcher-plans-to-identify-each-participant-in-a-certain-134584.html#p1150091
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders
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. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
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. NEW!!!, 11 New DS set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
close
