January 22, 2019 January 22, 2019 10:00 PM PST 11:00 PM PST In case you didn’t notice, we recently held the 1st ever GMAT game show and it was awesome! See who won a full GMAT course, and register to the next one. January 26, 2019 January 26, 2019 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 19 Nov 2011
Posts: 8

If a code word is defined to be a sequence of different
[#permalink]
Show Tags
Updated on: 28 Jan 2012, 03:02
Question Stats:
69% (01:08) correct 31% (01:24) wrong based on 1109 sessions
HideShow timer Statistics
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 5letter code words to the number of 4letter code words? A. 5 to 4 B. 3 to 2 C. 2 to 1 D. 5 to 1 E. 6 to 1
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by RadhaKrishnan on 28 Jan 2012, 02:59.
Last edited by Bunuel on 28 Jan 2012, 03:02, edited 1 time in total.
Added the OA




Math Expert
Joined: 02 Sep 2009
Posts: 52385

Re: Ratio
[#permalink]
Show Tags
28 Jan 2012, 03:02
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 5letter code words to the number of 4letter 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.
_________________
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? Extrahard Quant Tests with Brilliant Analytics




Manager
Joined: 24 Mar 2010
Posts: 64

Re: If a code word is defined to be a sequence of different
[#permalink]
Show Tags
23 Dec 2012, 12:29
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 > \(10 * 9 * 8 * 7\) Required Ratio > \((10 * 9 *8 * 7 * 6)/(10 * 9* 8 * 7)\) = \(6:1\)
_________________
 Stay Hungry, stay Foolish 




Senior Manager
Joined: 13 Aug 2012
Posts: 426
Concentration: Marketing, Finance
GPA: 3.23

Re: If a code word is defined to be a sequence of different
[#permalink]
Show Tags
28 Dec 2012, 05:43
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 5letter code words to the number of 4letter code words?
A. 5 to 4 B. 3 to 2 C. 2 to 1 D. 5 to 1 E. 6 to 1 Number of 5letter code formed from 10 letters: \(=10*9*8*7*6\) Number of 4letter code formed from 10 letters: \(=10*9*8*7\) Answer: 6 to 1 or E
_________________
Impossible is nothing to God.



Senior Manager
Joined: 13 Aug 2012
Posts: 426
Concentration: Marketing, Finance
GPA: 3.23

Re: If a code word is defined to be a sequence of different
[#permalink]
Show Tags
28 Dec 2012, 05:56
Orange08 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 5letter code words to the number of 4letter code words?
A. 5 to 4 B. 3 to 2 C. 2 to 1 D. 5 to 1 E. 6 to 1 Number of ways to form 5letter code: 10!/5! = 10*9*8*7*6 Number of ways to form 4letter code: 10!/6! = 10*9*8*7 Ratio: 6 to 1 Answer : E
_________________
Impossible is nothing to God.



Senior Manager
Joined: 28 Jul 2011
Posts: 345
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE: Accounting (Commercial Banking)

Re: Ratio
[#permalink]
Show Tags
30 Mar 2013, 08:04
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 5letter code words to the number of 4letter 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 aresearcherplanstoidentifyeachparticipantinacertain134584.htmlCan you please when to use permutaions or Combinations in these type of problems?
_________________
+1 Kudos If found helpful..



Math Expert
Joined: 02 Sep 2009
Posts: 52385

Re: Ratio
[#permalink]
Show Tags
31 Mar 2013, 07:51
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 5letter code words to the number of 4letter 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 aresearcherplanstoidentifyeachparticipantinacertain134584.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: aresearcherplanstoidentifyeachparticipantinacertain134584.html#p1150091
_________________
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? Extrahard Quant Tests with Brilliant Analytics



LBS Thread Master
Joined: 13 Jan 2015
Posts: 102
Location: United Kingdom
Concentration: Other, General Management

Re: If a code word is defined to be a sequence of different
[#permalink]
Show Tags
31 Jan 2015, 07:18
Hello Bunuel,
Thank you very much for responding.
My problem with your initial calculation is that when i do understand how you got 6! in the bottom part of your example above.
When i calculate it, it goes 10 Choose 5 is = 10*9*8*7*6 / 5*4*3*2*1
And then 10 Choose 4 i= 10*9*8*7 / 4*3*2*1
when I calculate 10 Choose 5 / 10 Choose 4.... I get 6/5
I do not know where the error is coming from
Thanks alot



Math Expert
Joined: 02 Sep 2009
Posts: 52385

Re: If a code word is defined to be a sequence of different
[#permalink]
Show Tags
31 Jan 2015, 07:23



Director
Joined: 17 Dec 2012
Posts: 625
Location: India

If a code word is defined to be a sequence of different
[#permalink]
Show Tags
18 Mar 2016, 01:42
Take 1 case: ABCDE for 5 letter code and ABCD for 4 letter code. You Choose 5 at a time and 4 at a time and order is important. So the formula is nPr. Therefore the ratio is 10P5/ 10P4 = 6:1 Hence E.
_________________
Srinivasan Vaidyaraman Sravna Holistic Solutions http://www.sravnatestprep.com
Holistic and Systematic Approach



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13368
Location: United States (CA)

Re: If a code word is defined to be a sequence of different
[#permalink]
Show Tags
05 Jan 2018, 15:46
Hi All, To calculate the number of 5letter codes and 4letter codes, we have to set up 2 permutations. There's a 'shortcut' though  since the answer choices are RATIOS, we don't actually have to calculate the total number of each type of code. Total 5letter codes = (10)(9)(8)(7)(6) Total 4letter codes = (10)(9)(8)(7) Notice how the number of 5letter codes is the total of 4letter codes multiplied by 6. Thus, the ratio of codes is 6:1 Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Intern
Joined: 25 Feb 2018
Posts: 1

Re: If a code word is defined to be a sequence of different
[#permalink]
Show Tags
15 May 2018, 07:48
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 5letter code words to the number of 4letter 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 \(P^4_{10}\); Answer: E. Hi Bunuel, I struggle with the the order of \(P^5_{10}\). From the theory I understood that the permutation is defined as: \(P^n_{k}\) n being the set of distinct objects and k being the number of objects chosen. Why is this upside down? Thanks!



Math Expert
Joined: 02 Sep 2009
Posts: 52385

Re: If a code word is defined to be a sequence of different
[#permalink]
Show Tags
15 May 2018, 08:22
panache67 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 5letter code words to the number of 4letter 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 \(P^4_{10}\); Answer: E. Hi Bunuel, I struggle with the the order of \(P^5_{10}\). From the theory I understood that the permutation is defined as: \(P^n_{k}\) n being the set of distinct objects and k being the number of objects chosen. Why is this upside down? Thanks! \(P^5_{10}\), \(P^{10}_5\), 10P5 are all the same: choosing 5 out of 10, when the order matters. Just different ways of writing the same. Could it be choosing 10 out of 5?
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 31 Mar 2018
Posts: 54

Re: If a code word is defined to be a sequence of different
[#permalink]
Show Tags
05 Nov 2018, 08:18
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 5letter code words to the number of 4letter code words?
A. 5 to 4 B. 3 to 2 C. 2 to 1 D. 5 to 1 E. 6 to 1 10P5 /10P4 . Why we used Permutations not combinations as here sequence is important (Code)



Senior Manager
Joined: 22 Feb 2018
Posts: 416

Re: If a code word is defined to be a sequence of different
[#permalink]
Show Tags
05 Nov 2018, 09:15
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 5letter code words to the number of 4letter code words?
A. 5 to 4 B. 3 to 2 C. 2 to 1 D. 5 to 1 E. 6 to 1 OA: E Number of \(5\) letter code words \(= 10*9*8*7*6\) Number of \(4\) letter code words \(= 10*9*8*7\) the ratio of the number of \(5\)letter code words to the number of \(4\)letter code words \(=\frac{ 10*9*8*7*6}{10*9*8*7}=\frac{6}{1}\)
_________________
Good, good Let the kudos flow through you



Director
Joined: 11 Feb 2015
Posts: 679

If a code word is defined to be a sequence of different
[#permalink]
Show Tags
06 Nov 2018, 08:44
The ratio of the number of 5letter code words to the number of 4letter code words chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J is given by 10P5/10P4 = 6:1 Option E is the correct Ans!!
_________________
"Please hit +1 Kudos if you like this post"
_________________ Manish
"Only I can change my life. No one can do it for me"




If a code word is defined to be a sequence of different &nbs
[#permalink]
06 Nov 2018, 08:44






