It is currently 22 Nov 2017, 04:27

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A company assigns product codes consisting of all the letter

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
Retired Moderator
avatar
Joined: 27 Aug 2012
Posts: 1184

Kudos [?]: 1961 [2], given: 152

Premium Member
A company assigns product codes consisting of all the letter [#permalink]

Show Tags

New post 01 Sep 2013, 07:49
2
This post received
KUDOS
9
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

54% (01:21) correct 46% (01:26) wrong based on 235 sessions

HideShow timer Statistics

A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 3 letters in its codes, and all letters can be repeated in any one code?

A.15600
B.16226
C.17576
D.18278
E.28572
[Reveal] Spoiler: OA

_________________

UPDATED : e-GMAT SC Resources-Consolidated || ALL RC Resources-Consolidated || ALL SC Resources-Consolidated || UPDATED : AWA compilations-109 Analysis of Argument Essays || GMAC's IR Prep Tool

Calling all Columbia (CBS) MBA Applicants: (2018 Intake) Class of 2020 !!! NEW !!!

GMAT Club guide - OG 11-12-13 || Veritas Blog || Manhattan GMAT Blog


KUDOS please, if you like the post or if it helps :-)

Kudos [?]: 1961 [2], given: 152

6 KUDOS received
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 627

Kudos [?]: 1388 [6], given: 136

Premium Member
Re: A company assigns product codes consisting of all the letter [#permalink]

Show Tags

New post 01 Sep 2013, 08:20
6
This post received
KUDOS
bagdbmba wrote:
A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 3 letters in its codes, and all letters can be repeated in any one code?

A.15600
B.16226
C.17576
D.18278
E.28572


The no of ways in which the company can make codes of 1 letter : 26
# for 2 letters : 26*26 = _ _ 6
# for 3 letters : _ _ 6 * 26 =_ _ _ _ 6

The total : By adding all of them , the units digit would be : 6+6+6 = _ _ _ _ _ 8

D.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Kudos [?]: 1388 [6], given: 136

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42302

Kudos [?]: 133019 [1], given: 12402

Re: A company assigns product codes consisting of all the letter [#permalink]

Show Tags

New post 01 Sep 2013, 10:58
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
bagdbmba wrote:
A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 3 letters in its codes, and all letters can be repeated in any one code?

A.15600
B.16226
C.17576
D.18278
E.28572


Similar question from GMAT Prep:
Quote:
A certain stock exchange designates each stock with a 1, 2, or 3 letter code, where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order constitute a different code, how many different stocks is it possible to uniquely designate with these codes?

A. 2,951
B. 8,125
C. 15,600
D. 16,302
E. 18,278


Discussed here: a-certain-stock-exchange-designates-each-stock-with-a-86656.html

Other similar questions to practice:
all-of-the-stocks-on-the-over-the-counter-market-are-126630.html
if-a-code-word-is-defined-to-be-a-sequence-of-different-126652.html
the-simplastic-language-has-only-2-unique-values-and-105845.html
a-4-letter-code-word-consists-of-letters-a-b-and-c-if-the-59065.html
a-certain-stock-exchange-designates-each-stock-with-a-86656.html
a-5-digit-code-consists-of-one-number-digit-chosen-from-132263.html
a-company-that-ships-boxes-to-a-total-of-12-distribution-95946.html
a-company-plans-to-assign-identification-numbers-to-its-empl-69248.html
the-security-gate-at-a-storage-facility-requires-a-five-109932.html
all-of-the-bonds-on-a-certain-exchange-are-designated-by-a-150820.html
a-local-bank-that-has-15-branches-uses-a-two-digit-code-to-98109.html
a-researcher-plans-to-identify-each-participant-in-a-certain-134584.html
baker-s-dozen-128782-20.html#p1057502
in-a-certain-appliance-store-each-model-of-television-is-136646.html
m04q29-color-coding-70074.html
john-has-12-clients-and-he-wants-to-use-color-coding-to-iden-107307.html
how-many-4-digit-even-numbers-do-not-use-any-digit-more-than-101874.html
a-certain-stock-exchange-designates-each-stock-with-a-85831.html

Hope it helps.
_________________

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

Kudos [?]: 133019 [1], given: 12402

1 KUDOS received
Retired Moderator
avatar
Joined: 27 Aug 2012
Posts: 1184

Kudos [?]: 1961 [1], given: 152

Premium Member
Re: A company assigns product codes consisting of all the letter [#permalink]

Show Tags

New post 03 Sep 2013, 08:28
1
This post received
KUDOS
Thanks Bunuel for not only referring to the solution but also sharing several similar problems for practice.
Really appreciate it.

+1 Sir!
_________________

UPDATED : e-GMAT SC Resources-Consolidated || ALL RC Resources-Consolidated || ALL SC Resources-Consolidated || UPDATED : AWA compilations-109 Analysis of Argument Essays || GMAC's IR Prep Tool

Calling all Columbia (CBS) MBA Applicants: (2018 Intake) Class of 2020 !!! NEW !!!

GMAT Club guide - OG 11-12-13 || Veritas Blog || Manhattan GMAT Blog


KUDOS please, if you like the post or if it helps :-)

Kudos [?]: 1961 [1], given: 152

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15565

Kudos [?]: 283 [0], given: 0

Premium Member
Re: A company assigns product codes consisting of all the letter [#permalink]

Show Tags

New post 02 Feb 2016, 07:56
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

Intern
Intern
avatar
Joined: 23 Feb 2013
Posts: 8

Kudos [?]: [0], given: 22

Re: A company assigns product codes consisting of all the letter [#permalink]

Show Tags

New post 06 Feb 2016, 14:33
mau5 wrote:
bagdbmba wrote:
A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 3 letters in its codes, and all letters can be repeated in any one code?

A.15600
B.16226
C.17576
D.18278
E.28572


The no of ways in which the company can make codes of 1 letter : 26
# for 2 letters : 26*26 = _ _ 6
# for 3 letters : _ _ 6 * 26 =_ _ _ _ 6

The total : By adding all of them , the units digit would be : 6+6+6 = _ _ _ _ _ 8

D.


How could I use the combinatorics formula to solve this? I'm not getting the correct answer if I try the formula: nCk= n!/k!(n-k)!

Kudos [?]: [0], given: 22

Expert Post
4 KUDOS received
SVP
SVP
User avatar
G
Joined: 12 Sep 2015
Posts: 1850

Kudos [?]: 2622 [4], given: 362

Location: Canada
Re: A company assigns product codes consisting of all the letter [#permalink]

Show Tags

New post 06 Feb 2016, 15:49
4
This post received
KUDOS
Expert's post
bagdbmba wrote:
A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 3 letters in its codes, and all letters can be repeated in any one code?

A.15600
B.16226
C.17576
D.18278
E.28572


1-letter codes
26 letters, so there are 26 possible codes

2-letter codes
There are 26 options for the 1st letter, and 26 options for the 2nd letter.
So, the number of 2-letter codes = (26)(26) = 26²

3-letter codes
There are 26 options for the 1st letter, 26 options for the 2nd letter, and 26 options for the 3rd letter.
So, the number of 3-letter codes = (26)(26)(26) = 26³

So, the TOTAL number of codes = 26 + 26² + 26³

IMPORTANT: Before we perform ANY calculations, we should first look at the answer choices, because we know that the GMAT test-makers are very reasonable, and they don't care whether we're able make long, tedious calculations. Instead, the test-makers will create the question (or answer choices) so that there's an alternative approach.

The alternative approach here is to recognize that:
26 has 6 as its units digit
26² has 6 as its units digit
26³ has 6 as its units digit

So, (26)+(26²)+(26³) = (26)+(___6)+(____6) = _____8

Since only D has 8 as its units digit, the answer must be D

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Kudos [?]: 2622 [4], given: 362

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15565

Kudos [?]: 283 [0], given: 0

Premium Member
Re: A company assigns product codes consisting of all the letter [#permalink]

Show Tags

New post 04 Jun 2017, 13:55
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

Intern
Intern
avatar
B
Joined: 30 Mar 2017
Posts: 39

Kudos [?]: 12 [0], given: 47

Location: United States (FL)
GMAT ToolKit User
Re: A company assigns product codes consisting of all the letter [#permalink]

Show Tags

New post 05 Jun 2017, 04:12
Bunuel

Isn't there double counting if we do 26 * 26 * 26?

Kudos [?]: 12 [0], given: 47

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1684

Kudos [?]: 910 [0], given: 5

Re: A company assigns product codes consisting of all the letter [#permalink]

Show Tags

New post 06 Jun 2017, 16:38
bagdbmba wrote:
A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 3 letters in its codes, and all letters can be repeated in any one code?

A.15600
B.16226
C.17576
D.18278
E.28572


A one-letter code can be formed in 26 ways.

A two-letter code can be formed in 26 x 26 = 26^2 ways.

A three-letter code can be formed in 26 x 26 x 26 = 26^3 ways.

Thus, the total number of codes is:

26 + 26^2 + 26^3

26(1 + 26 + 26^2)

26(1 + 26 + 676)

26(703) = 18,278

Notice that one need not do the multiplication out fully. We see that the units digit is an 8.

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 910 [0], given: 5

Director
Director
User avatar
G
Joined: 13 Mar 2017
Posts: 552

Kudos [?]: 134 [0], given: 64

Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: A company assigns product codes consisting of all the letter [#permalink]

Show Tags

New post 14 Aug 2017, 02:54
bagdbmba wrote:
A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 3 letters in its codes, and all letters can be repeated in any one code?

A.15600
B.16226
C.17576
D.18278
E.28572


So product codes can be o f 1 letter or 2 letter or 3 letters and all the letters can be repeated in any code.
So product codes possible = 26 + 26*26 + 26*26*26 = 26(1+26+26^2) = 26*(27+676) = 26* (703) = 18278

Answer D
_________________

MBA Social Network : WebMaggu

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

Kudos [?]: 134 [0], given: 64

Re: A company assigns product codes consisting of all the letter   [#permalink] 14 Aug 2017, 02:54
Display posts from previous: Sort by

A company assigns product codes consisting of all the letter

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.