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

It is currently 10 Dec 2018, 20:58

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 in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free lesson on number properties

     December 10, 2018

     December 10, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.

A certain stock exchange designates each stock with a one-, two- or th

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51073
Re: A certain stock exchange designates each stock with a one-, two- or th  [#permalink]

Show Tags

New post 29 Oct 2014, 02:48
1
usre123 wrote:
I dont know why , but I was thinking for one letter, it's 26,
Then for 2 same ones it would be 26^2
2 different ones would mean 26*25 * 2 (because a different order)
3 same would be 26^3, and 3 different would be 26*25*24*3!....Where am I (obviously) double counting?


How is 26^2 the number of two same letter words? How is 26^3 the number of three same letter words? Isn't both 26? AA, BB, CC, ..., ZZ and AAA, BBB, CCC, DDD, ..., ZZZ?

26^2 gives the number of ALL 2-letter words possible, the same way as 26^3 gives the number of ALL 3-letter words possible.
_________________

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

Intern
Intern
avatar
Joined: 14 Aug 2014
Posts: 3
GMAT ToolKit User
Re: A certain stock echange designates each stock with a  [#permalink]

Show Tags

New post 25 Nov 2014, 04:16
1
Hi,

I have a doubt. If this question mentioned that same letters used in a different order are considered same code, then how would we solve it?

Thanks
Manager
Manager
avatar
Joined: 30 Mar 2013
Posts: 109
GMAT ToolKit User
Re: A certain stock echange designates each stock with a  [#permalink]

Show Tags

New post 25 Nov 2014, 04:22
Bunuel wrote:
usre123 wrote:
I dont know why , but I was thinking for one letter, it's 26,
Then for 2 same ones it would be 26^2
2 different ones would mean 26*25 * 2 (because a different order)
3 same would be 26^3, and 3 different would be 26*25*24*3!....Where am I (obviously) double counting?


How is 26^2 the number of two same letter words? How is 26^3 the number of three same letter words? Isn't both 26? AA, BB, CC, ..., ZZ and AAA, BBB, CCC, DDD, ..., ZZZ?

26^2 gives the number of ALL 2-letter words possible, the same way as 26^3 gives the number of ALL 3-letter words possible.


Crystal clear when I read this, thanks!
Director
Director
avatar
S
Joined: 08 Jun 2010
Posts: 873
Re: A certain stock echange designates each stock with a  [#permalink]

Show Tags

New post 12 May 2015, 06:26
1
Bunuel wrote:
chicagocubsrule wrote:
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


1 letter codes = 26
2 letter codes = 26^2
3 letter codes = 26^3

Total = 26 + 26^2 + 26^3

The problem we are faced now is how to get the answer quickly. Note that the units digit of 26+26^2+26^3 would be (6+6+6=18) 8. Only one answer choice has 8 as unit digit: E (18,278). So I believe, even not calculating 26+26^2+26^3, that answer is E.


can not say a word for this excellent
Intern
Intern
avatar
Joined: 18 Jun 2014
Posts: 3
Re: A certain stock exchange designates each stock with a one-, two- or th  [#permalink]

Show Tags

New post 30 Nov 2015, 06:35
Hi I have a doubt:

by doing 26^3 are you not counting palindromes? I mean, for example ABA would not be double counted?
Intern
Intern
avatar
Joined: 29 Sep 2015
Posts: 6
Re: A certain stock exchange designates each stock with a one-, two- or th  [#permalink]

Show Tags

New post 30 Nov 2015, 14:10
lolivaresfer wrote:
Hi I have a doubt:

by doing 26^3 are you not counting palindromes? I mean, for example ABA would not be double counted?


It's fine since the question mentions: "the same letters used in a different order, constitute a different code"
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3228
Location: Canada
Re: A certain stock echange designates each stock with a  [#permalink]

Show Tags

New post 19 Apr 2016, 17:15
4
2
Quote:
A certain stock exchange designates each stock with a one-, two- or three-letter code, where each letter is selected from the 26 letters of the alphabets. If the letter maybe repeated and if the same letters used in different order constitude a different code, how many different stock is it possible to uniquely designate with these codes?

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


My approach is similar to that of Bhoopendra, with a TWIST at the end.

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 E has 8 as its units digit, the answer must be E

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com
Image

Intern
Intern
avatar
Joined: 10 Mar 2016
Posts: 16
Re: A certain stock echange designates each stock with a  [#permalink]

Show Tags

New post 19 Apr 2016, 20:14
GMATPrepNow wrote:
Quote:
A certain stock exchange designates each stock with a one-, two- or three-letter code, where each letter is selected from the 26 letters of the alphabets. If the letter maybe repeated and if the same letters used in different order constitude a different code, how many different stock is it possible to uniquely designate with these codes?

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


My approach is similar to that of Bhoopendra, with a TWIST at the end.

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 E has 8 as its units digit, the answer must be E

Cheers,
Brent



Thanks a lot!

To use this units digit trick is very clever. Is it just possible to use it for adding? I thought about it for a while and it should work for multyplying as well - am I right?
Manager
Manager
avatar
S
Joined: 24 Dec 2015
Posts: 59
Location: India
Concentration: Marketing, Technology
GMAT 1: 710 Q50 V35
GPA: 3.8
WE: Engineering (Computer Software)
GMAT ToolKit User Reviews Badge
Re: A certain stock echange designates each stock with a  [#permalink]

Show Tags

New post 14 May 2016, 22:59
chicagocubsrule wrote:
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


I was able to quickly arrive at the answer when I spotted the 8 in the units digit in the option E.
Looks like the OA marked in the Question post is incorrect. It shows as C is the correct option, while it actually is E.
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: A certain stock echange designates each stock with a  [#permalink]

Show Tags

New post 20 Jun 2017, 18:09
lagomez wrote:
chicagocubsrule wrote:
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


A 1-digit code can be created in 26 ways, a 2-digit code in 26^2 ways, and a 3-digit code in 26^3 ways.

Thus, the number of ways to create the 3 codes is:

26 + 26^2 + 26^3

We should recognize that 26, 26^2, and 26^3 all have units digits of 6. Thus, the sum of those 3 numbers will have a units digit of 8. The only answer choice that has a units digit of 8 is choice E. Thus, the answer must be 18,278.

Answer: E
_________________

Jeffery Miller
Head of GMAT Instruction

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

Intern
Intern
avatar
S
Joined: 12 Oct 2017
Posts: 40
Re: A certain stock exchange designates each stock with a one-, two- or th  [#permalink]

Show Tags

New post 28 Nov 2017, 19:00
- No. of ways to make one letter code: 26 (we have 26 different letters)
- No. of ways to make 2 letter code: 26 * 26 (each letter can combine with 25 other letter and with itself)
- No. of ways to make 3 letter code: 26 * 26 * 26
=> total possible codes = 26 + 26*26 + 26*26*26 =18278
Hence the answer is E.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9101
Premium Member
Re: A certain stock exchange designates each stock with a one-, two- or th  [#permalink]

Show Tags

New post 06 Dec 2018, 19:32
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

GMAT Club Bot
Re: A certain stock exchange designates each stock with a one-, two- or th &nbs [#permalink] 06 Dec 2018, 19:32

Go to page   Previous    1   2   [ 32 posts ] 

Display posts from previous: Sort by

A certain stock exchange designates each stock with a one-, two- or th

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.