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

It is currently 19 Jan 2019, 08:37

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 January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
  • FREE Quant Workshop by e-GMAT!

     January 20, 2019

     January 20, 2019

     07:00 AM PST

     07:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.
  • Free GMAT Strategy Webinar

     January 19, 2019

     January 19, 2019

     07:00 AM PST

     09:00 AM PST

    Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

A 3-character alpha-numeric code does have the following properties

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

Hide Tags

 
e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2456
A 3-character alpha-numeric code does have the following properties  [#permalink]

Show Tags

New post 29 May 2018, 00:54
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

84% (01:20) correct 16% (01:15) wrong based on 73 sessions

HideShow timer Statistics

A 3-character alpha-numeric code does have the following properties – the first character can be any number except 0 and 9, the second character can be any small letter between a to z, excluded, and the third character can have any of those characters possible for the first two places. How many such codes can be formed?

A. 26
B. 64
C. 520
D. 6144
E. 9360



Related Articles:

Article-1: Learn when to “Add” and “Multiply” in Permutation & Combination questions
Article-2: Fool-proof method to Differentiate between Permutation & Combination Questions
Article-3: 3 deadly mistakes you must avoid in Permutation & Combination

All Articles: Must Read Articles and Practice Questions to score Q51 !!!!

_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3334
Location: India
GPA: 3.12
Premium Member CAT Tests
A 3-character alpha-numeric code does have the following properties  [#permalink]

Show Tags

New post 29 May 2018, 02:04
1
EgmatQuantExpert wrote:
A 3-character alpha-numeric code does have the following properties – the first character can be any number except 0 and 9, the second character can be any small letter between a to z, excluded, and the third character can have any of those characters possible for the first two places. How many such codes can be formed?

A. 26
B. 64
C. 520
D. 6144
E. 9360


The 3 character alpha-numeric code has the following characters

First character - Any number except 0 and 9 - Total of 10 - 2 = 8 possibilities
Second character - Any small letter except a and z - Total of 26 - 2 = 24 possibilities
Third character - Any number except 0 and 9 or Any small letter except a and z - Total of 8 + 24 = 32 possibilities

In this case, to find the total number of possibilities, we can use the unit's digit to find the
answer as number ending 8 * number ending 4 * number ending 2 is a number ending 4.
Also, the answer must be close to 10*20*30 is a little more than 6000.
P.S when the answer options are far apart, we can use approximations to arrive at the answer

Therefore, Option D(6144) is the the total number of 3-character alpha-numberic codes.
_________________

You've got what it takes, but it will take everything you've got

Director
Director
User avatar
V
Joined: 11 Feb 2015
Posts: 675
Premium Member CAT Tests
Re: A 3-character alpha-numeric code does have the following properties  [#permalink]

Show Tags

New post 29 May 2018, 02:32
pushpitkc wrote:
EgmatQuantExpert wrote:
A 3-character alpha-numeric code does have the following properties – the first character can be any number except 0 and 9, the second character can be any small letter between a to z, excluded, and the third character can have any of those characters possible for the first two places. How many such codes can be formed?

A. 26
B. 64
C. 520
D. 6144
E. 9360


The 3 character alpha-numeric code has the following characters

First character - Any number except 0 and 9 - Total of 10 - 2 = 8 possibilities
Second character - Any small letter except a and z - Total of 26 - 2 = 24 possibilities
Third character - Any number except 0 and 9 or Any small letter except a and z - Total of 8 + 24 = 32 possibilities

In this case, to find the total number of possibilities, we can use the unit's digit to find the
answer as number ending 8 * number ending 4 * number ending 2 is a number ending 4.
Also, the answer must be close to 10*20*30 is a little more than 6000.
P.S when the answer options are far apart, we can use approximations to arrive at the answer

Therefore, Option C(6144) is the the total number of 3-character alpha-numberic codes.


I think your calculations and answer is correct but by mistake you have mentioned option C in your answer (in brackets though the actual answer is right). I hope this helps.
_________________

"Please hit :thumbup: +1 Kudos if you like this post" :student_man:

_________________
Manish :geek:

"Only I can change my life. No one can do it for me"

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3334
Location: India
GPA: 3.12
Premium Member CAT Tests
Re: A 3-character alpha-numeric code does have the following properties  [#permalink]

Show Tags

New post 29 May 2018, 02:56
Once again, thanks Manish!
_________________

You've got what it takes, but it will take everything you've got

Director
Director
User avatar
V
Joined: 11 Feb 2015
Posts: 675
Premium Member CAT Tests
Re: A 3-character alpha-numeric code does have the following properties  [#permalink]

Show Tags

New post 29 May 2018, 03:00
pushpitkc wrote:
Once again, thanks Manish!


You are welcome!! The short cuts of approximation and using the units digits are nice. Time saving.
_________________

"Please hit :thumbup: +1 Kudos if you like this post" :student_man:

_________________
Manish :geek:

"Only I can change my life. No one can do it for me"

e-GMAT Representative
User avatar
D
Joined: 04 Jan 2015
Posts: 2456
Re: A 3-character alpha-numeric code does have the following properties  [#permalink]

Show Tags

New post 31 May 2018, 00:55

Solution



Given:
    • The code is of 3-character alpha-numeric
    • 1st character can be any number except 0 and 9
    • 2nd character can be any small letter between a to z, excluded
    • 3rd character can be any of those characters possible for the first two places

To find:
    • Keeping all the constraints satisfied, how many such codes can be formed

Approach and Working:
    • As the 1st character can be any number except 0 and 9, number of possibilities exist for the first character = 8
    • As the 2nd character can be any small letter between a to z, excluded, number of possibilities exist for the second character = 24
    • As the 3rd character can be any of those characters possible for the first two places, number of possibilities exist for the third character = 8 + 24 = 32
    • Therefore, the total number of possible codes = 8 * 24 * 32 = 6144

Hence, the correct answer is option D.

Answer: D
_________________








Register for free sessions
Number Properties | Algebra |Quant Workshop

Success Stories
Guillermo's Success Story | Carrie's Success Story

Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD | Statistics-1 | Statistics-2 | Remainders-1 | Remainders-2
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line | Inequalities

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Manager
Manager
User avatar
G
Joined: 15 Feb 2018
Posts: 187
Premium Member
Re: A 3-character alpha-numeric code does have the following properties  [#permalink]

Show Tags

New post 23 Dec 2018, 15:19
Three different characters: C1 C2 C3
Theory: When calculating the number of items it is (xn-xa)+1

C1
8-1+1=8

C2
25th letter is y; 2nd letter is b
25-2+1=24

C3
8+24=32

Theory: Fundamental counting rule C1·C2·C3
8·24·32

I don't like multiplying 3 numbers together. I split the 8 up
(4·24)·(2·32)=96·64

Theory: the units digits of the answer results only from the units digits of the inputs
6·4=x4, so we know the answer ends in 4

B is too small. D must be the answer
GMAT Club Bot
Re: A 3-character alpha-numeric code does have the following properties &nbs [#permalink] 23 Dec 2018, 15:19
Display posts from previous: Sort by

A 3-character alpha-numeric code does have the following properties

  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®.