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

It is currently 20 Nov 2018, 23:59

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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

     November 22, 2018

     November 22, 2018

     10:00 PM PST

     11:00 PM PST

    Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
  • Free lesson on number properties

     November 23, 2018

     November 23, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same

  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: 50712
Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same  [#permalink]

Show Tags

New post 21 Aug 2016, 23:51
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

58% (02:06) correct 42% (02:14) wrong based on 118 sessions

HideShow timer Statistics

Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

A. 2,145
B. 6,435
C. 12,100
D. 12,870
E. 25,740

_________________

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

Most Helpful Community Reply
Intern
Intern
avatar
Joined: 18 Aug 2013
Posts: 12
Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same  [#permalink]

Show Tags

New post 22 Aug 2016, 07:09
7
1
Total 3 letter passwords = 26 * 25 * 24 = 15600

Total letters = 26 = symmetrical letters (11) + asymmetrical letters (x) => x = 15

Total no. of 3 letters passwords using asymmetrical letters = 15 * 14 * 13 = 2730 (no repetition allowed)

Hence, no. of 3 letter passwords using atleast one symmetrical letter = 15600 - 2730 = 12870 ---> Option D
General Discussion
Retired Moderator
avatar
G
Joined: 26 Nov 2012
Posts: 591
Premium Member
Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same  [#permalink]

Show Tags

New post 22 Aug 2016, 05:34
1
Bunuel wrote:
Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

A. 2,145
B. 6,435
C. 12,100
D. 12,870
E. 25,740



Since we are given atleast one symmetric letter in the three letter word we can take the following cases

1. All three
2. One symmetry and other two non
3. Two symmetry and one non
4. All the three letters can be arranged in 6 ways

( 11c3 + 11c1 * 15c2 + 11c2 * 15c1 ) * 6

( 11*10*9/ 6 + 11 * 15 * 14 / 2 + 11*10 / 2 * 15 ) * 6

12870

IMO option D is the correct answer..

OA please...will correct if I missed anything..
SVP
SVP
avatar
P
Joined: 12 Dec 2016
Posts: 1674
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
GMAT ToolKit User Premium Member
Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same  [#permalink]

Show Tags

New post 23 Apr 2017, 14:09
2
udyans123 wrote:
Total 3 letter passwords = 26 * 25 * 24 = 15600

Total letters = 26 = symmetrical letters (11) + asymmetrical letters (x) => x = 15

Total no. of 3 letters passwords using asymmetrical letters = 15 * 14 * 13 = 2730 (no repetition allowed)

Hence, no. of 3 letter passwords using atleast one symmetrical letter = 15600 - 2730 = 12870 ---> Option D


I am still confusing between kCn and kPn, I thought kPn should be applied to this question, can you explain the concepts for me?
Intern
Intern
avatar
B
Joined: 24 Apr 2017
Posts: 1
GMAT ToolKit User
Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same  [#permalink]

Show Tags

New post 07 May 2017, 21:58
A quick observation about the question.
Z is not a symmetric letter by this definition.
SVP
SVP
avatar
P
Joined: 12 Dec 2016
Posts: 1674
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
GMAT ToolKit User Premium Member
Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same  [#permalink]

Show Tags

New post 27 Aug 2017, 19:58
this tests the ability to calculate fast and accurate
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8869
Premium Member
Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same  [#permalink]

Show Tags

New post 19 Oct 2018, 02:30
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: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same &nbs [#permalink] 19 Oct 2018, 02:30
Display posts from previous: Sort by

Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same

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


cron
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®.