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

It is currently 16 Jul 2018, 21:07

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

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

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47025
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, 00:51
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

63% (01:50) correct 37% (02:20) wrong based on 102 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
5 KUDOS received
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, 08:09
5
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: 598
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, 06:34
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..
1 KUDOS received
SVP
SVP
avatar
P
Joined: 12 Dec 2016
Posts: 1876
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, 15:09
1
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, 22:58
A quick observation about the question.
Z is not a symmetric letter by this definition.
SVP
SVP
avatar
P
Joined: 12 Dec 2016
Posts: 1876
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, 20:58
this tests the ability to calculate fast and accurate
Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same   [#permalink] 27 Aug 2017, 20:58
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  

Events & Promotions

PREV
NEXT


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®.