GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
close

It is currently 02 Dec 2020, 07:56
Register
GMAT Club Tests
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel
PREVIOUS TOPIC
NEXT TOPIC
Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same
8 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
Tags :
Find Similar Topics 

Show Tags
Hide Tags

User avatar
V
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 68775
CAT Tests
Top Member of the Month
Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same [#permalink] New post  21 Aug 2016, 23:51
2
Expert Reply
11
Bookmarks
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

56% (02:39) correct 44% (02:55) wrong based on 158 sessions

Hide Show 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
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
New to the GMAT CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL. Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant

Questions' Banks and Collection:
PS: Standard deviation | Tough Problem Solving Questions With Solutions | Probability and Combinations Questions With Solutions | Tough and tricky exponents and roots questions | 12 Easy Pieces (or not?) | Bakers' Dozen | Algebra set | Mixed Questions | Fresh Meat
DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Most Helpful Expert Reply
User avatar
V
chetan2u
Math Expert
Joined: 02 Aug 2009
Posts: 9104
Reviews Badge
Top Member of the Month
Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same [#permalink] New post  09 Nov 2020, 02:21
1
Expert Reply
Nups1324 wrote:
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


What is wrong in my approach?

Symmetric letters (S)=11
Asymmetric letters (A)=15

3 case:

1 S and 2 AS = (11×15×14)×6 [6 is the number of ways] = 13860
OR
2 S and 1 AS = (11×10×15)×6 = 9900
OR
3 S = (11×10×9)×6 = 5940

Therefore, total ways = 29700

It would be great if you could help me out with the correct solution.



The main flaw is you have taken an approach that is lengthy, calculations intensive and error prone.

Now the flaw in the calculations.
If you calculate 15*14, it already includes the arrangement so you cannot multiply by 6.
1) 1 S and 2 AS = 11C1*15C2*3!=\(11*\frac{15*14}{2}*6\)
2) 1AS and 2S = 11C2*15*6=\(\frac{11*10}{2}\)*15*6
3) 3S=11*10*9
Add and you will get the answer. => 6930 + 4950 + 990 = 12,870

The better way would be
All ways-(ways none of S is there)
All ways =26*25*24
Ways where none is symmetric =15*14*13
Our answer, that is at least one is symmetric = 26*25*24-15*14*13=15600-2730=12870
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html


GMAT Expert
Signature Read More
Most Helpful Community Reply
avatar
udyans123
Intern
Intern
Joined: 18 Aug 2013
Posts: 11
Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same [#permalink] New post  22 Aug 2016, 07:09
9
1
Bookmarks
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
avatar
G
msk0657
Retired Moderator
Joined: 26 Nov 2012
Posts: 540
Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same [#permalink] New post  22 Aug 2016, 05:34
1
1
Bookmarks
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..
avatar
P
chesstitans
VP
VP
Joined: 12 Dec 2016
Posts: 1388
Location: United States
Schools: Stanford '19, Carroll '19, LBS '19
GMAT 1: 700 Q49 V33
GPA: 3.64
GMAT ToolKit User
Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same [#permalink] 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?
avatar
B
chaigmat
Intern
Intern
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] New post  07 May 2017, 21:58
1
A quick observation about the question.
Z is not a symmetric letter by this definition.
avatar
P
chesstitans
VP
VP
Joined: 12 Dec 2016
Posts: 1388
Location: United States
Schools: Stanford '19, Carroll '19, LBS '19
GMAT 1: 700 Q49 V33
GPA: 3.64
GMAT ToolKit User
Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same [#permalink] New post  27 Aug 2017, 19:58
this tests the ability to calculate fast and accurate
avatar
B
Nups1324
Manager
Manager
Joined: 05 Jan 2020
Posts: 118
Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same [#permalink] New post  08 Nov 2020, 07:24
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


Hi Bunuel ,

What is wrong in my approach?

Symmetric letters (S)=11
Asymmetric letters (A)=15

3 case:

1 S and 2 AS = (11×15×14)×6 [6 is the number of ways] = 13860
OR
2 S and 1 AS = (11×10×15)×6 = 9900
OR
3 S = (11×10×9)×6 = 5940

Therefore, total ways = 29700

It would be great if you could help me out with the correct solution.

Tagging others just in case
chetan2u GMATinsight IanStewart ScottTargetTestPrep yashikaaggarwal VeritasKarishma


Thank you :)

Posted from my mobile device
GMAT Club Bot
gmatclubot
[#permalink]
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Feedback

cron

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

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions