Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 20 Jul 2019, 05:40

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

In the Land of Oz only one or two-letter words are used. The

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 18 Oct 2010
Posts: 73
In the Land of Oz only one or two-letter words are used. The  [#permalink]

Show Tags

New post 02 Jun 2012, 02:38
1
13
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

50% (01:33) correct 50% (01:48) wrong based on 378 sessions

HideShow timer Statistics


In the Land of Oz only one or two-letter words are used. The local language has 66 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?

A. 65
B. 66
C. 67
D. 131
E. 132
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56303
Re: In the Land of Oz only one or two-letter words are used. The  [#permalink]

Show Tags

New post 02 Jun 2012, 06:36
9
3
In the Land of Oz only one or two-letter words are used. The local language has 66 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?

A. 65
B. 66
C. 67
D. 131
E. 132

The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...

The number of 1 letter words (X) that can be made from 66 letters is 66;
The number of 2 letter words (XX) that can be made from 66 letters is 66*66, since each X can take 66 values.
Total: 66+66*66.

Similarly:
The number of 1 letter words (X) that can be made from 65 letters is 65;
The number of 2 letter words (XX) that can be made from 66 letters is 65*65, since each X can take 65 values.
Total: 65+65*65.

The difference is (66+66*66)-(65+65*65)=132.

Answer: E.

Hope it's clear.
_________________
General Discussion
Manager
Manager
avatar
Joined: 12 May 2012
Posts: 69
Location: India
Concentration: General Management, Operations
GMAT 1: 650 Q51 V25
GMAT 2: 730 Q50 V38
GPA: 4
WE: General Management (Transportation)
Re: In the Land of Oz only one or two-letter words  [#permalink]

Show Tags

New post 02 Jun 2012, 03:42
I am getting the answer as 131 - D

Earlier there were 66 letters
No of two letter words = 66*65
Single letter word = 66
Total = 66^2

Now there were 65 letters
No of two letter words = 65*64
Single letter word = 65
Total = 65^2

Diff = 66^2 - 65^2 = 131 = lost words
Manager
Manager
avatar
Joined: 12 May 2012
Posts: 69
Location: India
Concentration: General Management, Operations
GMAT 1: 650 Q51 V25
GMAT 2: 730 Q50 V38
GPA: 4
WE: General Management (Transportation)
Re: In the Land of Oz only one or two-letter words  [#permalink]

Show Tags

New post 02 Jun 2012, 03:46
2
Alternate solution

The seventh letter (Let it be @) can be used with other 65 in two type of arrangents
one when seventh letter is in 1st slot @_ (65 ways)
another, when seventh letter is in 2nd slot _@ (65 ways)

seventh letter (@) itself

Lost words = 1 + 65 + 65 = 131
SVP
SVP
User avatar
G
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1814
GMAT 1: 780 Q51 V48
GRE 1: Q800 V740
Re: In the Land of Oz only one or two-letter words  [#permalink]

Show Tags

New post 02 Jun 2012, 04:19
Number of one letter words that can be made using 66 letters = 66
Number of two letter words that can be made using 66 letters = 66C2*2!
Total number of words using all 66 letters = 66 + 66C2 * 2!

Number of one letter words that can be made using 65 letters = 65
Number of two letter words that can be made using 65 letters = 65C2*2!
Total number of words using 65 letters = 65 + 65C2*2!

Number of words that the language has lost = 66 + 66C2*2! - (65+65C2*2!)
= 1 + 130
= 131

Choice D
_________________
GyanOne [www.gyanone.com]| Premium MBA and MiM Admissions Consulting

Awesome Work | Honest Advise | Outstanding Results

Reach Out, Lets chat!
Email: info at gyanone dot com | +91 98998 31738 | Skype: gyanone.services
Manager
Manager
avatar
Joined: 18 Oct 2010
Posts: 73
Re: In the Land of Oz only one or two-letter words  [#permalink]

Show Tags

New post 02 Jun 2012, 04:24
GyanOne wrote:
Number of one letter words that can be made using 66 letters = 66
Number of two letter words that can be made using 66 letters = 66C2*2!
Total number of words using all 66 letters = 66 + 66C2 * 2!

Number of one letter words that can be made using 65 letters = 65
Number of two letter words that can be made using 65 letters = 65C2*2!
Total number of words using 65 letters = 65 + 65C2*2!

Number of words that the language has lost = 66 + 66C2*2! - (65+65C2*2!)
= 1 + 130
= 131

Choice D



official answer is Definitely E , I have rechecked . Let's wait for expert solution.

Mean while please tell me how you got the total number of 2 letter words , Permutation tells me (66!)/(64!) which gives me 66*65 . But I can't figure out 65C2*2!
SVP
SVP
User avatar
G
Status: Top MBA Admissions Consultant
Joined: 24 Jul 2011
Posts: 1814
GMAT 1: 780 Q51 V48
GRE 1: Q800 V740
Re: In the Land of Oz only one or two-letter words are used. The  [#permalink]

Show Tags

New post 02 Jun 2012, 07:18
Bunuel on target as always
_________________
GyanOne [www.gyanone.com]| Premium MBA and MiM Admissions Consulting

Awesome Work | Honest Advise | Outstanding Results

Reach Out, Lets chat!
Email: info at gyanone dot com | +91 98998 31738 | Skype: gyanone.services
Manager
Manager
avatar
Joined: 18 Oct 2010
Posts: 73
Re: In the Land of Oz only one or two-letter words are used. The  [#permalink]

Show Tags

New post 02 Jun 2012, 07:25
Bunuel wrote:
In the Land of Oz only one or two-letter words are used. The local language has 66 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?

A. 65
B. 66
C. 67
D. 131
E. 132

The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...

The number of 1 letter words (X) that can be made from 66 letters is 66;
The number of 2 letter words (XX) that can be made from 66 letters is 66*66, since each X can take 66 values.
Total: 66+66*66.

Similarly:
The number of 1 letter words (X) that can be made from 65 letters is 65;
The number of 2 letter words (XX) that can be made from 66 letters is 65*65, since each X can take 65 values.
Total: 65+65*65.

The difference is (66+66*66)-(65+65*65)=132.

Answer: E.

Hope it's clear.


+1 awesome , solution
Manager
Manager
avatar
Joined: 12 May 2012
Posts: 69
Location: India
Concentration: General Management, Operations
GMAT 1: 650 Q51 V25
GMAT 2: 730 Q50 V38
GPA: 4
WE: General Management (Transportation)
Re: In the Land of Oz only one or two-letter words are used. The  [#permalink]

Show Tags

New post 02 Jun 2012, 19:24
Bunuel wrote:
In the Land of Oz only one or two-letter words are used. The local language has 66 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?

A. 65
B. 66
C. 67
D. 131
E. 132

The answer to the question is indeed E. The problem with above solutions is that they do not consider words like AA, BB, ...

The number of 1 letter words (X) that can be made from 66 letters is 66;
The number of 2 letter words (XX) that can be made from 66 letters is 66*66, since each X can take 66 values.
Total: 66+66*66.

Similarly:
The number of 1 letter words (X) that can be made from 65 letters is 65;
The number of 2 letter words (XX) that can be made from 66 letters is 65*65, since each X can take 65 values.
Total: 65+65*65.

The difference is (66+66*66)-(65+65*65)=132.

Answer: E.

Hope it's clear.


silly mistakes as ever..... :oops:
Thanks Bunuel
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56303
Re: In the Land of Oz only one or two-letter words are used. The  [#permalink]

Show Tags

New post 01 Jul 2013, 00:59
1
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Combinations: math-combinatorics-87345.html

DS questions on Combinations: search.php?search_id=tag&tag_id=31
PS questions on Combinations: search.php?search_id=tag&tag_id=52

Tough and tricky questions on Combinations: hardest-area-questions-probability-and-combinations-101361.html

_________________
Intern
Intern
avatar
Joined: 05 May 2013
Posts: 23
GMAT 1: 730 Q50 V39
GRE 1: Q800 V680
Re: In the Land of Oz only one or two-letter words are used. The  [#permalink]

Show Tags

New post 01 Jul 2013, 09:20
2
Let X be the seventh letter that will no longer be in use. Number of one letter words that use X =1. Number of two letter words that use X = 131 (65 with X as first letter, 65 w X as second letter and one as XX). This gives us a total of 1+131 =132 words that use X and which will no longer be available.
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9443
Location: Pune, India
Re: In the Land of Oz only one or two-letter words are used. The  [#permalink]

Show Tags

New post 01 Jul 2013, 21:50
10
1
Joy111 wrote:
In the Land of Oz only one or two-letter words are used. The local language has 66 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?

A. 65
B. 66
C. 67
D. 131
E. 132


Good Question.

An important thing to remember in such words/numbers/passwords questions is the step by step process.

Say we need to make 1 or 2 letter words, we need to consider 2 things if 'distinct letters' is not mentioned: the number of letters and repetitions allowed. We tend to ignore 'repetitions' because most questions say 'distinct letters'. The reason is that all different kinds of repetitions allowed need to be taken care of separately which makes the question cumbersome. GMAT doesn't give cumbersome questions. The good thing about this question is that there is only word which can have repetitions so calculations are not cumbersome but it is easy to ignore that word and arrive at the incorrect answer.

Say if G is discarded,

One letter words
Only 1 - G

Two letter words - all unique letters
65 different letters can be chosen alone with G and they can be arranged in 2! ways so 65*2 = 130

Two letter words - with repetition
Only 1 - GG

Total = 132
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Veritas Prep GMAT Instructor
User avatar
Joined: 11 Dec 2012
Posts: 312
Re: In the Land of Oz only one or two-letter words are used. The  [#permalink]

Show Tags

New post 02 Jul 2013, 13:36
4
Joy111 wrote:
In the Land of Oz only one or two-letter words are used. The local language has 66 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?

A. 65
B. 66
C. 67
D. 131
E. 132


There are quite a few ways to solve this problem. Bunuel showed one, Karishma another. I solved this a slightly different way, so feel free to use whichever method makes the most sense to you on test day. There is probably nothing more important on the GMAT quant section than mental agility, i.e. being able to solve any question in a variety of ways (algebra, concept, picking numbers, back solving, etc)

Let's break it down into 1-letter codes and 2-letter codes. 1 letter codes is trivial. You're losing one letter (let's call it G since it's the 7th letter).

The real magic is the two letter codes. If you drop G, you're losing every single word that has G_ or _G. That means 66 letters for G in the first spot and 66 letters for G in the second spot. However you're double counting GG, so you have to remove one. Thus for 2-letter codes you lose (66+66-1) = 131.

Adding back in the 1 for 1-letter codes gives a total of 132. Very similar to a probability or Venn diagram question where you often double count elements.

Hope this helps!
-Ron
_________________
Manager
Manager
User avatar
B
Joined: 18 Jul 2013
Posts: 73
Location: Italy
GMAT 1: 600 Q42 V31
GMAT 2: 700 Q48 V38
GPA: 3.75
Re: In the Land of Oz only one or two-letter words are used. The  [#permalink]

Show Tags

New post 10 Nov 2013, 13:23
hi, i solved it that way :

Total words lost = total words with 66 letters - total words with 65 letters

1) total words with 66 letters = 66 (total words with 1 letter) + 66P64 (total words with 2 different letters : AB, AC etc.) + 66 (total words of 2 identical letters : AA, BB etc.) = \(66+66*65+66\) = \(66*2+66*65\)

2) total words with 65 letters = 65 (total words with 1 letter) + 65P64 (total words with 2 different letters : AB, AC etc.) + 65 (total words of 2 identical letters : AA, BB etc.) = \(65+65*64+65\) = \(65*2+65*64\)

Finally the answer is :66*2+66*65 (1) -65*2-65*64 (2) = 2 + 65*(66-64) = 132
Intern
Intern
avatar
Joined: 08 Jun 2016
Posts: 13
Re: In the Land of Oz only one or two-letter words are used. The  [#permalink]

Show Tags

New post 10 Jul 2016, 14:09
I'm late to the party but whatever...

Total number of one-letter words without restriction: 66
Total number of two-letter words without restriction (order matters): 66P2 = 66*65
Total number of one-letter and two-letter words without restriction: 66*65 + 66

Total number of one-letter words with restriction: 65
Total number of two-letter words with restriction (order matters): 65P2 = 65*64
Total number of one-letter and two-letter words with restriction: 65*64 +65

-> Total number of words lost: 65*(66-64) + 66 - 65 = 131 (D)
Senior Manager
Senior Manager
User avatar
G
Joined: 03 Apr 2013
Posts: 273
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3
GMAT ToolKit User
Re: In the Land of Oz only one or two-letter words are used. The  [#permalink]

Show Tags

New post 28 Nov 2016, 05:34
Joy111 wrote:
In the Land of Oz only one or two-letter words are used. The local language has 66 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?

A. 65
B. 66
C. 67
D. 131
E. 132


The question must specify HOW ARE THE WORDS FROM THE LETTERS CONSTRUCTED. Whether repetition is allowed or not allowed must be specified. Bunuel please see.
_________________
Spread some love..Like = +1 Kudos :)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56303
Re: In the Land of Oz only one or two-letter words are used. The  [#permalink]

Show Tags

New post 28 Nov 2016, 05:48
ShashankDave wrote:
Joy111 wrote:
In the Land of Oz only one or two-letter words are used. The local language has 66 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?

A. 65
B. 66
C. 67
D. 131
E. 132


The question must specify HOW ARE THE WORDS FROM THE LETTERS CONSTRUCTED. Whether repetition is allowed or not allowed must be specified. Bunuel please see.


If the repetition were not allowed it would have been mentioned.
_________________
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2822
Re: In the Land of Oz only one or two-letter words are used. The  [#permalink]

Show Tags

New post 29 Nov 2016, 16:48
1
Joy111 wrote:
In the Land of Oz only one or two-letter words are used. The local language has 66 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?

A. 65
B. 66
C. 67
D. 131
E. 132


We are given that in the Land of Oz only one- or two-letter words are used. If all 66 letters can be used, then we have:

1-letter words = 66

2-letter words = 66^2

Thus, there are 66 + 66^2 words if all 66 letters can be used.

When the seventh letter is taken away, we have:

1-letter words = 65

2-letter words = 65^2

Thus, there are 65 + 65^2 words when the seventh letter is taken away.

The number of lost words is:

(66 + 66^2) - (65 + 65^2)

66 + 66^2 - 65 - 65^2

1 + 66^2 - 65^2

1 + (66 - 65)(66 + 65)

1 + (1)(131) = 132

Answer: E
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Senior Manager
Senior Manager
User avatar
G
Joined: 03 Apr 2013
Posts: 273
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3
GMAT ToolKit User
Re: In the Land of Oz only one or two-letter words are used. The  [#permalink]

Show Tags

New post 18 Jun 2017, 23:36
Joy111 wrote:
In the Land of Oz only one or two-letter words are used. The local language has 66 different letters. The parliament decided to forbid the use of the seventh letter. How many words have the people of Oz lost because of the prohibition?

A. 65
B. 66
C. 67
D. 131
E. 132


Two ways to do this one.

1.
with 66 letters, how many one or two letter words can we make?

\(67 * 66\) -------(1)

we can fill the first position with 67 different things(66 letters or a blank), and the second position with 66 different letters.

With 65 letters after removing the 7th letter, how many words do we have?

\(66 * 65\) -------(2)

(1) - (2)

= 132(E)

2.
Now that we have removed the 7th letter, we have lost all the single and double letter words that we could make which include this 7th letter.

Single letter words with 7th letter?

\(1\)

Double letter words?

\(2 * 65 + 1\) ---Double letter words by using 7th letter only once + Double letter word by using 7th letter twice

Total = 132(E)
_________________
Spread some love..Like = +1 Kudos :)
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 11717
Re: In the Land of Oz only one or two-letter words are used. The  [#permalink]

Show Tags

New post 20 Aug 2018, 12:02
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 Club Bot
Re: In the Land of Oz only one or two-letter words are used. The   [#permalink] 20 Aug 2018, 12:02
Display posts from previous: Sort by

In the Land of Oz only one or two-letter words are used. The

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





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