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

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swerve: Legendary Member; Posts: 2535; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Mon May 07, 2018 11:16 am

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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 OA is E.

Please, can anyone explain this PS question for me? I need help. I tried to solve it but I can't get the correct answer. Thanks.

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Source: Beat The GMAT — Problem Solving | Mon May 07, 2018 11:16 am

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Mon May 07, 2018 8:04 pm

swerve 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 OA is E.

Please, can anyone explain this PS question for me? I need help. I tried to solve it but I can't get the correct answer. Thanks.

Before the prohibition:

The number of 1-letter words = 66;
The number of 2-letter words = 66*66 = 66^2

Total number of words = 66 + 66^2

After the prohibition:

The number of 1-letter words = 65;
The number of 2-letter words = 65*65 = 65^2

Total number of words = 65 + 65^2

The number of words lost = [66 + 66^2] - [65 + 65^2] = 1 + [66^2 - 65^2] = 1 + (66 - 65)(66 + 65) = 1 + 1*(131) = 1 + 131 = 132.

The correct answer: E

Hope this helps!

-Jay
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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue May 08, 2018 8:37 am

Jay@ManhattanReview wrote:
swerve 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
Jay's approach (above) is exactly how I would have solved it.
The only way my approach differs is when we get to:

The number of words lost = [66 + 66Â²] - [65 + 65Â²]
At this point, we might notice that each of the 5 answer choices has a DIFFERENT UNITS DIGIT.
So, we can save some time by focusing solely on the UNITS DIGITS
For example, notice that 66Â² = ---6 [we need not concern ourselves with the other digits. We need only recognize that (66)(66) = some number with 6 as its units digit ]
Likewise 65Â² = (65)(65) = ----5

So, we get:
The number of words lost = [66 + 66Â²] - [65 + 65Â²]
= [66 + ---6] - [65 + ----5]
= (------2) - (----0)
= ------2

Since only answer choice E has a units digit of 2, the correct answer must be E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

by regor60 » Tue May 08, 2018 9:01 am

Or you can focus on the words no longer permitted.

One letter word = 1 word lost

Two letter word: call first letter the forbidden letter. Then there are 65 other letters except for the forbidden one that can't be paired so 65 choices. Multiply by 2 since the forbidden letter can be swapped to the second position = 130 lost words.

Finally, recognize you can have a two letter word with both letters being forbidden = 1 lost word

Total lost words 132, E

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed May 09, 2018 3:51 pm

swerve 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

Noting that the expression 66^2 - 65^2 is a difference of squares, we have:

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

1 + (1)(131) = 132

Answer: E

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