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

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swerve: Legendary Member; Posts: 2545; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Tue May 21, 2019 12:23 pm

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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

Source: Economist GMAT

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Source: Beat The GMAT — Problem Solving | Tue May 21, 2019 12:23 pm

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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 » Tue May 21, 2019 9:50 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

Source: Economist GMAT

Hi,

You only had posted this question previously. Here it is: https://www.beatthegmat.com/in-the-land ... 02027.html

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8152; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Thu May 23, 2019 4:11 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

Source: Economist GMAT

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

Alternate Solution:

Let x be the letter that is forbidden. Then, the people lost the following words: x, xx, ax, bx, cx, ... (there are 65 of them, one for all letters besides x) and xa, xb, xc, ... (there are 65 of them).

Thus, the people have lost 1 + 1 + 65 + 65 = 132 words.

Answer: E

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