Typewriter Question

This topic has expert replies
User avatar
Senior | Next Rank: 100 Posts
Posts: 58
Joined: Sat Sep 25, 2010 10:07 am
Location: Belgrade, Serbia/ New York, USA
Thanked: 1 times

Typewriter Question

by milanproda » Mon Dec 27, 2010 12:31 pm
Are there exactly 4 distinct keys that are working on the old typewriter?

1- An old typewriter is defective in such a way that its blank key is not functioning, and the typewriter allows only 4 letters per word by forcing a space character to be inserted after each four letter word. A monkey sitting at the typewriter is aware of this peculiarity, and presses only distinct keys for each four letter sequence. Some keys of this typewriter are not functioning.

2 A monkey is able to create 24 four letter words.

Answer: 3 Both Statements together are sufficient, but neither statement alone is sufficient

????
Milan Prodanovic
[email protected]
Source: — Data Sufficiency |

Legendary Member
Posts: 1337
Joined: Sat Dec 27, 2008 6:29 pm
Thanked: 127 times
Followed by:10 members

by Night reader » Mon Dec 27, 2010 12:49 pm
milanproda wrote:Are there exactly 4 distinct keys that are working on the old typewriter?

1- An old typewriter is defective in such a way that its blank key is not functioning, and the typewriter allows only 4 letters per word by forcing a space character to be inserted after each four letter word. A monkey sitting at the typewriter is aware of this peculiarity, and presses only distinct keys for each four letter sequence. Some keys of this typewriter are not functioning.

2 A monkey is able to create 24 four letter words.

Answer: 3 Both Statements together are sufficient, but neither statement alone is sufficient

????
Given: 4 distinct keys, find # keys-? distinct - not ?

st(1) constraint - only 4 letters per word => four slots (places) => monkey is checking the keys -distinct -working -not? :)
presses only distinct keys, but we don't know how many types monkey presses the keys and how many slots are filled. Not Sufficient;
st(2) monkey arranges all words in 24 ways, but we don't know how many distinct letters (keys) in the words. Not Sufficient;

Combining st(1&2) Find perm for 4 distinct keys placed in 4 slots => 4*3*2*1=24. Sufficient.

Answer C
Last edited by Night reader on Mon Dec 27, 2010 12:58 pm, edited 1 time in total.

User avatar
Senior | Next Rank: 100 Posts
Posts: 58
Joined: Sat Sep 25, 2010 10:07 am
Location: Belgrade, Serbia/ New York, USA
Thanked: 1 times

by milanproda » Mon Dec 27, 2010 12:57 pm
Thanks, I did not realize that this was a permutation problem. I assumed that becuase it would to be too time consuming to find all of the possible 4 letter words that the monkey wrote, that stem 2 would be insufficient.
Milan Prodanovic
[email protected]