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26 Jul 2014, 16:12
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
57% (01:11) correct
43%
(01:10)
wrong
based on 1406
sessions
History
Date
Time
Result
Not Attempted Yet
In how many ways can the letters of a particular word be arranged?
(1) If the first two letters were omitted, the number of arrangements of letters of shortened word would be 6
(2) There are 5 letters in the word
(1) If the first two letters were omitted, the number of arrangements of letters of shortened word would be 6
(2) There are 5 letters in the word
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26 Jul 2014, 16:13
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Official Solution:
In how many ways can the letters of a particular word be arranged?
(1) If the first two letters were omitted, the number of arrangements of letters of shortened word would be 6.
The above is clearly not sufficient as we do not have enough information about the number of repeated letters or the total number of letters in the word.
(2) There are 5 letters in the word.
We don't know how many letters are repeated in the word. Not sufficient.
(1)+(2) We know that there are 5 letters in the word, and the arrangement of the last three letters is 6. Therefore, we can deduce that the last three letters of the word are all different. However, we still do not have enough information to determine if the first two letters are distinct or whether they match any of the last three letters.
For instance, if the word is "goose," or "Aaron", then the total number of arrangements would be 5!/2!. If the word is "ooops," the total number of arrangements would be 5!/3!. If the word is "civic," the total number of arrangements would be 5!/(2!2!). On the other hand, if the word is "close," then there are no repeated letters, and the total number of arrangements would be 5!. Thus, the combined statements are still insufficient to determine the total number of arrangements of the letters in the word. Not sufficient.
Answer: E
Try NEW Combinations PS question.
In how many ways can the letters of a particular word be arranged?
(1) If the first two letters were omitted, the number of arrangements of letters of shortened word would be 6.
The above is clearly not sufficient as we do not have enough information about the number of repeated letters or the total number of letters in the word.
(2) There are 5 letters in the word.
We don't know how many letters are repeated in the word. Not sufficient.
(1)+(2) We know that there are 5 letters in the word, and the arrangement of the last three letters is 6. Therefore, we can deduce that the last three letters of the word are all different. However, we still do not have enough information to determine if the first two letters are distinct or whether they match any of the last three letters.
For instance, if the word is "goose," or "Aaron", then the total number of arrangements would be 5!/2!. If the word is "ooops," the total number of arrangements would be 5!/3!. If the word is "civic," the total number of arrangements would be 5!/(2!2!). On the other hand, if the word is "close," then there are no repeated letters, and the total number of arrangements would be 5!. Thus, the combined statements are still insufficient to determine the total number of arrangements of the letters in the word. Not sufficient.
Answer: E
Try NEW Combinations PS question.
General Discussion
26 Jul 2014, 17:56
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I believe the correct answer is E, solely for the fact that either statement doesn't disclose whether or not there are duplicate letters in the word.
Statement 1) if two letters were omitted there would be six possible combinations. This statement makes me assume that there are three unique letters that can combined in 3x2x1 ways, however there could be more than three letters where some are duplicates and form a total of six possible combinations. We also don't know about the first two letters.
Statement 2) there's five letters, clearly insufficient. Don't know if there are duplicates. Could be 5! Or 5!/2! Ect.
Statements together : I still don't know the first two letters. I know three of the five letters are unique from our first statement however the first two could be the same or different. Total combinations could be 5! Or 5!/2!
Statement 1) if two letters were omitted there would be six possible combinations. This statement makes me assume that there are three unique letters that can combined in 3x2x1 ways, however there could be more than three letters where some are duplicates and form a total of six possible combinations. We also don't know about the first two letters.
Statement 2) there's five letters, clearly insufficient. Don't know if there are duplicates. Could be 5! Or 5!/2! Ect.
Statements together : I still don't know the first two letters. I know three of the five letters are unique from our first statement however the first two could be the same or different. Total combinations could be 5! Or 5!/2!
