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17 Jul 2017, 04:48
Kudos
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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
17 Jul 2017, 04:48
Kudos
Bookmarks
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
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
General Discussion
22 Sep 2017, 21:21
Kudos
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I think this is a high-quality question and I agree with explanation.
