Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Certain word is written on a paper. What is the number of ar [#permalink]
26 Jul 2014, 15:13
1
This post received KUDOS
Expert's post
1
This post was BOOKMARKED
SOLUTION
Certain word is written on a paper. What is the number of arrangements of letters of that word ?
(1) If the first two letters were omitted, the number of arrangements of letters of shortened word would be 6. This one is clearly insufficient: we don't know how many letters are repeated in the word or even how many letters are there. Not sufficient.
(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 can deduce that the last three letters of the word are all different (hence their arrangement of 3! = 6) but we still don't know whether they repeat any of the first two letters. For example, if the word is goose, then the number of arrangements of its letters would be 5!/2! but if the word is close, then the number of arrangements of its letters would be 5!. Not sufficient.
Answer: E.
Try NEW Combinations PS question. _________________
Re: Certain word is written on a paper. What is the number of ar [#permalink]
26 Jul 2014, 16:56
1
This post received KUDOS
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!
Re: Certain word is written on a paper. What is the number of ar [#permalink]
26 Jul 2014, 19:16
1
This post received KUDOS
i think ans would be E bcoz 1. given that if first two letters are deleted, no of arrangements are 6 ie 3! based on this we know that totally we have 5 letters but we don't know anything about first two letters that means first two letters would be alike or unlike.(5!/2! or 5!) 2. no information regarding how many letters alike or unlike
Even though we use both options, we don't have any information about first two letters.
Certain word is written on a paper. What is the number of arrangements of letters of that 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
Kudos for a correct solution.
Key to answering this question is identifying how many Unique Letters there are assuming no other restrictions are noted.
Unfortunately, neither statements actually address whether all letters are unique or not.
Statement 1: This says that the word has at least 3 unique letters. It does not say anything whether the other letters are also unique Statement 2: This only gives us the number of letters. We do not know whether any of the letters have duplicates.
Combined: Neither statements address the question whether the first 2 letters are duplicates or not.
Certain word is written on a paper. What is the number of arrangements of letters of that 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
Kudos for a correct solution.
1) Insufficient. case i: the word has 8 letters and in last 6, 5 are repeating. so after removing first 2 letters, arrangement for last 6 = 6!/5! = 6 case ii: the word has 5 letters and in last 3 none is repeating. so after removing first 2, arrangement for last 3 = 3! = 6
2) Insufficient. 5 letters could mean 5!, 5!/2!, 5!/3!,...
Certain word is written on a paper. What is the number of arrangements of letters of that 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
Kudos for a correct solution.
Statement 1: even if we equate 8 to a permutation nPr and get the value ...we still don't know wether the first two letters are identical or not. INSUFFICIENT statement 2: knowing that there are 5 letter is again not enough to get a permutation. all the letters might be identical or all can be different. INSUFFICIENT.
taking both together: still not sufficient coz no information about the indentical letters.
Re: Certain word is written on a paper. What is the number of ar [#permalink]
29 Jul 2014, 13:12
Expert's post
SOLUTION
Certain word is written on a paper. What is the number of arrangements of letters of that word ?
(1) If the first two letters were omitted, the number of arrangements of letters of shortened word would be 6. This one is clearly insufficient: we don't know how many letters are repeated in the word or even how many letters are there. Not sufficient.
(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 can deduce that the last three letters of the word are all different (hence their arrangement of 3! = 6) but we still don't know whether they repeat any of the first two letters. For example, if the word is goose, then the number of arrangements of its letters would be 5!/2! but if the word is close, then the number of arrangements of its letters would be 5!. Not sufficient.
Answer: E.
Kudos points given to correct solutions.
Try NEW Combinations PS question. _________________
Certain word is written on a paper. What is the number of arrangements of letters of that 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
Kudos for a correct solution.
1) Insufficient. case i: the word has 8 letters and in last 6, 5 are repeating. so after removing first 2 letters, arrangement for last 6 = 6!/5! = 6 case ii: the word has 5 letters and in last 3 none is repeating. so after removing first 2, arrangement for last 3 = 3! = 6
2) Insufficient. 5 letters could mean 5!, 5!/2!, 5!/3!,...
(1) + (2) Insufficient arrangements = 5! or 5!/2!
so E.
These are not the only possible cases:
For abcde it would be 5!. For aacde it would be 5!/2!. For cccde it would be 5!/3!. For cdcde it would be 5!/(2!2!). _________________
Re: Certain word is written on a paper. What is the number of ar [#permalink]
30 Mar 2015, 00:49
1) after omitting the first 2, remaining arrangements are 6. This is possible in many ways : eg : if there are 3 letters left (3! = 6), also if there are letters left out of which 2 are repeated (4! / 2!*2! = 6). Thus more than one sol => NS. 2) Total = 5 letters. We dont know if any of those is repeated or not. Thus NS.
1 and 2 => Again whether letters are repeated or not, is not known. Thus the first 2 omitted letters can be same or different or same as one of the other letters. Thus total arrangements cant be calculated. Ans E.
thanks! _________________
Kudos!!
gmatclubot
Re: Certain word is written on a paper. What is the number of ar
[#permalink]
30 Mar 2015, 00:49
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Perhaps known best for its men’s basketball team – winners of five national championships, including last year’s – Duke University is also home to an elite full-time MBA...
Hilary Term has only started and we can feel the heat already. The two weeks have been packed with activities and submissions, giving a peek into what will follow...