Last visit was: 23 Apr 2024, 22:56 It is currently 23 Apr 2024, 22:56

GMAT Club Daily Prep
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

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.

# A certain computer program reorders the letters of any seven-letter se

SORT BY:
Tags:
Show Tags
Hide Tags
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3083
Own Kudos [?]: 4080 [25]
Given Kudos: 1851
Location: India
Tutor
Joined: 16 Oct 2010
Posts: 14816
Own Kudos [?]: 64887 [7]
Given Kudos: 426
Location: Pune, India
General Discussion
Intern
Joined: 28 Dec 2023
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 227
GMAT Focus 1:
645 Q84 V81 DI80
GPA: 3.55
Math Expert
Joined: 02 Sep 2009
Posts: 92883
Own Kudos [?]: 618648 [3]
Given Kudos: 81563
Re: A certain computer program reorders the letters of any seven-letter se [#permalink]
3
Kudos

user1592 wrote:
A certain computer program reorders the letters of any seven-letter sequence, and the position of a letter in the new order depends only on its position in the original order. The first run of the program changes the initial input ABCDEFG to the output DABCGEF. If the input to each subsequent run is the output from the preceding run, after how many runs will the output first equal the initial input ABCDEFG ?

A. 6
B. 7
C. 12
D. 14
E. 24

Why did we group the first 4 digits together and the last 3 together/only rearrange them within their own groups, instead of rearranging all 7? Is there something that indicates this in the question? I'm also confused about how to figure out the different patterns.

The question says that the position of a letter in the new order depends only on its position in the original order. Then we are told that ABCDEFG was reordered to DABCGEF.

ABCDEFG
DABCGEF

Observe that in the first four letters, ABCD, the change was that the first three letters and the fourth letters were switched: ABCD became DABC. In the last three letters, EFG, the first two letters and the third letter were switched: EFG became GEF.

Hence, the first four letters would change the following way:

ABCD - The initial order
1. DABC
2. CDAB
3. BCDA
4. ABCD - Back to the initial order

The last three letters would change the following way:

EFG - The initial order.
1. GEF
2. FGE
3. EFG - Back to the initial order

As we can see, the first four letters cycle back to the initial order after every 4 runs and the last three letters cycle back to the initial order after every 3 runs. Therefore, the entire word will cycle back to the initial order of ABCDEFG in 12 runs:

ABCD - EFG - The initial order
1. DABC - GEF
2. CDAB - FGE
3. BCDA - EFG
4. ABCD - GEF
5. DABC - FGE
6. CDAB - EFG
7. BCDA - GEF
8. ABCD - FGE
9. DABC - EFG
10. CDAB - GEF
11. BCDA - FGE
12. ABCD - EFG - Back to the initial order