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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
71% (02:13) correct
29%
(02:28)
wrong
based on 1007
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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
IMG-20231119-WA0000.jpg [ 366.81 KiB | Viewed 19578 times ]
A. 6
B. 7
C. 12
D. 14
E. 24
Attachment:
IMG-20231119-WA0000.jpg [ 366.81 KiB | Viewed 19578 times ]
gmatophobia
Important thing is to identify the pattern. For that, we need to write down the first few steps. I wrote down the positions and then changed them at every step.
1234567
Step 1: 4123756
Step 2: 3412675
Step 3: 2341567 (Last 3 digits are back in their place)
Step 4: 1234756 (First 4 digits are back in their place but last 3 are now messed up)
...
The first digits will follow a cycle of 4 steps and will be back in original order after 4 steps. The last 3 digits will follow a cycle of 3 steps and will be back in order after 3 steps. So both will be back in order for the first time after 12 steps - the LCM of 4 and 3.
Answer (C)
Pattern recognition is an important skill one must develop for GMAT. Here is another question that needs pattern recognition: https://anaprep.com/arithmetic-pattern- ... roperties/
27 Feb 2024, 00:30
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user1592
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
- DABC
- CDAB
- BCDA
- ABCD - Back to the initial order
The last three letters would change the following way:
EFG - The initial order.
- GEF
- FGE
- 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
- DABC - GEF
- CDAB - FGE
- BCDA - EFG
- ABCD - GEF
- DABC - FGE
- CDAB - EFG
- BCDA - GEF
- ABCD - FGE
- DABC - EFG
- CDAB - GEF
- BCDA - FGE
- ABCD - EFG - Back to the initial order
Answer: C.
