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26 Dec 2024, 04:05
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statement 1.
we can have three cases
1. Starting with A {and since the first letter is A we also know 4th letter which is also to be A} A _ _ A _ {we have to place B before 4th A because given} A _ B A _
and we have to mark C before B then the code would be ACBAC
2. Starting with B
3. Starting with C
Case 2 and Case 3 would produce different code so Statement 1 is not sufficient.
Satement 2.
with exactly one C we can produce many such codes
eg ABACB or CBABA etc
on combining we get 2 conditions now
1st is The first and fourth letters in the code are the same, as are the second and fifth letters. and There is exactly one C in the five-letter code.
so possible code could be BACBA.
we can have three cases
1. Starting with A {and since the first letter is A we also know 4th letter which is also to be A} A _ _ A _ {we have to place B before 4th A because given} A _ B A _
and we have to mark C before B then the code would be ACBAC
2. Starting with B
3. Starting with C
Case 2 and Case 3 would produce different code so Statement 1 is not sufficient.
Satement 2.
with exactly one C we can produce many such codes
eg ABACB or CBABA etc
on combining we get 2 conditions now
1st is The first and fourth letters in the code are the same, as are the second and fifth letters. and There is exactly one C in the five-letter code.
so possible code could be BACBA.
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes
A certain five-letter code may only be constructed with A’s, B’s, and C’s. If an A appears in any position but the first, it must be immediately preceded by a B. If a B appears in any position but the first, it must be immediately preceded by a C. What is the fifth letter in the code?
(1) The first and fourth letters in the code are the same, as are the second and fifth letters.
(2) There is exactly one C in the five-letter code.
A certain five-letter code may only be constructed with A’s, B’s, and C’s. If an A appears in any position but the first, it must be immediately preceded by a B. If a B appears in any position but the first, it must be immediately preceded by a C. What is the fifth letter in the code?
(1) The first and fourth letters in the code are the same, as are the second and fifth letters.
(2) There is exactly one C in the five-letter code.
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26 Dec 2024, 04:23
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Five letter code = _ _ _ _ _
If A appears in any position but first, B should come just before A.
If B appears in any position but first, C should come just before B.
We want to know the last letter (fifth).
STATEMENT 1 -
1st and 4th letters are same. So are the 2nd and 5th letter.
The code can be -
CCCCC = last letter C
or
CBACB = last letter B
Therefore, INSUFFICIENT.
STATEMENT 2 -
exactly 1 C in the code.
The only possible combination with 1 C and the given restrains is -
BACBA = last letter A
SUFFICIENT.
Therefore, FINAL ANSWER - Option B
If A appears in any position but first, B should come just before A.
If B appears in any position but first, C should come just before B.
We want to know the last letter (fifth).
STATEMENT 1 -
1st and 4th letters are same. So are the 2nd and 5th letter.
The code can be -
CCCCC = last letter C
or
CBACB = last letter B
Therefore, INSUFFICIENT.
STATEMENT 2 -
exactly 1 C in the code.
The only possible combination with 1 C and the given restrains is -
BACBA = last letter A
SUFFICIENT.
Therefore, FINAL ANSWER - Option B
Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes
A certain five-letter code may only be constructed with A’s, B’s, and C’s. If an A appears in any position but the first, it must be immediately preceded by a B. If a B appears in any position but the first, it must be immediately preceded by a C. What is the fifth letter in the code?
(1) The first and fourth letters in the code are the same, as are the second and fifth letters.
(2) There is exactly one C in the five-letter code.
A certain five-letter code may only be constructed with A’s, B’s, and C’s. If an A appears in any position but the first, it must be immediately preceded by a B. If a B appears in any position but the first, it must be immediately preceded by a C. What is the fifth letter in the code?
(1) The first and fourth letters in the code are the same, as are the second and fifth letters.
(2) There is exactly one C in the five-letter code.
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26 Dec 2024, 04:24
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Bunuel
12 Days of Christmas 2024 - 2025 Competition with $40,000 of Prizes
A certain five-letter code may only be constructed with A’s, B’s, and C’s. If an A appears in any position but the first, it must be immediately preceded by a B. If a B appears in any position but the first, it must be immediately preceded by a C. What is the fifth letter in the code?
(1) The first and fourth letters in the code are the same, as are the second and fifth letters.
(2) There is exactly one C in the five-letter code.
Statement (1):A certain five-letter code may only be constructed with A’s, B’s, and C’s. If an A appears in any position but the first, it must be immediately preceded by a B. If a B appears in any position but the first, it must be immediately preceded by a C. What is the fifth letter in the code?
(1) The first and fourth letters in the code are the same, as are the second and fifth letters.
(2) There is exactly one C in the five-letter code.
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The first and fourth letters in the code are the same, as are the second and fifth letters.
Let the code be X1 X2 X3 X4 X5. From this statement:
- X1=X4,
- X2=X5.
- X1=A, X2=C, and X3=B are valid under the rules, leading to ACBAC, with X5=C.
- X1=B, X2=A, and X3=C could lead to BACBA, with X5=A
Statement (1) alone is insufficient.
Statement (2):
[b]There is exactly one C in the five-letter code.[/b]
If there is only one C, it must be positioned in a way that allows the rules to be satisfied:
- A B must always follow a C if B is not in the first position.
- An A must always follow a B if A is not in the first position.
Let's try various positions for C
If we start with C, there is not possible combination, (CBA, the next two values post A can not be A or B according to the constraints, and we cannot add C due to the statement (2) condition)
If the second letter is C, there is not possible combination, (BCBA or ACBA, the next value post A can not be A or B according to the constraints, and we cannot add C due to the statement (2) condition)
If the third letter is C, there is not possible combination, (BACBA), therefore the 5th letter has to be A
Similarly, If the fourth letter or fifth letter is C, there is not possible combination
Therefore, only Statement (2) is sufficient.
