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Difficulty:
95%
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40% (02:22) correct
60%
(02:32)
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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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25 Dec 2024, 10:00
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Bunuel
Manhattan Prep Official Explanation:
This is a Data Sufficiency Logic problem. Carefully note the constraints: five letters; A’s, B’s, or C’s; any A not in the first position is immediately preceded by a B, and any B not in the first position is immediately preceded by an A. The question asks you to choose one (A, B, or C) for the fifth letter.
Statement (1): INSUFFICIENT. Multiple codes are possible with different fifth letters: ACBAC, BACBA, BCCBC, CBACB, CBCCB, CCBCC, CCCCC.
Statement (2): SUFFICIENT. If there is only one C in the code, then there must be a total of four A’s and B’s. There cannot be four A’s because a B would need to precede any A that did not appear in the first spot of the code. For a similar reason, there cannot be three A’s and only one B. There cannot be three or four B’s because the code would demand more than a single C. Thus there must be two A’s and two B’s.
As any B not in the first position must be preceded by a C, the only way there can be fewer C’s than B’s is for the code to begin with a B. Because there are equal numbers of A’s and B’s, and because B is the first letter of the code, A must be the second letter. C must be the third letter because it is the only letter that can be preceded by an A, leaving B and A as the fourth and fifth letters of the code, respectively: BACBA.
The correct answer is (B): Statement (2) alone is sufficient, but statement (1) is not sufficient.
General Discussion
25 Dec 2024, 09:45
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(1) There are many possibilities for a 5th letter - Insufficient
(2) Only the possibility ABCAB is valid, therefore the 5th letter is B - Sufficient
Option B
(2) Only the possibility ABCAB is valid, therefore the 5th letter is B - Sufficient
Option B
