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21 Jan 2026, 17:49
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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:
95%
(hard)
Question Stats:
83% (02:03) correct
17%
(01:39)
wrong
based on 53
sessions
History
Date
Time
Result
Not Attempted Yet
When Nancy returned home from the airport, she was unable to open her suitcase. She recalled setting a five-digit lock code using the digits 2, 3, 4, 6, and 8, with no digit repeated. She is certain that the third digit of the code is 3.
Is it necessarily true that the fifth digit of the code is 6?
(1) The first digit of the code is a divisor of the second digit.
(2) The fourth digit of the code is a multiple of the second digit.
Is it necessarily true that the fifth digit of the code is 6?
(1) The first digit of the code is a divisor of the second digit.
(2) The fourth digit of the code is a multiple of the second digit.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
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27 Jan 2026, 11:28
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Amity007 could you please recheck the answer, I think answer is C. Thanks
29 Jan 2026, 07:49
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Code format: d1 d2 d3 d4 d5
Available digits for positions 1, 2, 4, 5: {2, 4, 6, 8} (each used exactly once)
Question: Must d5 = 6?
Statement (1) alone: The first digit is a divisor of the second digit
From {2, 4, 6, 8}, find pairs where d1 divides d2:
- 2 divides: 4, 6, 8
- 4 divides: 8
- 6 and 8 don't divide any other available digits
Possible codes:
- d1 = 2, d2 = 4 → remaining {6, 8} for positions 4 and 5
- d1 = 2, d2 = 6 → remaining {4, 8} for positions 4 and 5
- d1 = 2, d2 = 8 → remaining {4, 6} for positions 4 and 5
- d1 = 4, d2 = 8 → remaining {2, 6} for positions 4 and 5
Multiple arrangements are possible, so d5 could be 6, 8, 4, or 2.
Statement (1) alone is NOT sufficient.
Statement (2) alone: The fourth digit is a multiple of the second digit
From {2, 4, 6, 8}, find pairs where d4 is a multiple of d2:
- 2 is a factor of: 2, 4, 6, 8 (but d4 ≠ d2)
- 4 is a factor of: 8
- 6 and 8 don't go into any other available digits
Similar analysis shows multiple possibilities for d5.
Statement (2) alone is NOT sufficient.
Both statements together:
Testing all cases where d1 divides d2 AND d4 is a multiple of d2:
• d1=2, d2=4: d4 must be 8 (only multiple of 4 left) and d5=6
• d1=2, d2=6: No multiple of 6 available so Impossible
• d1=2, d2=8: No multiple of 8 available so Impossible
• d1=4, d2=8: No multiple of 8 available so Impossible
Only valid code: 2 4 3 8 6
Available digits for positions 1, 2, 4, 5: {2, 4, 6, 8} (each used exactly once)
Question: Must d5 = 6?
Statement (1) alone: The first digit is a divisor of the second digit
From {2, 4, 6, 8}, find pairs where d1 divides d2:
- 2 divides: 4, 6, 8
- 4 divides: 8
- 6 and 8 don't divide any other available digits
Possible codes:
- d1 = 2, d2 = 4 → remaining {6, 8} for positions 4 and 5
- d1 = 2, d2 = 6 → remaining {4, 8} for positions 4 and 5
- d1 = 2, d2 = 8 → remaining {4, 6} for positions 4 and 5
- d1 = 4, d2 = 8 → remaining {2, 6} for positions 4 and 5
Multiple arrangements are possible, so d5 could be 6, 8, 4, or 2.
Statement (1) alone is NOT sufficient.
Statement (2) alone: The fourth digit is a multiple of the second digit
From {2, 4, 6, 8}, find pairs where d4 is a multiple of d2:
- 2 is a factor of: 2, 4, 6, 8 (but d4 ≠ d2)
- 4 is a factor of: 8
- 6 and 8 don't go into any other available digits
Similar analysis shows multiple possibilities for d5.
Statement (2) alone is NOT sufficient.
Both statements together:
Testing all cases where d1 divides d2 AND d4 is a multiple of d2:
• d1=2, d2=4: d4 must be 8 (only multiple of 4 left) and d5=6
• d1=2, d2=6: No multiple of 6 available so Impossible
• d1=2, d2=8: No multiple of 8 available so Impossible
• d1=4, d2=8: No multiple of 8 available so Impossible
Only valid code: 2 4 3 8 6
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
