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When all the boxes in a warehouse were arranged in stacks of 8, there were 4 boxes left over. If there were more than 80 but fewer than 120 boxes in the warehouse, how many boxes were there?

(1) If all the boxes in the warehouse had been arranged ins tacks of 9, there would have been no boxes left over.
(2) If all the boxes in the warehouse had been arranged in stacks of 12, there would have been no boxes left over
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient
  • d)
    EACH statement ALONE is sufficient to answer the question asked
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
When all the boxes in a warehouse were arranged in stacks of 8, there ...
Statement (1): If all the boxes in the warehouse had been arranged in stacks of 9, there would have been no boxes left over.
This statement implies that the total number of boxes in the warehouse is a multiple of 9. However, since there were 4 boxes left over when they were arranged in stacks of 8, we know that the total number of boxes is not divisible by 8. Therefore, the total number of boxes must be a multiple of 72 (which is the least common multiple of 8 and 9), plus 4.
Considering the given range (more than 80 but fewer than 120 boxes), the possible values for the total number of boxes are 84, 156, and so on.
Statement (1) alone is sufficient to answer the question.
Statement (2): If all the boxes in the warehouse had been arranged in stacks of 12, there would have been no boxes left over.
This statement tells us that the total number of boxes in the warehouse is a multiple of 12. However, since there were 4 boxes left over when they were arranged in stacks of 8, we know that the total number of boxes is not divisible by 8. Therefore, the total number of boxes cannot be a multiple of both 8 and 12.
Statement (2) alone does not provide enough information to answer the question.
Based on the analysis above, the correct answer is A: Statement (1) alone is sufficient, but statement (2) alone is not sufficient to answer the question asked.
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Most Upvoted Answer
When all the boxes in a warehouse were arranged in stacks of 8, there ...
Statement (1): If all the boxes in the warehouse had been arranged in stacks of 9, there would have been no boxes left over.
This statement implies that the total number of boxes in the warehouse is a multiple of 9. However, since there were 4 boxes left over when they were arranged in stacks of 8, we know that the total number of boxes is not divisible by 8. Therefore, the total number of boxes must be a multiple of 72 (which is the least common multiple of 8 and 9), plus 4.
Considering the given range (more than 80 but fewer than 120 boxes), the possible values for the total number of boxes are 84, 156, and so on.
Statement (1) alone is sufficient to answer the question.
Statement (2): If all the boxes in the warehouse had been arranged in stacks of 12, there would have been no boxes left over.
This statement tells us that the total number of boxes in the warehouse is a multiple of 12. However, since there were 4 boxes left over when they were arranged in stacks of 8, we know that the total number of boxes is not divisible by 8. Therefore, the total number of boxes cannot be a multiple of both 8 and 12.
Statement (2) alone does not provide enough information to answer the question.
Based on the analysis above, the correct answer is A: Statement (1) alone is sufficient, but statement (2) alone is not sufficient to answer the question asked.
Community Answer
When all the boxes in a warehouse were arranged in stacks of 8, there ...
Understanding the Problem
The problem states that when boxes in a warehouse were arranged in stacks of 8, there were 4 boxes left over. Therefore, we can express the total number of boxes, x, with the equation:
x = 8k + 4, where k is a non-negative integer.
Given the constraints, we know:
- 80 < x="" />< />
This implies:
- 80 < 8k="" +="" 4="" />< />
This can be simplified to:
- 76 < 8k="" />< />
- 9.5 < k="" />< />
Since k must be an integer, the possible values for k are 10, 11, 12, 13, and 14.
Now, calculating x for these values:
- k = 10 → x = 84
- k = 11 → x = 92
- k = 12 → x = 100
- k = 13 → x = 108
- k = 14 → x = 116
The potential values for x are: 84, 92, 100, 108, and 116.
Evaluating Statement (1)
Statement (1) states that if the boxes were arranged in stacks of 9, there would be no boxes left over. This means:
x mod 9 = 0
Checking each candidate:
- 84 mod 9 = 3 (not suitable)
- 92 mod 9 = 2 (not suitable)
- 100 mod 9 = 1 (not suitable)
- 108 mod 9 = 0 (suitable)
- 116 mod 9 = 8 (not suitable)
Thus, from Statement (1), the only value satisfying all conditions is 108.
Evaluating Statement (2)
Statement (2) indicates that if the boxes were arranged in stacks of 12, there would be no boxes left over. This means:
x mod 12 = 0
Checking each candidate:
- 84 mod 12 = 0 (suitable)
- 92 mod 12 = 8 (not suitable)
- 100 mod 12 = 4 (not suitable)
- 108 mod 12 = 0 (suitable)
- 116 mod 12 = 8 (not suitable)
Thus, from Statement (2), the suitable values are 84 and 108.
Conclusion
Since Statement (1) narrows it down to only one value (108), it is sufficient alone. Statement (2) provides multiple possibilities, hence it is not sufficient alone. Therefore, the correct answer is option ‘A’.
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When all the boxes in a warehouse were arranged in stacks of 8, there were 4 boxes left over. If there were more than 80 but fewer than 120 boxes in the warehouse, how many boxes were there?(1) If all the boxes in the warehouse had been arranged ins tacks of 9, there would have been no boxes left over.(2) If all the boxes in the warehouse had been arranged in stacks of 12, there would have been no boxes left overa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer?
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When all the boxes in a warehouse were arranged in stacks of 8, there were 4 boxes left over. If there were more than 80 but fewer than 120 boxes in the warehouse, how many boxes were there?(1) If all the boxes in the warehouse had been arranged ins tacks of 9, there would have been no boxes left over.(2) If all the boxes in the warehouse had been arranged in stacks of 12, there would have been no boxes left overa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about When all the boxes in a warehouse were arranged in stacks of 8, there were 4 boxes left over. If there were more than 80 but fewer than 120 boxes in the warehouse, how many boxes were there?(1) If all the boxes in the warehouse had been arranged ins tacks of 9, there would have been no boxes left over.(2) If all the boxes in the warehouse had been arranged in stacks of 12, there would have been no boxes left overa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When all the boxes in a warehouse were arranged in stacks of 8, there were 4 boxes left over. If there were more than 80 but fewer than 120 boxes in the warehouse, how many boxes were there?(1) If all the boxes in the warehouse had been arranged ins tacks of 9, there would have been no boxes left over.(2) If all the boxes in the warehouse had been arranged in stacks of 12, there would have been no boxes left overa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer?.
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If there were more than 80 but fewer than 120 boxes in the warehouse, how many boxes were there?(1) If all the boxes in the warehouse had been arranged ins tacks of 9, there would have been no boxes left over.(2) If all the boxes in the warehouse had been arranged in stacks of 12, there would have been no boxes left overa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. 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If there were more than 80 but fewer than 120 boxes in the warehouse, how many boxes were there?(1) If all the boxes in the warehouse had been arranged ins tacks of 9, there would have been no boxes left over.(2) If all the boxes in the warehouse had been arranged in stacks of 12, there would have been no boxes left overa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. 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If there were more than 80 but fewer than 120 boxes in the warehouse, how many boxes were there?(1) If all the boxes in the warehouse had been arranged ins tacks of 9, there would have been no boxes left over.(2) If all the boxes in the warehouse had been arranged in stacks of 12, there would have been no boxes left overa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice When all the boxes in a warehouse were arranged in stacks of 8, there were 4 boxes left over. If there were more than 80 but fewer than 120 boxes in the warehouse, how many boxes were there?(1) If all the boxes in the warehouse had been arranged ins tacks of 9, there would have been no boxes left over.(2) If all the boxes in the warehouse had been arranged in stacks of 12, there would have been no boxes left overa)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice GMAT tests.
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