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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 in stacks 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.
GMATTM Focus Sample Question from mba.com
(1) If all the boxes in the warehouse had been arranged in stacks 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.
GMATTM Focus Sample Question from mba.com
07 May 2023, 14:57
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Bunuel
Number of boxes = n
When all the boxes in a warehouse were arranged in stacks of 8, there were 4 boxes left over.
Therefore we can represent n as
n = 8x + 4; x is the quotient and is a non negative integer
Given
\(80 < n < 120\)
Statement 1
(1) If all the boxes in the warehouse had been arranged in stacks of 9, there would have been no boxes left over.
n = 9y
The number of boxes is a multiple of 9. As we know the range, the possible values of the number of boxes are
\(81 \quad 90 \quad 99 \quad 108 \quad 117\)
Out of the above values, only 108 can be represented in the form of '8x + 4', in which x is an integer.
Hence, the statement is sufficient to answer the question. We can eliminate B, C, and E.
Statement 2
(2) If all the boxes in the warehouse had been arranged in stacks of 12, there would have been no boxes left over
n = 12y
The number of boxes is a multiple of 12. As we know the range, the possible values of the number of boxes are
\(84 \quad 96 \quad 108\)
Out of the above values, values 84 and 108 can be represented in the form of '8x + 4', in which x is an integer.
As we are getting two different values for the value of n, the statement alone is not sufficient to answer the question. Eliminate D.
Option A
Updated on: 06 Sep 2023, 18:50
Originally posted by JeffTargetTestPrep on 03 Sep 2023, 16:43.
Last edited by JeffTargetTestPrep on 06 Sep 2023, 18:50, edited 1 time in total.
Last edited by JeffTargetTestPrep on 06 Sep 2023, 18:50, edited 1 time in total.
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Bunuel
80 < n = 8a + 4 < 120, where a is a positive integer, so n = 84, 92, 100, 108, or 116.
We need to answer the question:
n = ?
Statement One Alone:
=> If all the boxes in the warehouse had been arranged in stacks of 9, there would have been no boxes left over.
n = 9b, where b is a positive integer.
n must have been equal to 108, because 108 is the only possible value that is divisible by 9.
Statement one is sufficient. Eliminate answer choices B, C, and E.
Statement Two Alone:
=> If all the boxes in the warehouse had been arranged in stacks of 12, there would have been no boxes left over.
n = 12c, where c is a positive integer.
n could have been equal to 84 or 108, because these possible values are divisible by 12.
Statement two is not sufficient.
Answer: A
