All boxes in a certain warehouse were arranged in stacks of 12 boxes each, with no boxes left over. After 60 additional

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All boxes in a certain warehouse were arranged in stacks of 12 boxes each, with no boxes left over. After 60 additional boxes arrived and no boxes were removed, all the boxes in the warehouse were arranged in stacks of 14 boxes each, with no boxes left over. How many boxes were in the warehouse before the 60 additional boxes arrived?

(1) There were fewer than 110 boxes in the warehouse before the 60 additional arrived.
(1) There were fewer than 120 boxes in the warehouse after the 60 additional arrived.


OA B

Source: GMAT Prep

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BTGmoderatorDC wrote:
Thu Feb 11, 2021 5:20 pm
All boxes in a certain warehouse were arranged in stacks of 12 boxes each, with no boxes left over. After 60 additional boxes arrived and no boxes were removed, all the boxes in the warehouse were arranged in stacks of 14 boxes each, with no boxes left over. How many boxes were in the warehouse before the 60 additional boxes arrived?

(1) There were fewer than 110 boxes in the warehouse before the 60 additional arrived.
(1) There were fewer than 120 boxes in the warehouse after the 60 additional arrived.


OA B

Source: GMAT Prep
When a multiple of 12 (the original number of boxes) is increased by 60, the result is a multiple of 14 (the new number of boxes):
12x + 60 = 14y
6x + 30 = 7y
6(x+5) = 7y

Since the left side must be equal to a multiple of 7, x+5 must be equal to a multiple of 7.
Two smallest cases:
Case 1: x=2, with the result that x+5=7
Original number of boxes = 12x = 12*2 = 24
New number of boxes after the 60-box increase = 24+60 = 84

Case 2: x=9, with the result that x+5=14
Original number of boxes = 12x = 12*9 = 108
New number of boxes after the 60-box increase = 108+60 = 168

Statement 1: There were fewer than 110 boxes in the warehouse before the 60 additional arrived
Cases 1 and 2 both satisfy the condition that the original number of boxes is less than 110.
Since the original number of boxes can be different values, INSUFFICIENT.

Statement 2: There were fewer than 120 boxes in the warehouse after the 60 additional arrived.
Only Case 1 satisfies the condition that the new number of boxes is less than 120.
In Case 1, the original number of boxes = 24
SUFFICIENT.

The correct answer is B.
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