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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

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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

by M7MBA » Thu Sep 17, 2020 1:19 am

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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.

Answer: B

Source: GMAT Prep
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Source: — Data Sufficiency |
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Re: All boxes in a certain warehouse were arranged in stacks of 12 boxes each, with no boxes left over. After 60 additio

by deloitte247 » Sat Sep 19, 2020 1:38 am

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Before adding 60, all boxes can be arranged in stacks of 12 boxes i.e multiples of 12
After adding 60, all boxes can be arranged in stacks of 14 boxes i.e multiples of 14


Given that => 12b + 60 = 14c
Target question => How many boxes were in the warehouse before the 60 additional boxes arrived?
$$14c\ =\ 12b+60$$
$$c=\frac{12b+60}{14}=\frac{12\left(b+5\right)}{14}$$
$$c=\frac{6\left(b+5\right)}{7}$$
Since the boxes were arranged with no leftovers, 6(b+5) must be divisible by 7 without remainder . 6 is not divisible by 7 so (b+5) must be divisible by 7 without remainder
(b+5) = multiple of 7
b + 5 = 7n
b = 7n - 5 possible values of b = 2, 9, 16, 23, 30, 37

Statement 1 => There were fewer than 100 boxes in the warehouse before the 60 additional arrived
i.e 12b < 110
If b = 2 then 12b = 24
If b = 9 then 12b = 108
If b = 16 then 12b = 192
This is greater than 110 so there are only 2 possible values for box 24 or 108. Since we did not arrive at a definite answer, statement 1 is NOT SUFFICIENT

Statement 2 => There were fewer than 120 boxes in the warehouse after the 60 additional arrived
12b + 60 < 120
If b = 2; 12b + 60 = 84
If b = 9; 12b + 60 = 168
This is greater than 120 so the only value for boxes = 84
Statement 2 alone is SUFFICIENT

Answer = B
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