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# When all the boxes in a warehouse were arranged in stacks of 8, there

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Re: When all the boxes in a warehouse were arranged in stacks of 8, there [#permalink]
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
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Re: When all the boxes in a warehouse were arranged in stacks of 8, there [#permalink]
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Bunuel wrote:
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

GMAT™ Focus Sample Question from mba.com

The format of boxes stacked would be 8x+4. And total number of boxes is between 80 and 120. Only these boxes possible: 84, 84+8=92, 100, 108 and 116.

Now,

(1) Check multiples of 9 in above set. Only 108 is there. SUFFICIENT
(2) Check multiples of 12 in above set. 84 and 108 both possible. NOT SUFFICIENT
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When all the boxes in a warehouse were arranged in stacks of 8, there [#permalink]
Let t be the total number of boxes.

t = 8 (number of stacks) + 4

Since we're told that 80 < t < 120, possible values of t are 84, 92, 100, 108 and 116. In other words, one of these values = t.

S1. t is a multiple of 9.
Of the 5 possible values listed, only 108 is a multiple of 9.
SUFFICIENT

S2. t is a multiple of 12.
If the number is divisible by both 3 and 4, then the number is divisible by 12.
Of the 5 possible values listed, both 84 and 108 are divisible by 3 and 4, therefore divisible by 12.
INSUFFICIENT
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Re: When all the boxes in a warehouse were arranged in stacks of 8, there [#permalink]
from given info
possible boxes
80<box<120
88,96,104,112
84,92,100,108,116
#1
If all the boxes in the warehouse had been arranged ins tacks of 9, there would have been no boxes left over.
108 is only option
sufficient
#2
If all the boxes in the warehouse had been arranged in stacks of 12, there would have been no boxes left over

84 & 108 possible
insufficient
option A is correct

Bunuel wrote:
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

GMAT™ Focus Sample Question from mba.com
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When all the boxes in a warehouse were arranged in stacks of 8, there [#permalink]
JeffTargetTestPrep wrote:
Bunuel wrote:
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

80 < n = 8a + 4 < 120, where a is a positive integer, so n = 84, 88, 92, 96, 100, 104, 108, 112, 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.

Dear JeffTargetTestPrep, n can not be equal to 88, 96 and other multiples of 8 in the given range since in that case the "a" would not be an integer.
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Re: When all the boxes in a warehouse were arranged in stacks of 8, there [#permalink]
Thank you, AliGmz !
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Re: When all the boxes in a warehouse were arranged in stacks of 8, there [#permalink]

Bunuel wrote:
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

GMAT™ Focus Sample Question from mba.com

­The question uses the concepts of division and remainders.

When all the boxes in a warehouse were arranged in stacks of 8, there were 4 boxes left over.
This means n = 8a + 4 (when number of boxes is divided by 8, 4 are remianing)

(1) If all the boxes in the warehouse had been arranged ins tacks of 9, there would have been no boxes left over.

This means n = 9b
By hit and trial, I will find the first solution for b which should be even as b = 4
n = 36 is the first value that satisfies both conditions.
Next value of n will be 36 + LCM (8 and 9) = 36   + 72 = 108. Next value will be 36  +  72*2 which is more than 120 so not acceptable.
Hence there is only one value of n and that is 108. Sufficient alone.

(2) If all the boxes in the warehouse had been arranged in stacks of 12, there would have been no boxes left over

This means n = 12b
Again by hit and trial, n = 36 is the first value that satisfies both conditions.
Next value of n will be 36 + LCM (8 and 12) = 36   + 24 = 60. Next value will be 36  +  24*2 = 84. We will get another value of n as 36 + 24*3 = 108
which is also acceptable.
Hence there are 2 acceptable values of n here: 84 and 108. Not sufficient alone.

Check out the concepts of division and remainders here:https://youtu.be/A5abKfUBFSc
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Re: When all the boxes in a warehouse were arranged in stacks of 8, there [#permalink]
JeffTargetTestPrep wrote:
Bunuel wrote:
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

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.