AAPL wrote:The number of boxes in a warehouse can be divided evenly into 6 equal shipments by boat or 27 equal shipments by truck. What is the smallest number of boxes that could be in the warehouse?
A. 27
B. 33
C. 54
D. 81
E. 162
Let N = the number of boxes in the warehouse
If the boxes in a warehouse can be divided evenly into 6 equal shipments (by boat), then
N is divisible by 6
If the boxes in a warehouse can be divided evenly into 27 equal shipments (by truck), then
N is divisible by 27
What is the smallest number of boxes that could be in the warehouse?
So, we're looking for the LEAST COMMON MULTIPLE (LCM) of
6 and
27
From here,
one approach is to just check the the answer choices, starting from A.
A. 27 is not a multiple of
6. ELIMINATE
B. 33 is not a multiple of
6. ELIMINATE
C. 54 IS a multiple of both
6 and
27. So, the correct answer must be C
Approach #2:
6 = (2)(3)
27 = (3)(3)(3)
So, the LCM must have ONE 2 and THREE 3's
In other words, LCM = (2)(3)(3)(3) = 54
Answer: C
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
