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khandelwal.ab
- Junior | Next Rank: 30 Posts
- Posts: 21
- Joined: Sun Aug 01, 2010 11:22 am
What is the remainder when 2^39 is divided by 39?
A)0
B)1
C)2
D)8
E)7
OA-D
A)0
B)1
C)2
D)8
E)7
OA-D
The remainder of a product is a product of the remainders of each factor.
Break down into large factors:
2^39 = 2^9 * 2^9 * 2^9 * 2*9 * 8
Calculate remainder of each factor:
2^9 = 512, divided by 39 gives a remainder of 5
8 divided by 39 gives a remainder of 8
Multiply the remainders of the 5 factors and try to reduce to a remainder less than 39 by subtracting multiples of 39:
5*5*5*5*8 = 125*40 = 125*(39+1) = 125*39 + 125 = 125*39 + 3*39 + 8
So the reduced remainder is 8.
In general, such a laborous problem won't appear on GMAT, unless there is a faster shortcut.
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