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01 Feb 2015, 15:42
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
66% (01:35) correct
34%
(01:48)
wrong
based on 118
sessions
History
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Give n is a positive integer, what is the reminder when 3^n is divided by 10?
1. n is a multiple of 3.
2. n is a multiple of 4
1. n is a multiple of 3.
2. n is a multiple of 4
01 Feb 2015, 16:03
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Hi Turkish,
This DS question has a hidden Number Property pattern built into it. You can TEST VALUES to answer the question (and discover the pattern).
We're told that N is a positive integer. We're asked for the remainder when 3^N is divided by 10.
Fact 1: N is a multiple of 3
IF...
N = 3
3^3/10 = 27/10 = 2remainder7 so the answer to the question is 7
IF....
N = 6
3^6/10 = 729/10 = 72remainder9 so the answer to the question is 9
Fact 1 is INSUFFICIENT
Fact 2: N is a multiple of 4
IF....
N = 4
3^4/10 = 81/10 = 8remainder1 so the answer to the question is 1
3^(multiple of 4) creates a pattern.
3^2 = 9, so 3^4 = (3^2)(3^2) = (9)(9) = 81
IF....
N = 8
we have (3^4)(3^4) = (81)(81) = a big number that ends in 1, so the remainder when 3^8/10 is 1.
IF....
N = 12
we have (3^4)(3^4)(3^4) = (81)(81)(81) = a really big number that ends in 1, so the remainder when 3^12/10 is 1.
This pattern means that the remainder will ALWAYS = 1 under these circumstances.
Fact 2 is SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
This DS question has a hidden Number Property pattern built into it. You can TEST VALUES to answer the question (and discover the pattern).
We're told that N is a positive integer. We're asked for the remainder when 3^N is divided by 10.
Fact 1: N is a multiple of 3
IF...
N = 3
3^3/10 = 27/10 = 2remainder7 so the answer to the question is 7
IF....
N = 6
3^6/10 = 729/10 = 72remainder9 so the answer to the question is 9
Fact 1 is INSUFFICIENT
Fact 2: N is a multiple of 4
IF....
N = 4
3^4/10 = 81/10 = 8remainder1 so the answer to the question is 1
3^(multiple of 4) creates a pattern.
3^2 = 9, so 3^4 = (3^2)(3^2) = (9)(9) = 81
IF....
N = 8
we have (3^4)(3^4) = (81)(81) = a big number that ends in 1, so the remainder when 3^8/10 is 1.
IF....
N = 12
we have (3^4)(3^4)(3^4) = (81)(81)(81) = a really big number that ends in 1, so the remainder when 3^12/10 is 1.
This pattern means that the remainder will ALWAYS = 1 under these circumstances.
Fact 2 is SUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich
01 Feb 2015, 16:15
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The remainder of \(3^n/10\) depends on the units digit of \(3^n\)
If we calculate the first several exponents of \(3^1, 3^2\) ... we see the units digits repeat 3, 9, 7, 1...
Statement 1: Insufficient because the units digits of \(3^3\) and \(3^6\) are 7 and 9, respectfully, so the remainder is different for multiples of 3
Statement 2: Sufficient because the units digits is always 1 for 3 raised to the power of some multiple of 4
B is correct.
If we calculate the first several exponents of \(3^1, 3^2\) ... we see the units digits repeat 3, 9, 7, 1...
Statement 1: Insufficient because the units digits of \(3^3\) and \(3^6\) are 7 and 9, respectfully, so the remainder is different for multiples of 3
Statement 2: Sufficient because the units digits is always 1 for 3 raised to the power of some multiple of 4
B is correct.
