yoyhan wrote:Hi,
I would very much appreicate if someone could explain question 125 in the 2016 OG quant review for me!
The question is:
What is the remainder when 3^24 is divided by 5?
WRITE IT OUT and LOOK FOR A PATTERN.
3¹/5 = 3/5 = 0 R3.
3²/5 = 9/5 = 1 R4.
3³/5 = 27/5 = 5 R2.
3�/5 = 81/5 = 16 R1.
3�/5 = 243/5 = 48 R3.
3�/5 = 729/5 = 145 R4.
Notice the pattern exhibited by the remainders:
3, 4, 2, 1...3, 4....
The remainders repeated in a CYCLE OF 4:
3, 4, 2, 1.
Implication:
Every exponent that is a MULTIPLE OF 4 will yield a remainder of 1.
From here, the cycle will repeat:
Every exponent that is a (MULTIPLE OF 4) + 1 will yield a remainder of 3.
Every exponent that is a (MULTIPLE OF 4) + 2 will yield a remainder of 4.
Every exponent that is a (MULTIPLE OF 4) + 3 will yield a remainder of 2.
The next exponent that is a MULTIPLE OF 4 will yield a remainder of 1.
And so on.
Since 24 is a multiple of 4, dividing 3²� by 5 will yield a remainder of
1.
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