Alterego wrote:
What is the remainder when
43^{86} is divided by 5?
A) 0
B) 1
C) 2
D) 3
E) 4
Please provide a detail explanation on how you achieved the correct answer.
Thanks
First, you have to come into terms that the GMAT doesn't expect you to calculate for the value of 43^86.
Second, you have to know that when it comes to these kinds of questions, the only digit that matters is the units digit of the number.
Always try to enumerate the powers of the said number to LOOK FOR THE PATTERN:
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81 (see it's still easy to multiply 3 from the previous digit, it's still "time-friendly")
3^5 = 243 (it's still time-friendly here)
3^6 = (now it becomes counter-productive to calculate 243*3; so what do we do then? let's just multiply the units digit by 3) = 3*3 = 9
3^7 = _ _ _ 7 (7 is the last digits, although I don't know if it's a four digit number of 5, doesn't matter)
Are you seeing the pattern? If you haven't, check out the corresponding units digit for each power
when raised to 1, the units digit is 3
raised to 2, the units digit is 9
raised to 3, the units digit is 7
raised to 4, the units digit is 1
raised to 5, the units digit is 3 <--- "the cycle begins again"
raised to 6, the units digit is 9
Now we know that raised to 6, the units digit is 9, the question says that 43 should be raised to 86 (which is equal to raised to 6, check our pattern). This means the units digit is 9
Now let's divide 9 by 5
What's the remainder? 4
Answer: (E)
(kudos?
)
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81% (01:24) correct
