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11 Nov 2022, 13:49
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
81% (00:45) correct
19%
(01:08)
wrong
based on 176
sessions
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Not Attempted Yet
GMATCoachBen
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Expert reply
11 Nov 2022, 14:23
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Bunuel
First, find the units digit pattern for powers of 2:
2^1 = 2 (1st step in our pattern)
2^2 = 4 (2nd step)
2^3 = 8 (3rd step)
2^4 = 16 (4th step)
Note that if we continue writing out the pattern, we only need to multiply the units digit of 16 by 2 (we only care about the "6", not the "1")
2^5 --> 6*2 = 12 --> ends in 2
We can see that the pattern repeats for every 4 numbers: 2, 4, 8, 6...
Therefore, if the power is a multiple of 4, the units digit will be a 6.
For example:
2^40 ends in a 6
2^41 ends in a 2
2^42 ends in a 4
2^43 ends in an 8
2^44 ends in a 6
So, the next step is to find where the power of 2222 lands in the pattern.
The quickest way is to notice that 2220 is a multiple of 4, because the last 2 digits are a multiple of 4. Therefore, 2^2220 would end in a 6.
So, 2222 is 2 steps farther in our pattern, which goes "2,4,8,6", and therefore ends in a 4, so the answer is C.
To become very quick and accurate on these, flashcards are helpful, such as the ones below:
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12 Dec 2023, 06:26
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↧↧↧ Detailed Video Explanation to the Problem ↧↧↧
We need to find the units digit of \(2^{2222}\)
Lets start by finding the cyclicity of units' digit in powers of 2
\(2^1\) units’ digit is 2
\(2^2\) units’ digit is 4
\(2^3\) units’ digit is 8
\(2^4\) units’ digit is 6
\(2^5\) units’ digit is 2
That means that units digit of power of have a cycle of 4
=> We need to divide the power (2222) by 4 and check what is the remainder
2222 divided by 4 gives 2 remainder
=> Units digit of \(2^{2222}\) = Units digit of \(2^2\) = 4
So, Answer will be C
Hope it helps!
MASTER how to find Units digit of Power of 2
We need to find the units digit of \(2^{2222}\)
Lets start by finding the cyclicity of units' digit in powers of 2
\(2^1\) units’ digit is 2
\(2^2\) units’ digit is 4
\(2^3\) units’ digit is 8
\(2^4\) units’ digit is 6
\(2^5\) units’ digit is 2
That means that units digit of power of have a cycle of 4
=> We need to divide the power (2222) by 4 and check what is the remainder
2222 divided by 4 gives 2 remainder
=> Units digit of \(2^{2222}\) = Units digit of \(2^2\) = 4
So, Answer will be C
Hope it helps!
MASTER how to find Units digit of Power of 2
