number properties

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Source: — Data Sufficiency |

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by Anurag@Gurome » Tue Jan 31, 2012 5:51 am
In other words, what is the unit's digit of 2^k?

Now, the unit's digits of powers of 2 have a cycle of 4.
  • # Unit's digit of 2^(multiple of 4) = 6
    # Unit's digit of 2^[(multiple of 4) + 1] = 2
    # Unit's digit of 2^[(multiple of 4) + 2] = 4
    # Unit's digit of 2^[(multiple of 4) + 3] = 8
Statement 1:
Say, k = 10, unit's digit of 2^10 = 2^(8 + 2) = 4
Say, k = 20, unit's digit of 2^20 = 6

Not sufficient

Statement 2: Unit's digit of 2^k will be 6.

Sufficient

The correct answer is B.
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