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digit appears in the units

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digit appears in the units

by sanju09 » Fri Jul 23, 2010 6:36 am
What digit appears in the units place in the number obtained when 2^320 is multiplied out?
A. 0
B. 2
C. 4
D. 6
E. 8

[spoiler]Source: majortests.com[/spoiler]
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by kvcpk » Fri Jul 23, 2010 6:46 am
sanju09 wrote:What digit appears in the units place in the number obtained when 2^320 is multiplied out?
A. 0
B. 2
C. 4
D. 6
E. 8

[spoiler]Source: majortests.com[/spoiler]
Last digits of
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 6

320 is divisible by 4

Hence the last digit will be 6
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by selango » Fri Jul 23, 2010 7:04 am
I also got strucked after finding the repeating pattern.

320 is divisible by 2 also.

How to pick the exponent?
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by surajgarg » Fri Jul 23, 2010 7:14 am
selango wrote:I also got strucked after finding the repeating pattern.

320 is divisible by 2 also.

How to pick the exponent?
Hi Elango,

Just divide the exponent given in the problem by the maximum exponent after which the pattern repeats. And check what's the remainder.

Exponent in the problem = 320
Maximum exponent after which the pattern repeats = 4

320/4 gives reminder 0. So pick the digit corresponding to exponent 4.

For example if the exponent was 322.

Then 322/4 gives a remainder 2. In such a case pick the digit corresponding to 2 which is 4.

Hope this explanation helps.
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by selango » Fri Jul 23, 2010 7:15 am
Got it.Thanks
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by outreach » Sat Jul 24, 2010 1:26 am
2 has a cyclicity of 4
320/4 remainder is 0
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