digit appears in the units

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

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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Source: Beat The GMAT — Problem Solving | Fri Jul 23, 2010 6:36 am

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

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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selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

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?

--Anand--

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surajgarg: Senior | Next Rank: 100 Posts; Posts: 51; Joined: Mon May 10, 2010 11:55 pm; Thanked: 4 times

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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selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Fri Jul 23, 2010 7:15 am

Got it.Thanks

--Anand--

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outreach: Legendary Member; Posts: 748; Joined: Sun Jan 31, 2010 7:54 amFollowed by: 3 members; Thanked: 46 times

by outreach » Sat Jul 24, 2010 1:26 am

2 has a cyclicity of 4
320/4 remainder is 0

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