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Numbers questions

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pkmme
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Numbers questions [#permalink] New post   11 Jun 2011, 12:18
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

50% (00:00) correct 50% (00:00) wrong based on 2 sessions
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find the attached question.



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puneetj
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Re: Numbers questions [#permalink] New post   11 Jun 2011, 13:32
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reminder is 8

you need to use the cyclicity properties of numbers

3^1 will end in = 3
3^2 will end in= 9
3^3 will end in= 7
3^4 will end in= 1
3^5 will end in = 3

....

so 3^21 will end in 3

Similarly
6^1 will end in 6
6^2 will end in 6

so 6^55 will ALWAYS end in 6

So 3^21 * 6^55 will always end in 8 (3*6)

So the reminder when divided by 10 will always be 8
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Re: Numbers questions [#permalink] New post   12 Jun 2011, 11:36
the answer is correct.
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puneetj
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Re: Numbers questions [#permalink] New post   12 Jun 2011, 11:46
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pkmme wrote:
the answer is correct.


pkmme - Don't be shy to give a kudos then 8-)
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sudhir18n
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Re: Numbers questions [#permalink] New post   12 Jun 2011, 12:07
puneetj wrote:
pkmme wrote:
the answer is correct.


pkmme - Don't be shy to give a kudos then 8-)


given u njoy:)
its 8
i use CRT method

3^21*6^55/10

(3^2)10*3 *6^55
(-1)^10*3*6/10
18/10 =8
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Spidy001
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Re: Numbers questions [#permalink] New post   12 Jun 2011, 12:54
when a number is divided by 10 , last digit is the remainder.

so we have to find the unit digit of the given expression


( 3^(21)*6^(55))/10


3 has cyclicity of 4 => 3^(21) will have same unit digit as 3^1 = 3

unit digit of 6^any positive number = 6

=> remainder of ( 3^(21)*6^(55))/10 = remainder of (3*6/10) = remainder of (18/10)

= 8
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puneetj
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Re: Numbers questions [#permalink] New post   12 Jun 2011, 14:38
sudhir18n wrote:
puneetj wrote:
pkmme wrote:
the answer is correct.


pkmme - Don't be shy to give a kudos then 8-)


given u njoy:)
its 8
i use CRT method

3^21*6^55/10

(3^2)10*3 *6^55
(-1)^10*3*6/10
18/10 =8



Thank you Sudhir....still waiting for a one from pkmme
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amit2k9
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Re: Numbers questions [#permalink] New post   13 Jun 2011, 00:29
3 with exponential power raised repeats after 4.

thus 3^21 will have units digit = 3
also, 6 with exponential power raised will always provide 6 in the units digit.

thus, 3*6 = 18.

remainder = 8.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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gmatclubot
Re: Numbers questions [#permalink]
13 Jun 2011, 00:29
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