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(3^32)/50 gives remainder and {.} denotes fractional part of

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(3^32)/50 gives remainder and {.} denotes fractional part of  [#permalink]

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New post 04 Nov 2009, 00:49
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(3^32)/50 gives remainder and {.} denotes fractional part of that.The fractional part is of the form (0.bx). The value of x could be
1. 2
2. 4
3. 6
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Intern
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Re: Numbers 2  [#permalink]

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New post 04 Nov 2009, 04:31
7
1
powers of 3 give same last digit at specific intervals. which is:
Power - last digit
1 - 3
2 - 9
3 - 7
4 - 1

Hence, 32nd power of 3 will also be ending with 1. Now, all these numbers ending with 1, when divided by 5 give result ending in XXXX.2, and hence when divided by 50 should result in xxx.X2. Hence the value of x in the question should be 2. OA -1

Is it right?
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Re: Numbers 2  [#permalink]

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New post 04 Nov 2009, 19:42
kalpeshchopada7 wrote:
powers of 3 give same last digit at specific intervals. which is:
Power - last digit
1 - 3
2 - 9
3 - 7
4 - 1

Hence, 32nd power of 3 will also be ending with 1. Now, all these numbers ending with 1, when divided by 5 give result ending in XXXX.2, and hence when divided by 50 should result in xxx.X2. Hence the value of x in the question should be 2. OA -1

Is it right?


Good work. Thats 2.
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Re: Numbers 2  [#permalink]

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New post 16 Feb 2012, 06:15
Bunuel, the first part is systematic. The second part is kind of fuzzy:

Quote:
Now, all these numbers ending with 1, when divided by 5 give result ending in XXXX.2


What if instead of five there were a different number.

Is there a more systematic approach to these kind of problems?

Thank you.
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Re: Numbers 2  [#permalink]

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New post 16 Feb 2012, 10:21
nonameee wrote:
Bunuel, the first part is systematic. The second part is kind of fuzzy:

Quote:
Now, all these numbers ending with 1, when divided by 5 give result ending in XXXX.2


What if instead of five there were a different number.

Is there a more systematic approach to these kind of problems?

Thank you.


Solution above is pretty systematic.

If you are interested in the easiest approach for different numbers then it'll depend on that numbers and answer choices.
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Re: (3^32)/50 gives remainder and {.} denotes fractional part of  [#permalink]

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New post 21 Mar 2012, 09:17
Can anybody explain to me why 1 was divided by 5? If I divide a number that ends with 1 by 50, all kinds of different remainders and therefore digits could result.
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Re: (3^32)/50 gives remainder and {.} denotes fractional part of  [#permalink]

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New post 21 Mar 2012, 11:03
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Re: (3^32)/50 gives remainder and {.} denotes fractional part of  [#permalink]

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New post 07 Apr 2012, 11:49
for such kind of problems how to realize from what power of an integer should i start looking for the pattern?
since, if start listing the powers of three from 0, ill get the unit digit of 3^32=...7
3^0=1
3^1=3
3^2=9
3^3=27
...
suppose its possible to face with a problem when it'll be crucial to know this
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Re: (3^32)/50 gives remainder and {.} denotes fractional part of  [#permalink]

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New post 07 Apr 2012, 12:03
Galiya wrote:
for such kind of problems how to realize from what power of an integer should i start looking for the pattern?
since, if start listing the powers of three from 0, ill get the unit digit of 3^32=...7
3^0=1
3^1=3
3^2=9
3^3=27
...
suppose its possible to face with a problem when it'll be crucial to know this


When looking for a pattern of the last digit of a^n ALWAYS start from n=1 (otherwise if you start from n=0 then all integers will have 1 as the first number in pattern).

For more check: math-number-theory-88376.html
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Re: (3^32)/50 gives remainder and {.} denotes fractional part of  [#permalink]

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New post 19 Oct 2012, 01:48
virtualanimosity wrote:
(3^32)/50 gives remainder and {.} denotes fractional part of that.The fractional part is of the form (0.bx). The value of x could be
1. 2
2. 4
3. 6


\(= 3^{32}\)

\(= (3^{4})^{8}\)

\(3^{4} =81 =50 +31\)

\(= (M50 + 31)^{8}\)

\(= 31^{8}\)

Last digit 1

For division by 10 & multiple thereof ... find the last digit

So remainder is 1/50

i.e 0.02 --- 0.bx

x=2

Option 1
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(3^32)/50 gives remainder and {.} denotes fractional part of  [#permalink]

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New post 10 Dec 2015, 07:31
1
virtualanimosity wrote:
(3^32)/50 gives remainder and {.} denotes fractional part of that.The fractional part is of the form (0.bx). The value of x could be
1. 2
2. 4
3. 6


This question tests your knowledge about cyclicity of the numbers.
Cyclicity: The power after which the units digit of a number repeats itself

Eg:\(2^1\) = 2, \(2^2\)= 4, \(2^3\) = 8, \(2^4\) = 16,\(2^5\) = 32
The units digit repeats after 4 powers hence cyclicity = 4
2, 3, 7, 8: Cyclicity 4
5, 6: Cyclicity 1
4,9: Cyclicity 2


\(3^{32}\) will end with the units digit 1
\(3^{32}\) will be of the form ----1
Therefore \(3^{32}\)/50 will be of the form ----.b2
Hence x = 2
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Re: (3^32)/50 gives remainder and {.} denotes fractional part of  [#permalink]

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Re: (3^32)/50 gives remainder and {.} denotes fractional part of   [#permalink] 24 Nov 2019, 19:01
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