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What is the 6th digit of 201^3?

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Manager
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What is the 6th digit of 201^3?  [#permalink]

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New post 21 Aug 2018, 10:05
1
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A
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E

Difficulty:

  55% (hard)

Question Stats:

41% (00:56) correct 59% (00:49) wrong based on 51 sessions

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What is the 6th digit of \(202^3\)?

1) 0
2) 2
3) 4
4) 6
5) 8
Director
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Re: What is the 6th digit of 201^3?  [#permalink]

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New post 21 Aug 2018, 10:27
2
1
Afc0892 wrote:
What is the 6th digit of \(202^3\)?

1) 0
2) 2
3) 4
4) 6
5) 8


\(202^3\)=\((200+2)^3\)=\(200^3+2^3+3*200*2(200+2)\)
=8000000+8+1200*202

No need of addition or multiplication.

00(last two digits of 1st term- 6th and 7th digit respectively)+8(the only digit of 2nd term-this is added because it may lead to a carry forward that will increase the magnitude of 6th digit)+00(last two digits of 1200 as 1200 multiplied by any number will yield a number with last two digits zero)=08, where 0 is the 6th digit.

Ans. (A)
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Re: What is the 6th digit of 201^3?  [#permalink]

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New post 28 Aug 2018, 22:20
Bunuel chetan2u

Please explain in a way I can understand.
And an approach to solve such problems with respect to any place of the digit asked.

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What is the 6th digit of 201^3?  [#permalink]

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New post 28 Aug 2018, 22:55
AdityaHongunti wrote:
Bunuel chetan2u

Please explain in a way I can understand.
And an approach to solve such problems with respect to any place of the digit asked.

Posted from my mobile device


Hi,

I am yet to see a question which looks for 6th digit of an expansion.
the 6th digit itself is confusing as 6th could be from right or from left, so you need not worry about such questions.
But yes you should know how to find units digit - cyclicity
or tens digit - remainder when divided by 10.
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: What is the 6th digit of 201^3?  [#permalink]

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New post 28 Aug 2018, 23:44
1
PKN wrote:
Afc0892 wrote:
What is the 6th digit of \(202^3\)?

1) 0
2) 2
3) 4
4) 6
5) 8


\(202^3\)=\((200+2)^3\)=\(200^3+2^3+3*200*2(200+2)\)
=8000000+8+1200*202

No need of addition or multiplication.

00(last two digits of 1st term- 6th and 7th digit respectively)+8(the only digit of 2nd term-this is added because it may lead to a carry forward that will increase the magnitude of 6th digit)+00(last two digits of 1200 as 1200 multiplied by any number will yield a number with last two digits zero)=08, where 0 is the 6th digit.

Ans. (A)



Good way , didn't think of this way the first time I saw the question.!!
I just multiplied it 3 times :grin:
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Re: What is the 6th digit of 201^3?  [#permalink]

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New post 28 Aug 2018, 23:53
CounterSniper wrote:
PKN wrote:
Afc0892 wrote:
What is the 6th digit of \(202^3\)?

1) 0
2) 2
3) 4
4) 6
5) 8


\(202^3\)=\((200+2)^3\)=\(200^3+2^3+3*200*2(200+2)\)
=8000000+8+1200*202

No need of addition or multiplication.

00(last two digits of 1st term- 6th and 7th digit respectively)+8(the only digit of 2nd term-this is added because it may lead to a carry forward that will increase the magnitude of 6th digit)+00(last two digits of 1200 as 1200 multiplied by any number will yield a number with last two digits zero)=08, where 0 is the 6th digit.

Ans. (A)



Good way , didn't think of this way the first time I saw the question.!!
I just multiplied it 3 times :grin:


Thank you CounterSniper,

Kudos!! for your honesty !! (I just multiplied it 3 times :grin:)
_________________

Regards,

PKN

Rise above the storm, you will find the sunshine

Re: What is the 6th digit of 201^3? &nbs [#permalink] 28 Aug 2018, 23:53
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