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

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Senior Manager
Joined: 18 Jul 2018
Posts: 374
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
What is the 6th digit of 201^3?  [#permalink]

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21 Aug 2018, 09:05
1
00:00

Difficulty:

55% (hard)

Question Stats:

42% (01:00) correct 58% (00:51) wrong based on 55 sessions

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What is the 6th digit of $$202^3$$?

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

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Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: What is the 6th digit of 201^3?  [#permalink]

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21 Aug 2018, 09:27
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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PKN

Rise above the storm, you will find the sunshine

Senior Manager
Joined: 20 Sep 2016
Posts: 459
Re: What is the 6th digit of 201^3?  [#permalink]

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28 Aug 2018, 21:20
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.

Posted from my mobile device
Math Expert
Joined: 02 Aug 2009
Posts: 7041
What is the 6th digit of 201^3?  [#permalink]

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28 Aug 2018, 21:55
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.
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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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Director
Joined: 20 Feb 2015
Posts: 796
Concentration: Strategy, General Management
Re: What is the 6th digit of 201^3?  [#permalink]

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28 Aug 2018, 22:44
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
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: What is the 6th digit of 201^3?  [#permalink]

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28 Aug 2018, 22:53
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

Thank you CounterSniper,

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

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, 22:53
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