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The largest number amongst the following that will perfectly [#permalink]
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17 Oct 2008, 09:28
The largest number amongst the following that will perfectly divide 101^100  1 is (a) 100 (b) 10,000 (c) 100100 (d) 100,000 (e) 100,000,00 == Message from GMAT Club Team == This is not a quality discussion. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.



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Re: Largest number [#permalink]
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19 Oct 2008, 17:14
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singaks wrote: The largest number amongst the following that will perfectly divide 101^100  1 is
(a) 100 (b) 10,000 (c) 100100 (d) 100,000 (e) 100,000,00 101^100  1^100 =(1011) (101^99 + .... + 1) =100 (.....) Hence, A



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Re: Largest number [#permalink]
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19 Oct 2008, 17:26
Thanks.., but that is not the OA....anyone ?



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Re: Largest number [#permalink]
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19 Oct 2008, 18:45
its C pls post the OA.
thanks!



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Re: Largest number [#permalink]
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19 Oct 2008, 18:49
Sorry its not C either...I also went for C...We are running out of choices...



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Re: Largest number [#permalink]
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19 Oct 2008, 20:20
singaks wrote: The largest number amongst the following that will perfectly divide 101^100  1 is
(a) 100 (b) 10,000 (c) 100100 (d) 100,000 (e) 100,000,00 lets see 101^2, is 10201, 101^3 is 1030301 you will notice that the 3rd digit from the left will become 0, when we hit ^10, so based on that 100,000,00 will divide it E it is..



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Re: Largest number [#permalink]
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19 Oct 2008, 20:42
Sorry Guys....The OA is not even E....Since we are down to only 2 options...I will give the answer...The OA is B...can anybody wrestle is one ???



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Re: Largest number [#permalink]
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19 Oct 2008, 20:54
singaks wrote: Sorry Guys....The OA is not even E....Since we are down to only 2 options...I will give the answer...The OA is B...can anybody wrestle is one ??? actually i just made a mistake posting my ans...the working is actually correct..ans should be b... 101*101=101^2 or 10201 101*101*101=101^3 or 1030301 101^10 will get you XXXXX001 101^100 will get XXX00001 which is divisible by 10,000 after you 1 from the unit digit..



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Re: Largest number [#permalink]
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19 Oct 2008, 22:09
Fresinha, is it necessary that 101^100 will result in XXXXX00001? I am not doubting you answer but just want to confirm the rule.



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Re: Largest number [#permalink]
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19 Oct 2008, 23:04
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I would have surely answered this wrong in the real exam. However, after spending more than 5 mins, here is my explanation of the OA.
101^1001 = (1011)*(101^99 + 101^98 + 101^97 + .......+1) = 100 * ((101^99 + 101^98 + 101^97 + .......+1) = 100 * (1011) * (101^98 + 101^97 + ........ + 1) = 100 * 100 * (101^98 + 101^97 + ........ + 1)
Thus, the above expression will be completely divisible by 100, 10000, 1000000, ....etc.
Since the largests of the numbers in the answer choices from the series above is 10000, hence B should be the answer.



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Re: Largest number [#permalink]
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20 Oct 2008, 12:48
Could you please explain how did you factor 101^100 1.. I could not get it. Thanks
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Re: Largest number [#permalink]
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20 Oct 2008, 17:15
Hi scthakur
Could you explain how you broke down the equation please



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Re: Largest number [#permalink]
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20 Oct 2008, 23:23
kman wrote: Hi scthakur
Could you explain how you broke down the equation please a^n  1 can be written as (a1)(a^n1 + a^n2 + a^n3 + ......+1). For example, a^31 = (a1)(a^2 + a + 1). a^41 = (a1)(a^3 + a^2 + a + 1)



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Re: Largest number [#permalink]
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20 Oct 2008, 23:51
scthakur wrote: I would have surely answered this wrong in the real exam. However, after spending more than 5 mins, here is my explanation of the OA.
101^1001 = (1011)*(101^99 + 101^98 + 101^97 + .......+1) = 100 * ((101^99 + 101^98 + 101^97 + .......+1) = 100 * (1011) * (101^98 + 101^97 + ........ + 1) = 100 * 100 * (101^98 + 101^97 + ........ + 1)
Thus, the above expression will be completely divisible by 100, 10000, 1000000, ....etc.
Since the largests of the numbers in the answer choices from the series above is 10000, hence B should be the answer. doesnt this mean that 100,000,000 is a factor, which would be E? unless the comma is in the wrong place on answer choice E.



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Re: Largest number [#permalink]
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21 Oct 2008, 07:03
singaks wrote: The largest number amongst the following that will perfectly divide 101^100  1 is
(a) 100 (b) 10,000 (c) 100100 (d) 100,000 (e) 100,000,00 Ithink its not a Gmat question becasue it will test u with Eulers law. which i guess is not in GMAT. Anyways .. i cant explain u the rule here... Eulers rule says..If M and N are 2 co primes to each other.. HCF (M,N) = 1 and N= a^p*b^q.......remainder ( M^#(N)/N) = 1. where #N = N( 11/a)(11/b)..are Euler Totient function .. here 101 and 100 are co primes 101 ( 11/101) = 100 hence the expression 101^100 will be divisble by 10000 will give an remainder of 1 101^100  1 is +11 = 0. hence the whole expression is divisble by 10000. I am sure its tough to understand.. but please let me know if u have any doubts...



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Re: Largest number [#permalink]
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21 Oct 2008, 07:05
yezz wrote: singaks wrote: The largest number amongst the following that will perfectly divide 101^100  1 is
(a) 100 (b) 10,000 (c) 100100 (d) 100,000 (e) 100,000,00 Ithink its not a Gmat question becasue it will test u with Eulers law. which i guess is not in GMAT. Anyways .. i cant explain u the rule here... Eulers rule says..If M and N are 2 co primes to each other.. HCF (M,N) = 1 and N= a^p*b^q.......remainder ( M^#(N)/N) = 1. where #N = N( 11/a)(11/b)..are Euler Totient function .. here 101 and 100 are co primes 101 ( 11/101) = 100 hence the expression 101^100 will be divisble by 10000 will give an remainder of 1 101^100  1 is +11 = 0. hence the whole expression is divisble by 10000. I am sure its tough to understand.. but please let me know if u have any doubts... I got this reply from one Guru and i dont get it myslef == Message from GMAT Club Team == This is not a quality discussion. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.




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