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# Exponent

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Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
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19 May 2011, 02:26
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Difficulty:

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2^30*2^30*2^30*2^30=?

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19 May 2011, 07:01
2^{30} = 2^{10} * 2^{10} * 2^{10)

2^{10} = 1024

hence last two digits of 1024 * 1024 * 1024 =

Rof [1024 * 1024 * 1024 ] / 100 = Rof[512 * 1024 * 1024]/ 50

= Rof[12 * 24 * 24 ] / 50 = Rof[6 * 24 * 24] / 25

= Rof [ 6 * (-1) * (-1)] /25 = 6 Hence for last two digits 25 * 4 = 100 means 6 * 4 = 24.

Thus 24 is the last two digits for 1024 * 1024 * 1024.

Now in expression 1024 ^ {3} * 1024 ^ {3} * 1024 ^{3} * 1024 ^{3} we need to find the last two digits.

Hence, 24 * 24 * 24 * 24 will give the last two digits of the expression.

Rof[ 24 * 24 * 24 * 24 ]/ 100 = Rof [ 6 * 24 * 24 * 24] /25 = Rof [ 6 * (-1) * (-1) * (-1) ] / 25 = -6/25

thus remainder is 25-6 = 19.

hence last two digits will be 25 * 4 means 19* 4 = 76.

Thus look for an answer option having last two digits 76.
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19 May 2011, 07:44
What is the question ?
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Director
Status: No dream is too large, no dreamer is too small
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19 May 2011, 09:14
hussi9 wrote:
What is the question ?

2^30*2^30*2^30*2^30=2^?
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Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
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100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
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Joined: 12 Oct 2009
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19 May 2011, 19:16
2^120 or as amit2k9 explained

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Re: Exponent &nbs [#permalink] 19 May 2011, 19:16
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