MBA .com Prac test one some nuts, i couldnt crack : GMAT Problem Solving (PS)
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# MBA .com Prac test one some nuts, i couldnt crack

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Manager
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MBA .com Prac test one some nuts, i couldnt crack [#permalink]

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19 Apr 2010, 10:53
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A ) 5^21 *4^11= 10^n * 2 : find hte value of n

choices : 11, 21, 22, 32, 23. how to find??
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ASHISH DONGRE
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Re: MBA .com Prac test one some nuts, i couldnt crack [#permalink]

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19 Apr 2010, 11:34
5^21 * 4^11 = 10^n * 2

10^n * 2 = 5^21 * 4^11
=(5^11 * 4^11 ) * 5^10
= (5 * 4 )^11 * 5^10
= (20)^11 * 5^10
= 2^11 * 10^11 * 5^10
= 2* ( 5*2)^10 * 10^11
= 2* 10^20
n = 20
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Re: MBA .com Prac test one some nuts, i couldnt crack [#permalink]

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19 Apr 2010, 21:38
RHS: 10^n * 2 = 5^n * 2 ^n * 2
LHS: 5^21 * 4^11 = 5^21 * 2^22 = 5^21 * 2^21 * 2

compare both & u get n = 21
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Re: MBA .com Prac test one some nuts, i couldnt crack [#permalink]

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19 Apr 2010, 22:50
meghash3 wrote:
A ) 5^21 *4^11= 10^n * 2 : find hte value of n

choices : 11, 21, 22, 32, 23. how to find??

this can be done as under.
$$5^{21} *4^{11}= 10^n * 2$$
$$5^{21} *(2^2)^{11} = 2^n * 5^n * 2$$
$$2^{22} * 5^{21} = 2^{n+1} * 5^n$$
comparing both sides for the powers of 2 or 5, we see that n+1 = 22 and n = 21
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Re: MBA .com Prac test one some nuts, i couldnt crack   [#permalink] 19 Apr 2010, 22:50
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