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vinayreguri: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Sat May 07, 2011 6:16 am

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by vinayreguri » Sun Jun 12, 2011 6:23 am

Find the value of (5^(5x+1)-5^(5x-1)+24)/(2.4*5^5x+12)

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Source: Beat The GMAT — Problem Solving | Sun Jun 12, 2011 6:23 am

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by Frankenstein » Sun Jun 12, 2011 6:40 am

Hi,
(5^(5x+1)-5^(5x-1)+24)/(2.4*5^5x+12) = (5^2*5^(5x-1)-5^(5x-1)+24)/(2.4*(5^5x+5))
= ((5^2-1)*5^(5x-1)+24)/(2.4*5*(5^(5x-1) + 1)) = (24*(5^(5x-1) +1)/(12*(5^(5x-1) + 1)) = 2

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by Anurag@Gurome » Sun Jun 12, 2011 6:59 am

vinayreguri wrote:Find the value of (5^(5x+1)-5^(5x-1)+24)/(2.4*5^5x+12)

(5^(5x + 1) = (5^5x)*(5^1) = 5*(5^5x)
(5^(5x - 1) = (5^5x)*(5^-1) = (5^5x)*(1/5) = 0.2*(5^5x)

... (5^(5x + 1) - 5^(5x - 1) + 24)/(2.4*5^5x + 12)
= (5*(5^5x) - 5*(5^5x) + 24)/(2.4*5^5x + 12)
= [(5 - 0.2)*(5^5x) + 24]/[2.4*(5^5x) + 12]
= [4.8*(5^5x) + 24]/[2.4*(5^5x) + 12]
= 2*[2.4*(5^5x) + 12]/[2.4*(5^5x) + 12]
= 2

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vinayreguri: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Sat May 07, 2011 6:16 am

by vinayreguri » Sun Jun 12, 2011 7:13 am

Anurag@Gurome

is this a level 650+ Q

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sunilrawat: Master | Next Rank: 500 Posts; Posts: 112; Joined: Sun Jun 13, 2010 9:20 am; Thanked: 5 times; GMAT Score:640

by sunilrawat » Sun Jun 12, 2011 7:17 am

(5^(5x+1)-5^(5x-1)+24)/(2.4*5^5x+12)
= (5^5x(5-1/5)+24)/(12(2/10*5^5x-1)+1)
= (24(5^5x-1+1))/(12(5^5x-1)+1)
= 2

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