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MrWhite
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MrWhite
My method is as follows:

2004: X
2005: \(\frac{4X}{5}\)
2006: \(\frac{4X}{5} * \frac{11}{10} = \frac{22X}{25}\)
2007: X

% increase from 2006 to 2007 = \(\frac{3}{25}\) = 12%

I am getting 12% - (C), but official answer says its 14% - (D).

Could someone please help me understand where I am going wrong :)

Everything's fine, but you made a small mistake
it's not 3/25, it's 3/22, %change = (Next-Previous/Previous)*100
=(1-(22/25))/(22/25)
=(3/25)/(22/25)
=3/22
=0.136
Multiply by 100, it's 13.6%, close to 14%
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'04 = 100
'05 = 80
'06 = 88
'07 = 100

'06 -> '07 = 88 -> 100

Change to 8800 and 10,000

1% of 8800 is 88 -> Eliminate a) and B) and we will try D) First.

88x14 = (80+8)(10+4) = 800+320+80+32 = 1232 (I used foil just to multiply 88x14 so that I won't make a mistake)
8800+1232 = 10,032 which is aprox 10,000

Thus 14% and D) is answer
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KarishmaB Is there smart way to approach this question apart from the conventional wya i.e (12/ 88) * 100 = 13.6 = 14% increase.
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MrWhite
A certain company's yearly revenue was 20% less in 2005 than in 2004 and 10% greater in 2006 than in 2005. If the company's revenue in 2007 was equal to it's yearly revenue in 2004, which of the following is closest to the percent increase in the company's yearly revenue from 2006 to 2007?

(A) 5%
(B) 10%
(C) 12%
(D) 14%
(E) 15%

Attachment:
2024-01-25_12-42-51.png
­There are 3 successive percentage changes which lead to overall no change i.e. a multiplication factor of 1 overall.

\( \frac{4}{5} * \frac{11}{10} * x = 1\)

\(x = \frac{50}{44}\) which means an increase of 6/44 *100 = about 14%

Answer (D)

Video on multiplication factors in percentages: https://youtu.be/HxnsYI1Rws8
Post on successive percentage changes: https://anaprep.com/arithmetic-successi ... e-changes/
 
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