An investor purchased 100 shares of stock X at 6 1/8 dollars per share and sold them all a year later at 24 dollars per

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An investor purchased 100 shares of stock X at 6 1/8 dollars per share and sold them all a year later at 24 dollars per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?

(A) 92%
(B) 240%
(C) 280%
(D) 300%
(E) 380%


OA C

Source: GMAT Prep

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BTGmoderatorDC wrote:
Mon Sep 13, 2021 7:49 pm
An investor purchased 100 shares of stock X at 6 1/8 dollars per share and sold them all a year later at 24 dollars per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?

(A) 92%
(B) 240%
(C) 280%
(D) 300%
(E) 380%


OA C

Source: GMAT Prep
The formula for percentage change is:

\(\dfrac{\text{new}}{\text{old}} - 1\)

\(\text{new} = 24\ast 0.98 \Rightarrow 24\ast \dfrac{49}{50}\)

\(\text{old} =6\dfrac{1}{8} \ast 1.02 \Rightarrow \dfrac{49}{8} \ast \dfrac{51}{50}\)

\(\dfrac{\text{new}}{\text{old}} \ast \dfrac{8 \ast 50}{8\ast 50}=\dfrac{192\ast 49}{49\ast 51}=\dfrac{192}{51}=\dfrac{384}{102}\)

So the approximate percentage gain the investor made is slightly less than \(384\% - 100 \% = 284\%\)

Therefore, C