GMAT Practice Question: On Monday, the opening price of a certain stock was 100 dollars per share and its closing price...
Question
On Monday, the opening price of a certain stock was 100 dollars per share and its closing price was 110 dollars per share. On Tuesday the closing price of the stock was 10 percent less than its closing price on Monday, and on Wednesday the closing price of the stock was 4 percent greater than its closing price on Tuesday. What was the approximate percent change in the price of the stock from its opening price on Monday to its closing price on Wednesday?
- A decrease of 6%
- A decrease of 4%
- A decrease of 1%
- An increase of 3%
- An increase of 4%
Topics: word problems, percentages, translations, approximations
Solution
Step 1
We translate \textbf{\text{"At the opening of a trading day at a certain stock exchange, the price per share of stock K was 8 dollars"}} and \textbf{\text{"its closing price was 110 dollars per share"}} into variables.
O_M = 100 C_M = 110
Step 2
We translate \textbf{\text{"On Tuesday the closing price of the stock was 10 percent less than its closing price on Monday"}} using relative percent decrease.
C_T = (1 - \frac{10}{100}) \times C_M = 0.9 \times C_M
Step 3
We translate \textbf{\text{"on Wednesday the closing price of the stock was 4 percent greater than its closing price on Tuesday"}} using relative percent increase.
C_W = (1 + \frac{4}{100}) \times C_T = 1.04 \times C_T
Step 4
We translate \textbf{\text{"What was the approximate percent change in the price of the stock from its opening price on Monday to its closing price on Wednesday?"}} using the percent change formula.
C_T = 0.9 \times 110 = 99 C_W = 1.04 \times 99 = 102.96 \text{Percent change} = \frac{102.96 - 100}{100} \times 100\% \approx 2.96\%
Answer
An increase of approximately 3% (Answer D)
