PSAT Math Grid-Ins Question 52: Answer and Explanation

Question: 52

The Great Depression began in 1929 and lasted until 1939. It was a period of extreme poverty, marked by low prices and high unemployment. The main catalytic event to the Great Depression was the Wall Street Crash (stock market crash). The Dow, which measures the health of the stock market, started Black Thursday (October 24, 1929) at approximately 306 points.

By the end of business on Black Thursday, the Dow had dropped by 2 percent. Over the course of Friday and the half-day Saturday session, there was no significant change. Unfortunately, the market lost 13 percent on Black Monday, followed by another 12 percent on Black Tuesday. What was the total percent decrease from opening on Black Thursday to closing on Black Tuesday? Round your answer to the nearest whole percent and ignore the percent sign when entering your answer.

Correct Answer: 25

Explanation:

25

Difficulty: Hard

Category: Problem Solving and Data Analysis/Rates, Ratios, Proportions, and Percents

Getting to the Answer: Percent change is given by the ratio . To find the total percent change, you'll need to work your way through each of the days, and then use the ratio. Jot down the Dow value at the end of each day as you go. Do not round until you reach your final answer. First, calculate the value of the Dow at closing on Black Thursday: it opened at 306 and decreased by 2%, which means the value at the end of the day was 100 - 2 = 98% of the starting amount, or 306 × 0.98 = 299.88. Then, it decreased again on Monday by 13% to close at 100 - 13 = 87% of the opening amount, or 299.88 × 0.87 = 260.8956. Finally, it decreased on Tuesday by another 12% to end at 100 - 12 = 88% of the starting amount, or 260.8956 × 0.88 = 229.588. Now, use the percent change formula to calculate the percent decrease from opening on Black Thursday (306) to closing on Black Tuesday (229.588):

The Dow had a total percent decrease of approximately 25% between opening on Black Thursday and closing on Black Tuesday.