PSAT Math Grid-Ins Question 76: Answer and Explanation

Question: 76

There are currently 6,210 fish in a lake. If the number of fish in the lake increased by 15 percent during the last year and 20 percent during the year before that, how many more fish are in the lake currently than in the lake two years ago?

Correct Answer: 1710

Explanation:

1710

Difficulty: Hard

Getting to the Answer: Work backward using the known information to find the actual number of fish in the lake for each of the past two years. You know the increase in the number of fish over the last year was 15%, so you can set up the following equation, where x represents the actual number of fish last year:

Now, do the same process for the previous year. You know that 5,400 represents the number of fish after an increase of 20%, so you can call the original number of fish at the beginning of the first year y and use the following equation to find y:

Now you have the starting number of fish from two years ago, so you can subtract this from the current number to find the actual change in the number of fish over the entire two years: 6,210 - 4,500 = 1,710.

Grid in 1710.