SAT Percentages Practice Question 2 (Hard)

Math · Problem-Solving and Data AnalysisHard

The price of a stock increased by $p\%$ in one month and then decreased by $30\%$ the following month. At the end of the two months, the price was $112\%$ of the original price. What is the value of $p$ ?

Student-produced response: enter your answer.

Show answer and explanation

Answer: 60

A $p\%$ increase multiplies the price by $1 + \frac{p}{100}$ , and a $30\%$ decrease multiplies it by $0.70$ . So $(1 + \frac{p}{100})(0.70) = 1.12$ . Dividing gives $1 + \frac{p}{100} = 1.6$ , so $p = 60$ .

Answering $42$ comes from adding percents ( $p - 30 = 12$ ), which ignores that the $30\%$ decrease applies to the already-increased price.

Ask Owl about this question Next question

Got it wrong? On SAT Owl, Owl looks at the answer you chose and explains the exact mistake, then gives you similar questions until it sticks. Get your predicted SAT score free.