Problem-Solving and Data Analysis: Percentages and Proportions

Worked Examples: SAT Strategy

Practice Questions

Level 1: Easy (Foundational SAT)

1. What is $20%$ of $440$? (Grid-in)
2. Out of $300$ seeds that were planted, $80%$ sprouted. How many of these seeds sprouted?
   • A) $24$
   • B) $80$
   • C) $240$
   • D) $280$
3. A pair of shoes originally costs $\$80$. If the shoes are on sale for $25%$ off, what is the sale price of the shoes?
   • A) $\$20$
   • B) $\$55$
   • C) $\$60$
   • D) $\$100$
4. In a poll of $200$ voters, $130$ voted for Candidate A and the rest voted for Candidate B. What percentage of the polled voters voted for Candidate B? (Grid-in)
5. {|l|c|c|c|} & Right-Handed & Left-Handed & Total
   Male & 42 & 8 & 50
   Female & 45 & 5 & 50
   Total & 87 & 13 & 100
   Based on the table above, what is the probability of randomly selecting a female who is left-handed from the entire group?
   • A) $\frac{5}{100}$
   • B) $\frac{5}{50}$
   • C) $\frac{5}{13}$
   • D) $\frac{13}{100}$

Level 2: Medium (Standard SAT)

1. A store purchases a jacket from a supplier for $\$40$. The store marks up the price by $50%$ to sell to customers. During a clearance sale, the store discounts the jacket by $20%$ off the selling price. What is the clearance price of the jacket?
   • A) $\$48$
   • B) $\$52$
   • C) $\$58$
   • D) $\$60$
2. $72$ is $p%$ of $120$. What is the value of $p$? (Grid-in)
3. The price of a plane ticket increased by $15%$ from March to April. If the ticket cost $\$345$ in April, what was the price of the ticket in March?
   • A) $\$293.25$
   • B) $\$300.00$
   • C) $\$330.00$
   • D) $\$396.75$
4. {|l|c|c|c|} & Cat & Dog & Total
   Has a Yard & 12 & 38 & 50
   No Yard & 24 & 6 & 30
   Total & 36 & 44 & 80
   Based on the table, if a person who owns a dog is chosen at random, what is the probability that this person has a yard? (Grid-in)
5. A number $x$ is increased by $25%$ to get $y$. Then, $y$ is decreased by $40%$ to get $z$. If $z = 60$, what is the value of $x$? (Grid-in)

Level 3: Hard (Advanced SAT)

1. The regular price of a shirt at a store is $\$11.70$. The sale price of the shirt is $80%$ less than the regular price, and the sale price is $30%$ greater than the store's cost for the shirt. What was the store's cost, in dollars, for the shirt? (Grid-in)
2. $150$ is $p%$ greater than $40$. What is the value of $p$? (Grid-in)
3. In a company, $60%$ of the employees are female, and $40%$ are male. If $30%$ of the female employees and $25%$ of the male employees take the bus to work, what percentage of ALL employees take the bus to work?
   • A) $27.5%$
   • B) $28%$
   • C) $55%$
   • D) $58%$
4. {|l|c|c|c|} & Passed & Failed & Total
   Studied & $x$ & 10 & 90
   Did not Study & 15 & $y$ & 60
   Total & 95 & 55 & 150
   According to the partially completed table above, what is the value of $x - y$? (Grid-in)
5. If $a$ is $50%$ of $b$, and $b$ is $120%$ of $c$, what percentage of $c$ is $a$?
   • A) $60%$
   • B) $70%$
   • C) $170%$
   • D) $240%$

Level 4: Very Hard (Slightly beyond SAT)

1. The price of an investment portfolio decreases by $x%$ in Year 1. In Year 2, the portfolio's new value increases by $2x%$. If the value of the portfolio at the end of Year 2 is exactly equal to its original value before Year 1, and $x > 0$, what is the value of $x$? (Grid-in)
2. A population of a town increased by $p%$ from 2010 to 2015, and then decreased by $p%$ from 2015 to 2020. If the town's population in 2020 was $9% $ less than its population in 2010, what is the value of $p$? (Grid-in)
3. In a certain survey, $70%$ of respondents answered "Yes" to Question 1. Of those who answered "Yes" to Question 1, $40%$ answered "Yes" to Question 2. If exactly $140$ respondents answered "Yes" to BOTH questions, how many total people responded to the survey?
   • A) 200
   • B) 350
   • C) 500
   • D) 700
4. An electronics retailer buys a computer for $C$ dollars. The retailer marks up the price by $25%$ to create the list price. Later, the retailer offers a discount of $d%$ off the list price. If the discounted price is exactly $10%$ less than the original cost $C$, what is the value of $d$? (Grid-in)
5. The total cost of an item, including an $8%$ sales tax, is $\$135$. A customer returns the item and receives a full refund, but the store charges a $15%$ restocking fee based on the item's price before tax. How much money, in dollars, does the store keep as a restocking fee? (Grid-in)