Worked Examples: SAT Strategy
Example 1: Easy (Percentages in Equations)
Question: The result of increasing the quantity $x$ by $400%$ is 60. What is the value of $x$? [3]
SAT Strategy: A common trap is to simply multiply by 4. Remember that an
increase of $400%$ means the new amount is $100% + 400% = 500%$ of the original amount.
- Convert $500%$ to a decimal multiplier: $5.0$.
- Set up the equation: $5.0x = 60$.
- Divide by 5: $x = 12$.
- Answer: 12.
Example 2: Medium (Margin of Error Inference)
Question: An analyst estimated the mean price of a carton of grape tomatoes to be $\$4.23$, with an associated margin of error of $\$0.08$. Which statement is plausible about the mean price for all locations? [4]
SAT Strategy: The SAT always treats the margin of error as a range of
plausible values around the sample statistic. It is never a guaranteed absolute.
- Find the lower bound: $\$4.23 - \$0.08 = \$4.15$.
- Find the upper bound: $\$4.23 + \$0.08 = \$4.31$.
- The true population mean is plausibly located anywhere within this interval.
- Answer: It is plausible that the mean price is between $\$4.15$ and $\$4.31$.
Example 3: Hard (Evaluating Polls & Populations)
Question: In a poll, 483 out of 803 voters selected at random responded they would vote for Angel Cruz. If 6,424 people vote in the actual election, by how many votes would Angel Cruz be expected to win? [5]
SAT Strategy: Do not just find the number of votes for Cruz. The question asks for the
margin of victory (the difference between Cruz and the opponent).
- Find the number of poll votes for the opponent: $803 - 483 = 320$.
- Find the poll margin of victory: $483 - 320 = 163$ votes.
- Set up a proportion to scale the margin to the full population: $\frac{163}{803} = \frac{x}{6,424}$.
- Solve for $x$: $x = 6,424 \times \left(\frac{163}{803}\right) = 1,304$.
- Answer: 1,304.
Practice Questions
Level 1: Easy (Foundational SAT)
- What is $20%$ of $440$? (Grid-in) [6]
- $13$ is $p%$ of $25$. What is the value of $p$? (Grid-in) [7]
- $4, 10, 18, 4, 4, 5, 6, 5$
What is the median of the data set shown? [8]
- A) $4$
- B) $5$
- C) $7$
- D) $14$
- On a street with 7 houses, 2 houses are blue. If a house from this street is selected at random, what is the probability of selecting a house that is blue? [9]
- A) $\frac{1}{7}$
- B) $\frac{2}{7}$
- C) $\frac{5}{7}$
- D) $\frac{2}{5}$
- The table summarizes the distribution of color and shape for 100 tiles of equal area. There are 30 total red tiles. If one of these 100 tiles is selected at random, what is the probability of selecting a red tile? (Express your answer as a decimal or fraction). (Grid-in) [10]
Level 2: Medium (Standard SAT)
- To estimate the proportion of a population that has a certain characteristic, a random sample was selected. The proportion is estimated to be $0.49$, with an associated margin of error of $0.04$. Which conclusion is most appropriate? [11]
- A) It is plausible that the proportion is between $0.45$ and $0.53$.
- B) It is plausible that the proportion is less than $0.45$.
- C) The proportion is exactly $0.49$.
- D) It is plausible that the proportion is greater than $0.53$.
- Scott selected 20 employees at random from all 400 employees at a company. He found that 16 of the employees in this sample are enrolled in exactly three professional development courses. Based on this, what is the best estimate of the total number of employees at the company enrolled in exactly three courses? [12]
- A) $16$
- B) $320$
- C) $380$
- D) $384$
- $210$ is $p%$ greater than $30$. What is the value of $p$? (Grid-in) [13]
- 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) [14]
- A table summarizes members of an organization by age. There are $135$ total members, and $107$ of them are at least 40 years old. If a member is selected at random, what is the probability that the selected member is at least 40 years old? [15]
- A) $\frac{28}{135}$
- B) $\frac{35}{135}$
- C) $\frac{100}{135}$
- D) $\frac{107}{135}$
Level 3: Hard (Advanced SAT)
- Five sea turtles each have a nest. The original data set of the number of eggs laid is: $149, 144, 148, 136, 139$. A sixth nest with $121$ eggs is added to create a new data set. Which correctly compares the means of the two data sets? [16]
- A) The mean of the original data set is greater than the mean of the new data set.
- B) The mean of the original data set is less than the mean of the new data set.
- C) The means of both data sets are equal.
- D) There is not enough information to compare the means.
- An analyst estimated the mean price of a carton of tomatoes in Utah to be $\$4.23$, with an associated margin of error of $\$0.08$. Which statement is plausible about the mean price for all locations in Utah? [4]
- A) It is between $\$4.15$ and $\$4.31$.
- B) It is either less than $\$4.15$ or greater than $\$4.31$.
- C) It is exactly $\$4.23$.
- D) It is greater than $\$4.31$.
- Two dot plots represent the number of glue sticks brought in by students for Class A and Class B. Both dot plots are perfectly symmetrical and have the exact same shape, though Class B's values are centered at a higher number. Which statement best compares their standard deviations? [17]
- A) Class A's standard deviation is less than Class B's.
- B) Class A's standard deviation is equal to Class B's.
- C) Class A's standard deviation is greater than Class B's.
- D) There is not enough information.
- A poll of 803 randomly selected voters showed 483 would vote for Angel Cruz and 320 for Terry Smith. If 6,424 people vote in the actual election, by how many votes would Angel Cruz be expected to win? [18]
- A) $163$
- B) $1,304$
- C) $3,864$
- D) $5,621$
- A weight of 39 pounds is added to an original data set of 71 tortoise weights. If the original mean was 17 pounds, which statement best compares the mean and median of the new data set to the original? [19]
- A) The mean of the new data set is greater, and the median of the new data set is greater.
- B) The mean of the new data set is greater, and the medians of the two data sets could be equal.
- C) The mean of the new data set is less, and the median is less.
- D) The mean of the new data set is less, and the medians are equal.
Level 4: Very Hard (Slightly beyond SAT)
- A store marks up the wholesale cost of a jacket by $40%$. During a clearance sale, the store applies a $25%$ discount to the marked-up price. If the final sale price of the jacket is $\$126$, what was the original wholesale cost, in dollars? (Grid-in)
- Class X has 20 students with a mean test score of 80. Class Y has 30 students. If the combined mean test score for all 50 students in both classes is 86, what is the mean test score for Class Y? (Grid-in)
- At a high school, $60%$ of students participate in sports, $40%$ participate in music, and $20%$ participate in both sports and music. If a student is selected at random, what is the probability, expressed as a decimal, that the student participates in neither sports nor music? (Grid-in)
- Data set $P$ consists of the values $\{2, 2, 2, 8, 8, 8\}$. Data set $Q$ consists of the values $\{4, 4, 4, 6, 6, 6\}$. Which of the following statements is true regarding the standard deviations of the two data sets?
- A) The standard deviation of $P$ is greater than that of $Q$.
- B) The standard deviation of $P$ is less than that of $Q$.
- C) The standard deviations of $P$ and $Q$ are equal.
- D) The standard deviations cannot be compared without calculating the exact means.
- A researcher conducts a survey to estimate a population proportion. If the researcher wants to reduce the margin of error to exactly half of its original size while keeping the same confidence level, by what factor must the researcher multiply the original sample size? (Grid-in)
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