## 1.

The Correct Answer is (C) — You know that each “house” in the pictograph represents 100 residences. Since the graphic shows 2.5 houses in county A, there are 2.5 × 100 = 250 residences. Each residence needs at least half a square mile of land, so county A needs $\small&space;\frac{250}{2}&space;=&space;125$ square miles of land.

## 2.

The Correct Answer is (H) — To solve this question, evaluate the expression inside the brackets as usual, and then apply the absolute value to your result: |—20 + 7 | = |–13| = 13.

## 3.

The Correct Answer is (B) — First, find the sum of the given numbers: 154 + 784 + 324 = 1,262. Since the digit in the ones place is less than 5, you can round it down to get 1,260.

If you chose (A) or (E), you rounded to the nearest hundreds.

If you chose (C), you forgot to round your result.

If you chose (D), you rounded to the correct place, but up instead of down.

## 4.

The Correct Answer is (J) — To solve this question, be sure to read the table carefully. 30 vehicle owners indicated that they owned a truck from the year 2010–2016.

If you chose (H), you probably found the number of vehicle owners who owned a truck from the years 2000–2009.

If you chose (K), you found the number of vehicle owners surveyed in total.

## 5.

The Correct Answer is (E) — To find the probability of selecting a SUV owner, divide the number of people who own a SUV by the total number of vehicle owners surveyed: $\small&space;\frac{10\text{ SUVs}}{90\text{ Vehicles Total}}=\frac19$ .

## 6.

The Correct Answer is (F) — This question is asking you which of the numbers has only prime number factors, meaning no composite numbers can divide into it (other than the number itself). You can eliminate (G), (H), and (K) because 60, 120, and 140 are all divisible by 10. You can also eliminate (J) because 126 is divisible by 6. The only factors of 26 are 1, 2, 13 and 26; so the remaining answer is indeed correct.

## 7.

The mean is the sum of the data set divided by the number of items in the set: $\small&space;\frac{8+11+22+23+98}{5}= \frac{162}{5}=32.4$. The median is the middle value, which is 22. Therefore, the difference between mean and median is 32.4 — 22 = 10.4.

If you chose (C) or (E), you found either the median or the mean and stopped there.

## 8.

The Correct Answer is (G) — To find the lowest common multiple of a set of numbers, multiply their prime factors together, without repeating shared factors more than once.

The LCM is 24 x 3 = 48.

If you picked (J), you multiplied all of the numbers together, thereby repeating the shared factors.

(H) and (K) are also multiples of the set of numbers, but not the lowest common multiple possible.

## 9.

The Correct Answer is (C) — In order for Christina to distribute her 1,560 candies evenly, her number of friends should be a factor of 1,560; conversely, a number of friends that would not allow this would not be a factor. You can eliminate (A), (B), (D), and (E) because 3, 5, 10, and 13 all go into 1,560. When you divide 1,560 by 7, (C), you are left with a remainder. Therefore, 7 is not a factor.

## 10.

The Correct Answer is (K) — All even numbers are divisible by 2, so doubling any number will always yield an even number, and you can eliminate (F) and (G). Two odd numbers multiplied together will always yield an odd number, so (H) is incorrect as well. Similarly, since x is odd, x2 = x × x will also be odd, eliminating (J). Since x2 is odd, subtracting 1 will make it an even number.

## 11.

The Correct Answer is (E) — You know that each of the 28 guests will consume 2 hamburgers, so Tyler needs $2\times28=56$ hamburgers. Since buns are sold in packages of 6, he will need $\frac{56}{6}=9.\overline{3}$ packages of buns. Buying a third of a package is not possible, so he will need to buy at least 10 whole packages.

## 12.

The Correct Answer is (J) — The lowest common denominator is $2\times3\times5=30$. You can now sum and simplify the fractions:

$\frac{1}{6}+\frac{1}{2}+\frac{1}{5}=\frac{5}{30}+\frac{15}{30}+\frac{6}{30}=\frac{26}{30}=\frac{13}{15}$

## 13.

The Correct Answer is (D) — There is a total of 25 students, and according to the graph, 3 students wrote that they took 4 minutes to complete the problem. Therefore, the percentage of students who took 4 minutes is equal to: $\frac{3}{25}\times100=12\%$.

If you picked any of the other choices, you probably read the graph wrong and found the percentage of students who wrote a different number of minutes to complete the problem.

## 14.

The Correct Answer is (K) — By the second month of college, Carla spent 400 – 200 = 200 more dollars. The percent increase is equal to the change in spending divided by the original amount spent, or $\frac{400-200}{200}\times100=100\%$.

If you chose (J), you probably divided the change in spending, 200 dollars, by the new amount, 400 dollars, instead.

## 15.

The Correct Answer is (D) — To find expected value, which is just a weighted average, sum the result of each possible outcome multiplied by its probability (out of 1). From the table given to you: $(3\times0.1)+(4\times0.2)+(5\times0.1)+(6\times0.4)+(7\times0.2)=5.4$.

If you got (C), you forgot to account for the different probabilities of each roll and calculated the average of 3, 4, 5, 6, and 7.

## 16.

The Correct Answer is (G) — There are 5 letters, so the number of permutations—ways they can be rearranged where order matters—is equal to 5!. However, the letter L is repeated twice, so 5! must be divided by 2! in order to eliminate repeated arrangements.

If you got (J), you didn’t notice the repeated letter L.

If you got (K), you calculated the number of rearrangements assuming you could repeat letters.

If you got (F) or (H), you used either the formula for permutations or combinations with n = 5 objects and r = 2 spaces, without carefully reading the question itself.

## 17.

The Correct Answer is (D) — Since one value is added both above and below x, the middle value of the set, the median will remain unchanged. However, the mean will increase because the value added above x (the original mean) is significantly larger than the new value added below x. Therefore, the mean is now greater than the median.

## 18.

The Correct Answer is (G) — To find the probability of two independent events both occurring, you multiply their individual probabilities.

If you chose (J), you found the probability of either or both of the events occurring—the union instead of the intersection of the two.

## 19.

The Correct Answer is (A) — Since you cannot fully evaluate the expression inside of the absolute value signs due to the variable, you need to “split” the equation into two cases depending on what sign x causes the final expression to have. One where the expression is positive and remains so, and another where it is negative and the absolute value acts as a minus 1 multiplied throughout. Solving both equations will give you the two possible values for x:

\small&space;\begin{align*}&space;13-2x&=3&space;\:\:\:&&space;\:\:\:&space;-(13-2x)&space;&=3\\&space;-2x&=-10&space;&&space;2x&space;&=16\\&space;x&=5&space;&&space;x&space;&=8&space;\end{align*}

## 20.

The Correct Answer is (J) — Jordan runs 12 miles in 36 + 54 = 90 minutes, which is 1.5 hours. To find the average speed, recall that speed is distance over time: $\small&space;\frac{12\text{&space;miles}}{1.5\text{&space;hours}}=8\text{&space;miles&space;per&space;hour}$.