## 1.

The Correct Answer is (C) — Multiplying through gives $\inline&space;-6x+2c=\frac{-6c^2-3cx}{c}&space;+&space;5c$. Simplifying the right side gives -6x + 2c = -6c - 3x + 5c, which can be further simplified to -6x + 2c = -c – 3x. Rearranging gives 3c = 3x, so c = x.

## 2.

The Correct Answer is (D) — If the mean of 6 integers is 30, their sum must be 180. Similarly, if the mean of 5 integers (since one was removed) is 34, their sum must be 170. The difference between these two numbers is 10, which must be the number that was removed.

## 3.

The Correct Answer is (D) — The y-intercept is defined as the value of y when x is zero. Plugging zero in for x in the equation gives 6.

## 4.

The Correct Answer is (A) — The slope of the line is 1/3 and the y-intercept is 0, so the equation is $\inline&space;y=\frac{1}{3}x+0$.

## 5.

The Correct Answer is (D) — Plugging in 6 for x gives 6/2 + 3 ≤ 2(6) – 9, or 6 ≤ 3, which is false.

## 6.

The Correct Answer is (C) — Scenario I can be represented as y = 5x + b. Scenario III can be represented as y = 3x + b. Scenario II, however, would require an exponential term.

## 7.

The Correct Answer is (B) — Based on the graph, the total number of students enrolled in 2009 was 2500.

## 8.

The Correct Answer is (B) — Between 2007 and 2008, the number of students in the public sector increased, but the number of students in the private sector and the number of students overall decreased.

## 9.

The Correct Answer is (D) — For every gray finch, there are two black finches, and for every two black finches, there are four spotted finches. So out of every seven finches (1 gray + 2 black + 4 spotted), four will be spotted.

## 10.

The Correct Answer is (C) — This is the only equation that satisfies all values of x for f(x).

## 11.

The Correct Answer is (C) — Rearranging gives 0 = x2 + x – 20 and factoring gives 0 = (x + 5)(x – 4), so x = -5 or x = 4. Plugging these values into x2x gives 12 and 30, and both of these values are between 11 and 31.

## 12.

The Correct Answer is (C) — If the number of events had held steady at a, the events over the 28 days would have totaled 4a. Since events decreased by 25%, only 75% of the events will occur. 75% of 4a is 3a.

## 13.

The Correct Answer is (A) — A company saw an increase in stock price if its y-coordinate (stock price in 2011) is greater than its x-coordinate (stock price in 2010); in other words, if a company lies above the line y = x, it saw an increase. The company at (25, 25) saw neither an increase nor a decrease.

## 14.

The Correct Answer is (B) — 30 correct answers would give 60 points; the remaining 15 incorrect or unanswered questions give -15 points. 60 – 15 = 45.

## 15.

The Correct Answer is (C) — 70 milliliters are dumped on the ground 60 times per minute, for a total of 4200 milliliters dumped per minute. Over 5 minutes this will result in 21000 milliliters, or 21L, dumped on the ground.

## 16.

The Correct Answer is (A)x + y = 9 can be rewritten as y = 9 – x. Plugging this value in for y in the equation x2 + y2 = 45 gives us x2 + (9 – x)2 = 45. Expanding and simplifying gives us 2x2 – 18x + 36 = 0, and dividing both sides by two gives us x2 – 9x + 18 = 0. Factoring gives (x – 3)(x – 6) = 0, so the possible values of x are 3 and 6.

## 17.

The Correct Answer is (C) — Setting the two equations equal to each other gives –x2 + 4 = 2x + 1. Rearranging gives 0 = x2 + 2x – 3, and factoring gives (x – 1)(x + 3) = 0, so the possible values for x are 1 and -3. Since (a, b) is in quadrant 1, we must use 1 as the value of x. Plugging this back in to either equation gives us y = 3, so ab = 1 × 3 = 3.

## 18.

The Correct Answer is (B) — The question can be written as a + b = 2|ab|. Let a = 6. Then setting b = 2, we can see that 6 + 2 = 2|6 — 2|, so (A) is not the correct answer. Similarly, 18 + 6 = 2|18 — 6|, so (C) is not the correct answer. However, 12 + 6 ≠ 2|12 — 6|, so 12 is not a possible value.

## 19.

The Correct Answer is (D) — If Jenny has a 3 and a 6, the points from those cards is equal to (3 × 2) + (6 × 3) = 24. That means that the third card is worth 48 – 24 = 24 points. Since 24/3 = 8, her third card must have been an 8.

## 20.

The Correct Answer is (C) — The smallest number that is divisible by both 3 and 5 is 15. That means that 1/15 of the numbers from 1 to 1000 will be divisible by both 3 and 5. 1000/15 = 66.67, but we round down to 66 to stay within the range of 1 to 1000. So 66 out of the 1000 numbers will be divisible by 3 and 5, giving us a probability of 33/500.

## 21.

The Correct Answer is (B) — Percent increase can be calculated by dividing the newer value by the older value. Company B had an increase of $37.80/$35.80 = 1.0559 = 105.59%, the highest of the three companies.

## 22.

The Correct Answer is (B) — The growth between 36 and 48 hours is much smaller than the growth between 12 and 24 hours and 24 and 36 hours.

## 23.

The Correct Answer is (D) — There are three integers each with value 3d, three integers each with value e, and six integers each with value f. This gives us a total of 12 integers. The total value for the first group is 9d (three groups of single integers, each with value 3d, gives 3d + 3d + 3d = 9d); the total value for the second group is 3e (one group of 3 integers, each with value e, gives e + e + e = 3e); the total value for the third group is 6f (one group of 6 integers, each with value f). To find the average, we can write (9d + 3e + 6f)/12. Simplifying gives (3d + e + 2f)/4.

## 24.

The Correct Answer is (C) — Given that event v has already occurred, we can say that the chances of v having happened on this Tuesday are 100%. We can get 100% by dividing 28% (the probability that v will happen) by 28% (the probability that v has happened). To find the probability of event w also having happened on Tuesday, given that v happened, we can divide 19% (the probability that w will happen) by 28% (the probability that v has happened), which gives us 67.8%. Rounding gives us 68%.

## 25.

The Correct Answer is (B)g(3) can be found by plugging in 1 for x in the first equation: g(2(1) + 1) = 4g(1) + 1 + 1. So g(3) = 4g(1) + 2, but we know that g(1) = 3. So g(3) = 4(3) + 2 = 14.

## 26.

The Correct Answer is (D) — If the average of a set of four numbers is x, their sum must be 4x. Similarly, if the average of a set of five numbers is x + 2, their sum must be 5x + 10. So adding the fifth number brought the sum from 4x to 5x + 10, meaning that in terms of x, that number was x + 10.

## 27.

The Correct Answer is (B) — The x-intercept occurs when y = 0, as shown in the given ordered pairs. Setting the equation equal to zero and factoring gives -(x – 1)(x + 5), so |a + b| = |1 – 5| = 4.

## 28.

The Correct Answer is (40) — Since vertically opposite angles are equal (“vertically” here means that they share a vertex), the internal angles of the triangle are x, 51, and 89 degrees. Since the sum of the angles in every triangle is 180 degrees, x = 180 – (51 + 89) = 40.

## 29.

The Correct Answer is (5) — The slope of line s is 3 (slope = rise/run = 9/3 = 3), so s also passes through (0, 5).

## 30.

The Correct Answer is (460) — Since one meter = 100 cm (1 × 102 cm), one cubic meter = 1003 cm3 (1 × 106 cm3). So 1.9 m3 = 1.9 × 106 cm3 of ice. Since 1 cm3 of ice melts into 0.92 cm3 of water, we can multiply 1.9 × 106 × 0.92 cm3 = 1,748,000 cm3 of water. To convert cm3 to gallons, we use the relationship given: there are approximately 3800 cm3 in a gallon, which we can write as 3800 cm3/gallon. To cancel out the units, we need to divide our 1,748,000 cm3 of water by cm3/gallon: $\inline&space;\frac{1,748,000&space;\text{&space;cm}^3}{3800&space;\frac{\text{cm}^3}{\text{gallon}}}&space;=&space;460&space;\text{&space;gallons}$.

## 31.

The Correct Answer is (392) — 179.4 km3 of water every year for six years = 179.4 km3 × 6 = 1076.4 km3 of water. To convert to cm of sea level rise, we use the relationship given: 1000 km3 leads to a 364 cm rise, so to cancel our units (km3), we need to multiply by 364 cm/1000 km3. 1076.4 km3 × (364 cm/1000 km3) = 392cm.