1.

The Correct Answer is (C) — Multiplying through gives . 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 .

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: .

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.