1.

The Correct Answer is (D) — Using FOIL, (3x – 2)(x + 1) = 3x2 + 3x – 2x – 2. This simplifies to 3x2 + x – 2.

2.

The Correct Answer is (C) — -16(5)2 + 128(5) = 240

3.

The Correct Answer is (A) — 2(-3) – 3(4) = -18

4.

The Correct Answer is (A) — To figure out depreciation, we first calculate the difference in value $930 - $570 = $360. The computer has lost $360. Since this was over the course of three years, divide $360/3 to arrive at a linear yearly depreciation of $120.

5.

The Correct Answer is (D) — Since each inch represents 2 feet, 5 by 6 inches represents 10 by 12 feet. 10 × 12 = 120 square feet.

6.

The Correct Answer is (D) — There are 20 + 70 + 90 + 40 = 220 students who are involved in clubs, according to the graph. With 250 total students, this leaves 250 – 220 or 30 students who are not involved in a club.

7.

The Correct Answer is (A) — The scatterplot trend line is a parabola, and so is represented by a quadratic formula — C) and D) are eliminated because they are linear equations. Plugging in the value of 3 for x, y = 11 for B). This is incorrect, so answer A) must be the correct answer. 3(32) + 1 = 28, so this checks out.

8.

The Correct Answer is (A) — Cost for a drill and electric saw from John’s tools = 0.90 × ($50 + $30) = $72. Cost for a drill and electric saw from Lin’s tools = 0.85 × ($55 + $25) = $68. $72 - $68 = $4.

9.

The Correct Answer is (C) — Reading the chart, only two sets have more even than negative numbers.

10.

The Correct Answer is (B) — 200,000 × (0.75 – 0.50) = 50,000

11.

The Correct Answer is (C). . 15.6 seconds × 5 files = 78 seconds. This is equal to 78 seconds/(60 seconds/minute) or 1.3 minutes.

12.

The Correct Answer is (C) — The value of Offer 1 = 20 × 5 + 15 × 10 + 4 × 25 = 350 cents. The value of Offer 2 = 25 × 5 + 5 × 10 + 8 × 25 = 375 cents. Because Maria is evaluating the coins based on worth, C) is the correct answer.

13.

The Correct Answer is (C) — Since the newborn’s increases by 30% in the first month, a weight of w at the end of the first month implies a weight of w/1.3 at the beginning of the month. Since w × 1.3/1.3 = w, this equation checks out.

14.

The Correct Answer is (B) — The only answer choice that adds to 25% according to the demographic pie chart is B), since we know that Europe is itself equal to 25% and that Other is equal to half or 50% of the chart.

15.

The Correct Answer is (B) — 25% of the immigrants in the city come from Europe, and 20% of the European immigrant come from France. Since there are a total of 1500 immigrants, 0.25 × 0.20 × 1500 = 75.

16.

The Correct Answer is (B) — 0.10 × number = 12. Solving this, number = 120. 0.05 × 0.5 × 120 = 3.

17.

The Correct Answer is (C)ba = -24 can be rearranged as –a = –b – 24. Adding this to the first equation, you get 0 = -3b – 27, or b = -9. Plugging this back into the equation gives –a = 9 – 24, or a = 15. a + b = 15 – 9 or 6.

18.

The Correct Answer is (C) — The sum of three consecutive odd integers can be expressed as n + (n + 2) + (n + 4), where n is an odd integer. This simplifies to 3n + 6. 290 – 6 = 284, which is not divisible by three and D) is incorrect. 26 – 6 is not divisible by three and B) is incorrect. 23 – 6 = 17, which is not divisible by three and A) is incorrect. 105 – 6 = 99, which is divisible by three, so C) is the answer.

19.

The Correct Answer is (D) — 2x + 7x + 3x = 12x = 180. x = 15. The largest angle is 7x or 7(15) = 105 degrees.

20.

The Correct Answer is (C) — The average of Set A is 85 and the number of elements in the set is 5, so the sum of all elements in Set A is 85 × 5. The average of Set A and Set B is the sum of both sets divided by the total number of elements in both set. Let n = the number of elements in set B, then 5(85 + 13 × n) = 70 × (n + 5). Simplifying, 85 + 13n = 14n + 70 and n = 15.

21.

The Correct Answer is (C) — The shark spends 1/4, or 2/8 of its time sleeping, leaving 3/4 of time remaining. 1/2 of 3/4 is 3/8; this is the amount of time the shark spends hunting. 1 – 2/8 – 3/8 = 3/8. The shark has (3/8)d remaining.

22.

The Correct Answer is (C) — The sample contains 370/750 or 49.3% females. Out of a population of 31,000 people we would expect 31,000 × 49.3% = 15,283 females, so A) is wrong. The sample contains 275/750 or 36.7% females 65 years or younger; this equates with 31,000 × 36.7% or 11,377 for the population, so B) is wrong. There are 225/750 females between 19 and 65 years of age or 30% of the sample; this equate to 31,000 × 30% or 9,300 females for the population, so C) is correct.

23.

The Correct Answer is (A) — 2x2 – 2y2 = 72, simplifies to (xy)(x + y) = 36. Since x = y = 18, xy is equal to 2.

24.

The Correct Answer is (A) — (10x + 35)0.5 = x + 6 simplifies to 10x + 35 = x2 + 12x + 36. Rearranging this we get 0 = x2 + 2x + 1. This equation factors to 0 = (x + 1)(x + 1), so x = -1. x/2 is equal to -1/2.

25.

The Correct Answer is (D) — There are 60 technicians. 30/60 have worked for 6 years or more, or 50%.

26.

The Correct Answer is (C)f(2) = 8 + a, f(3) = 18 + a, and f(5) = 50 + a. 8 + a + 18 + a = 50 + a. Solving for a, we arrive at a = 24.

27.

The Correct Answer is (D) — Adding 3x + 4y = 12 to 4x + 2y = -5 gives us 7x + 7y = 7. Dividing the equation by 7, x + y = 1.

28.

The Correct Answer is (3) — According to these two equations 21/k = 7. Solving this gives k = 3.

29.

The Correct Answer is (7) — The ratio of odd to even integers is 5:1. 1/6 of the integers in the group are even. 42/6 = 7 even integers.

30.

The Correct Answer is (587) — The resonant frequency of the A string is 440. F = v/2l. Since v is a constant, and the length decreased by the new length is equal to 3/4 of the original length. Balancing both sides of the equation, F(4/3) = v/(2l(3/4)). Multiplying 440 by 4/3 rounds to 587Hz.

31.

The Correct Answer is (293) — Both the A and D string lengths are decreased by half. According to the equation F = v/2l, the original frequency would increase by half as per F(2/1) = v/(2l(1/2)). The resonant frequency on the A string is therefore 440 × 2 or 880 is the new frequency. The resonant frequency on the D string is 293.7, therefore 293.7 × 2 or 587.4 is the new frequency. |880 – 587.4|= 292.6 Hz, which rounds to 293Hz.