1. A: The sum of the two given angles is 140°. The measure of the third angle is equal to the difference of 180° and 140°, or 40°.
2. E: The amount he will need for 3 desserts is equal to the product of 2 1/2 and 3, or 7 1/2.
3. C: Application of the 50% discount gives the expression, 320 - 0.50(320), which equals 160. Application of the additional 20% discount to this amount, gives the expression, 160 - 0.20(160), which equals 128. Thus, the sale price of the desk was $128.
4. A: 25% is larger than any of the percentages given for the other destinations, thus the beach is the most common destination.
5. B: The number of students going to the mountains is equal to the product of 0.12 and 500, which equals 60.
6. E: The following proportion may be written: (1/4)/1=6/x. Solving for x gives x = 24. Thus, there are 24 milliliters in 6 teaspoons.
7. D: The correct graph should show one ray, with a closed point on the integer, -2, which points to the left, and another ray, with a closed point on the integer, 3, which points to the right.
8. E: The following proportion may be written: (1/4)/20=(3 1/2)/x, which simplifies to 1/4 x=70, where x = 280. Thus, there are actually 280 miles between the two cities.
9. D: The new length may be represented by the expression, L + 2, while the new width may be represented by the expression, W + 2. Thus, the area is equal to the product of the two dimensions, or (L + 2)(W + 2).
10. D: Removal of 9 pair will ensure that she has one of each color because all 3 colors will be represented. Removal of 7 pair may include only pairs of black and white socks, while not including a red pair.
11. C: The fractions in Choice C may be converted to the following decimals: 0.25, 0.68, 0.6875, 0.75, which are indeed in order from least to greatest.
12. C: The average may be written as (365+7+24)/3, which equals 132.
13. A: Moving the decimal 5 places to the right gives 175,000.
14. C: The average may be written as (0.03(2800+3200+3600))/3, which equals 96.
15. E: The following proportion may be written: (1/3)/15=(3 2/3)/x, which simplifies to 1/3 x=165/3, where x = 165. Thus, there are actually 165 miles between the two cities.
16. A: Simple interest may be calculated using the formula, I = Prt, where P represents the principal amount, r represents the rate, and t represents the length of time. Substituting 200 for I, 4000 for P, and 0.05 for r gives 200 = (4000)(0.05)t. Thus, t = 1. It will take him 1 year to earn $200 in simple interest.
17. D: The following equation may be solved for x: 650 = 0.012x. Dividing both sides of the equation by 0.012 gives x = 54,166.67. Thus, the assessed value of his property is $54,166.67.
18. B: The problem may be modeled with the equation, 23.80 = x - 0.15x, which simplifies to 23.80 = 0.85x. Dividing both sides of the equation by 0.85 gives x = 28. So, the regular price of the lamp is $28.
19. C: The expression, 750 - 0.15(750), may be used to represent the price, after the first discount. This amount is $637.50. Taking an additional 10% off of the discounted price is represented by the expression, 637.50 - 0.10(637.50), which equals 573.75. Thus, the price after both discounts is $573.75.
20. A: The problem may be modeled and solved, using the equation, 0.85x = 136. Solving for x gives x = 160.
21. B: The following proportion may be written: 150/20=x/2. Solving for x gives x = 15. Thus, the height of the tree is 15 feet.
22. C: Dividing a positive number by a negative number gives a negative quotient. For example, 4/(-2)=-2.
23. D: 1/8=0.125, which is equivalent to 12.5%.
24. A: In order to change the mixed number to an improper fraction, the denominator should first be multiplied by the whole number. Next, the numerator should be added to this product. The resulting value should be placed over the original denominator of the fractional portion of the mixed number. 4 3/5=23/5 because (5 x 4) + 3 = 23 and 23 divided by 5 is written as 23/5.
25. E: The following equation may be used to solve the problem: 133x + 0.15(133x) = 2294.25. Solving for x gives x = 15. So, the driver has not paid 15 tickets.
26. B: Six hours passed, from 6:30 A.M. to 12:30 P.M. Thirty-five more minutes passed from 12:30 P.M. to 1:05 P.M. So, it took him 6 hours and 35 minutes to finish the race.
27. A: The circle is divided into 3 equal sections, whereby 2 of them of are shaded. Thus, the represented fraction is 2/3.
28. B: The decimals may be multiplied as integers. However, the decimal will have six place values to the right of the decimal.
29. D: The ratio may be written as 32/56, which reduces to 4/7. Thus, the ratio of games lost to games played is 4: 7.
30. E: 5/6=15/18 because the numerator and denominator of the first fraction are both multiplied by 3.
31. B: The following proportion may be written: 120/8=x/15. Solving for x gives x = 225. She earns $225 for 15 hours of work.
32. B: 7,500 tires were sold in each of the years, 1998 and 2000. This number was the least amount sold in a year, as evidenced by one and a half tires shown for these years, as compared to two and two and a half for the other two years.
33. B: Using the number of tires shown, the year of 1999 may be represented by the expression, 1 1/2+1/3 (1 1/2), which equals 2. Since 2 is 1/3 more than 1 1/2, the number of tires sold in 1999 was 1/3 more than the number sold in 1998.
34. B: The average may be written as (7500+10000+7500+12500)/4, which equals 9,375.
35. B: The percent increase may be represented as (40-20)/20, which equals 1. 1 = 100%. So, the percent increase was 100%.
36. D: ΕΝΑ=μικρό2, so the area may be written as ΕΝΑ=52; A = 25. The area of the square is 25 square units.
37. C: The first equation may be solved for x. Doing so gives x = 2. Substituting 2 for x, into the second equation, gives 3(2) + 4, or 10.
38. B: Each of the base angles measures 65°, since the triangle is isosceles. Thus, the same of the base angles is 130°. The measure of angle B is equal to the difference of 180° and 130°, or 50°.
39. D: The average may be written as (8+12+15+21+x+11)/6=17, which simplifies to (67+x)/6=17. Multiplying both sides of the equation by 6 gives 67 + x = 102. Subtracting 67 from both sides of the equation gives the solution of x = 35.
40. B: The solution may be represented by the expression, 25 - (11.23 + 8.32), which equals 5.45. Thus, she has $5.45 left over.
