Percent

Percents For questions in the Quantitative Comparison format (“Quantity A” and “Quantity B” given), the answer choices are always as follows: (A) Quantity A is greater. (B) Quantity B is greater. (C) The two quantities are equal. (D) The relationship cannot be determined from the information given. Where answer choices do not appear on Quantitative Comparison questions in this book, you should choose A, B, C or D based on the above. For questions followed by a numeric entry box | |, you are to enter your own answer in the box. For questions followed by a fraction-style numeric entry box == =, you are to enter your answer in the form of a fraction. You are not required to reduce fractions. For example, if the answer is — , you may enter or any equivalent fraction. All numbers used are real numbers. All figures are assumed to lie in a plane unless otherwise indicated. Geometric figures are not necessarily drawn to scale. You should assume, however, that lines that appear to be straight are actually straight, points on a line are in the order shown, and all geometric objects are in the relative positions shown. Coordinate systems, such as xy-planes and number lines, as well as graphical data presentations, such as bar charts, circle graphs, and line graphs, are drawn to scale. A symbol that appears more than once in a question has the same meaning throughout the question. Quantity A Quantity B 1. 50 as a percent of 30 The percent increase from 30 to 30 2. If Ken’s salary were 20% higher, it would be 20% less than Lorena’s. If Lorena’s salary is $60,000, what is Ken’s salary? (A) $36,000 (B) $40,000 (C) $42,500

(D) $42,850 (E) $45,000 Greta’s salary was x thousand dollars per year, then she received a y% raise. Annika’s salary was y thousand dollars per year, then she received an x% raise. x and y are positive integers. Quantity B Quantity A , The dollar amount of Annika’s The dollar amount of Greta’s raise , raise Roselba’s annual income exceeds twice Jane’s annual income and both pay the same positive percent of their respective incomes in transportation fees. Quantity A Quantity B The annual amount Jane pays in ~ Half the annual amount Roselba transportation fees pays in transportation fees An item’s price was discounted by 16%. Later, the discounted price was increased by 16%. Quantity B Quantity A . : The price after the discount and The original price , increase . 12 1s 5% of what number? . 7% of 9 1s what percent of 7?

14. 10% of 30% of what number is 200% of 6? 15. If y # 0, what percent of 3% of 50 is 40% of y? L % 16. If a # 0, 200% of 4% of a is what percent of g‘? 2 L % 17. If positive integer m were increased by 20%, decreased by 25%, and then increased by 60%, the resulting number would be what percent of m? | % Quantity A The price of an item after five Quantity B consecutive 10% discounts are 50% of the price of the item 18. applied 19. Raymond borrowed $450 at 0% interest. If he pays back 0.5% of the total amount every 7 days, beginning exactly 7 days after the loan was disbursed, and has thus far paid back $18, with the most recent payment made today, how many days ago did he borrow the money?

(A) 6 B) 8 (C) 25 (D) 42 (E) 56 At a warehouse, an order was shipped out, reducing the number of parts in inventory by half. Then a shipment of parts was received, increasing the current number of parts in inventory by 50%. Quantity A Quantity B The number of parts in inventory The number of parts in inventory 20. before the two shipments after the two shipments A house valued at $200,000 two years ago lost 40% of its value in the first year and a further 20% of that reduced value during the second year. Quantity A Quantity B 21. The current value of the house $100,000 22. 1% of 200% of 360 is what percent of 0.1% of 60? L % 23. If Mary has half as many cents as Nora has dollars, then Nora has what percent more cents than Mary does? (100 cents = 1 dollar) (A) 100% B) 200% ©) 1,990% (D) 19,900% (E) 20,000%

28. Aloysius spends 50% of his income on rent, utilities, and insurance, and 20% on food. If he spends 30% of the remainder on video games and has no other expenditures, what percent of his income is left after all of the expenditures? (A) 30% B) 21% C) 20% D) 9% E) 0% 29. In 1970, company X had 2,000 employees, 15% of whom were women, and 10% of these women were executives. In 2012, the company had 12,000 employees, 45% of whom were women. If 40% of those women were executives, what was the percent increase in the number of women executives from 1970 to 20127 | % 30. 75% of all the boys and 48% of all the girls at Smith High School take civics. If there are 20% fewer boys than there are girls in the school, what percent of all the students take civics? L % Airline A and airline B both previously charged $400 for a certain flight. Airline A then reduced its price by 25%. Airline B responded by reducing its price by 55% but adding $150 in fees. Then, airline A increased its reduced price by 10%. 31. Quantity A Quantity B The final price of the flight on The final price of the flight on airline A airline B

p is 75% of g and p equals 2r. Quantity A Quantity B 32. 0.375¢q r 0<x<100 Quantity A Quantity B 33, x% of 0.5% of 40,000 0.05% of 2,000% of 40x Profit Per Student (in Dollars) at Dan’s Dojo, 2000-2004 2000 60 2001 80 2002 80 2003 100 2004 162 34. At Dan’s Dojo, the percent increase from 2004 to 2005 (not shown) was the same as the percent increase from 2000 to 2001. What was the profit per student for 20057 S 35. If x is 0.5% of'y, then y is what percent of x? (A) 199% (B) 200% (C) 2,000%

(D) (E) 15 20 By the end of July, a certain baseball team had played 80% of the total games to be played that season and had won 50% of those games. Of the remaining games for the season, the team won 60%. Quantity A . Quantity B Percent of total games won for 52% 40. the season Quantity A Quantity B 41. 0.4% of 4% of 1.25 0.002 42. Jane has a 40-ounce mixture of apple juice and seltzer that is 30% apple juice. If she pours 10 more ounces of apple juice into the mixture, what percent of the mixture will be seltzer? 43. (A) 33% (B) 44% (C) 50% (D) 56% (E) 67% Half of the shirts in a closet are white and 30% of the remaining shirts are gray. 'thy_A. : Quantity B The percent of the shirts in the 20% closet that are not white or gray.

The length and width of a painted rectangle were each increased by 10%. Quantity A . . Quantity B The percent increase in the area : 10% 44. of the painted rectangle 45. If 35% of x equals 140, what is 20% of x? (A) 9.8 (B) 39.2 C) &0 (D) 320 (E) 400 46. A population of a colony of bacteria increases by 20% every 3 minutes. If at 9:00am the colony had a population of 144,000, what was the population of the colony at 8:54am? (A) 100,000 (B) 112,000 (C) 120,000 (D) 121,000 (E) 136,000 The price of an item is greater than $90 and less than $150. Quantity A Quantity B The price of the item after a 10%- The price of the item after a $10- off discount and then a $20-off off discount and then a 20%-off 47. discount discount 48. The number that i1s 20% less than 300 is what percent greater than 1807

(E) 200 52. 16 ounces of birdseed mix contains 10% sesame seed by weight. How much sesame seed must be added to produce a mix that is 20% sesame seed by weight? (A) 1 ounce (B) 1.6 ounces (C) 2 ounces (D) 2.4 ounces (E) 4 ounces a, b, and c are positive. Quantity A Quantity B 53. (a+b)% ofc c% of (a + b) Conference Ticket Advance Discounts 5-29 days in advance 15% 30-59 days in advance 30% 60-89 days in advance 40% 54. Helen paid $252 for a conference ticket. If she had purchased the ticket one day later, she would have paid $306. How many days in advance did she purchase the ticket? (A) 5 B) 30 (C) 59 (D) 60 (E) 89