1、GMAT（ QUANTITATIVE）数学模拟试卷 5及答案与解析 一、 QUANTITATIVE 1 Greg sells gaskets. On three sales, Greg has received commissions of $385, $70, and $190, and he has one additional sale pending. If Greg is to receive an average (arithmetic mean) commission of exactly $220 on the four sales, then the fourth commi
2、ssion must be: （ A） $135 （ B） $155 （ C） $220 （ D） $235 （ E） $645 2 In an effort to plan out expenses, the Roberts family is representing its annual budget as a circle graph. Each sector of the graph is proportional to the amount of the budget it represents. If “clothes and shoes“ takes up 54 of the
3、chart, how much of the Robertss $20,000 annual budget is dedicated to clothes and shoes? （ A） $1,500 （ B） $3,000 （ C） $4,500 （ D） $5,000 （ E） $5,400 3 What is the value of 3x2-1.8x+0.3 for x=0.6? （ A） -0.3 （ B） 0 （ C） 0.3 （ D） 1.08 （ E） 2.46 4 Over a three-week period, the price of an ounce of gold
4、increased by 25% in the first week, decreased by 20% in the following week, and increased by 5% in the third week. If the price of gold was G dollars per ounce at the beginning of the three weeks, what was the price, in terms of G, at the end of the three weeks? （ A） 0.95G （ B） G （ C） 1.05G （ D） 1.1
5、G （ E） 1.15G 5 If a cube has a total surface area of 96, what is its volume? （ A） 16 （ B） 36 （ C） 64 （ D） 81 （ E） 96 6 The table below shows the enrollment in various classes at a certain college. Although no student is enrolled in all three classes, 15 are enrolled in both Biology and Physics, 10 a
6、re enrolled in both Biology and Calculus, and 12 are enrolled in both Physics and Calculus. How many different students are in the three classes? （ A） 51 （ B） 88 （ C） 90 （ D） 125 （ E） 162 7 In a nationwide poll, P people were asked 2 questions. If 2/5 answered “yes“ to question 1, and of those 1/3 a
7、lso answered “yes“ to question 2, which of the following represents the number of people polled who did not answer “yes“ to both questions? （ A） 2/15 P （ B） 3/5 P （ C） 3/4 P （ D） 5/6 P （ E） 13/15 P 7 The following data sufficiency problems consist of a question and two statements, labeled (1) and (2
8、), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwi
9、se), you must indicate whether . Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. . Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. . BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. . EACH statement ALONE
10、is sufficient. . Statements (1) and (2) TOGETHER are NOT sufficient. 8 A certain salad dressing made only of oil and vinegar is premixed and sold in the grocery store. What is the ratio of oil to vinegar in the mix? (1) An 18.6-ounce bottle of the salad dressing contains 12.4 ounces of vinegar. (2)
11、In a 32-ounce bottle of the salad dressing, there is half as much oil as there is vinegar. 9 At a certain pancake festival with 600 attendees in which every attendee ate at least 1 pancake, how many people had only 1 pancake? (1) At the festival there were 1,200 pancakes served, and no person had mo
12、re than 3 pancakes. (2) Seventy-two percent of the attendees at the festival had 2 or more pancakes. 10 A rectangle is equal in area to a square with sides of length 12. Is the diagonal of the rectangle greater in length than 20? (1) The rectangle has a length of 16. (2) The rectangle has a width of
13、 9. 11 A type of candy comes in two flavors, sweet and sour, and in two colors, yellow and green. The color and flavor of the individual pieces of candy are not related. If in a certain box of this candy 1/4 of the yellow pieces and 5/7 of the green pieces are sour, what is the ratio of the number o
14、f yellow pieces to the number of green pieces in the box? (1) In the box, the number of sweet yellow pieces is equal to the number of sour green pieces. (2) In the box, the number of green pieces is two less than the number of yellow pieces. 12 In isosceles triangle ABC, what is the value of C? (1)
15、The measure of B is 47 (2) The measure of A is 90 13 In the rectangular quadrant system shown above, which quadrant, if any, contains no point (x, y) that satisfies the equation 3x+5y=-2? （ A） none （ B） （ C） （ D） （ E） 14 If a copier makes 3 copies every 4 seconds, then continues at this rate, how ma
16、ny minutes will it take to make 9,000 copies? （ A） 60 （ B） 100 （ C） 120 （ D） 200 （ E） 3,000 15 To be considered grade AA, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AA eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg ome
17、let, assuming that only grade AA eggs are used, the shells are all discarded, and no mass is lost in the cooking process? （ A） 800 （ B） 840 （ C） 864 （ D） 900 （ E） 1,080 16 （ A） 0.0008 （ B） 0.001 （ C） 0.008 （ D） 0.04 （ E） 0.08 17 What is the ratio of ? （ A） 9 （ B） 3 （ C） 1 （ D） 1:3 （ E） 1:27 18 A gro
18、up of 7 fishermen chartered a boat for a day to fish for flounder. The boat costs x dollars per day to rent. If the group can find 3 more fishermen on the docks who are willing to come aboard and share the rental costs, how much less will the rental cost be per person in terms of x? （ A） x/70 （ B） x
19、/35 （ C） 3x/70 （ D） 3x/10 （ E） 3x/7 19 The size of a flat-screen television is given as the length of the screens diagonal. How many square inches greater is the screen of a square 34-inch flat-screen television than a square 27-inch fiat-screen television? （ A） 106.75 （ B） 213.5 （ C） 427 （ D） 729 （
20、 E） 1,156 19 The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your
21、 knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether . Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. . Statement (2) ALONE is sufficient, but statement (1) alone is not sufficie
22、nt. . BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. . EACH statement ALONE is sufficient. . Statements (1) and (2) TOGETHER are NOT sufficient. 20 What is the value of n? (1) n4=256 (2) n3n2 21 An employee at a company was given the task of making a large number
23、 of copies. He spent the first 45 minutes making copies at a constant rate on copier A, but copier A broke down before the task was completed. He then spent the next 30 minutes finishing the task on copier B, which also produced copies at a constant rate. How many total minutes would the task have t
24、aken had copier A not broken down? (1) Copier A produced twice as many copies in its first 5 minutes of operation as copier B produced in its first 15 minutes. (2) Copier B produces 10 copies per minute. 22 If ab0, is c an integer? (1) c=5a-2b (2) a=2b 23 x=0.57y9. If y denotes the thousandth digit
25、in the decimal representation of x above, what digit is y? (1) If x were rounded to the nearest tenth, the result would be 0.6. (2) If x were rounded to the nearest hundredth, the result would be 0.58. 24 Is integer y 0? (1) -(2+y) 0 (2) (2+y)2 0 25 If 4 and 11 are the lengths of two sides of a tria
26、ngular region, which of the following can be the length of the third side? .5 . 13 . 15 （ A） only （ B） only （ C） and only （ D） and only （ E） , , and 26 A certain truck uses 18 gallons of diesel fuel in traveling 270 miles. In order for the truck to travel the same distance using 10 gallons of diesel
27、 fuel, by how many miles per gallon must the trucks fuel mileage be increased? （ A） 8 （ B） 9 （ C） 12 （ D） 15 （ E） 27 27 The figure above represents a window, with the shaded regions representing openings for glass and the pale regions representing the wood panels between and around the glass. If the
28、 window is 4.5 feet high by 2.5 feet wide, and if each of the wooden panels is exactly 4 inches thick, what is the total surface area, in square inches, of glass in the window? (1 foot=12 inches; figure not drawn to scale) （ A） 189 （ B） 378 （ C） 448 （ D） 756 （ E） 1,620 28 If 3(x2+x)-7=x2+2(4+x2), th
29、en x= （ A） 5 （ B） 6 （ C） 9 （ D） 15 （ E） 25 29 Suzies Discount Footwear sells all pairs of shoes for one price and all pairs of boots for another price. On Monday the store sold 22 pairs of shoes and 16 pairs of boots for $650. On Tuesday the store sold 8 pairs of shoes and 32 pairs of boots for $760
30、. How much more do pairs of boots cost than pairs of shoes at Suzies Discount Footwear? （ A） $2.50 （ B） $5.00 （ C） $5.50 （ D） $7.50 （ E） $15.00 30 For any 3 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3? . Ordering the 3 nu
31、mbers numerically, from highest to lowest, and then selecting the middle number. . Dividing each of the numbers by 3 and then adding the results together. . Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. （ A） only （ B） only （ C） and only （ D） an
32、d only （ E） None of the above 31 A hat company ships its hats, individually wrapped, in 8-inch by 10-inch by 12-inch boxes. Each hat is valued at $7.50. If the companys latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes, what wa
33、s the minimum value of the order? （ A） $960 （ B） $1,350 （ C） $1,725 （ D） $2,050 （ E） $2,250 32 Chauncy, an English bulldog, received 1,618 votes in the Mr. Bulldog USA competition, giving him approximately 20 percent of the vote. Approximately what percent of the remaining votes would he have needed
34、 to receive in order to win 30 percent of the total votes? （ A） 10% （ B） 12.5% （ C） 15% （ D） 17.5% （ E） 20% 32 The following data sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the stat
35、ements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you must indicate whether . Statement (1) ALONE is sufficient, but statement (2) alo
36、ne is not sufficient. . Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. . BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. . EACH statement ALONE is sufficient. . Statements (1) and (2) TOGETHER are NOT sufficient. 33 If 8 skiers raced
37、 down a course multiple times in one day, and each skier used a different pair of skis on each run, what is the total number of different skis used by the 8 skiers during the day? (1) No skier shared any skis with any other skier. (2) Each skier made exactly 12 runs during the day. 34 The symbol rep
38、resents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 7 4? 35 Salespeople at a certain car dealership are paid a $250 commission on every car they sell up to their monthly quota, and $500 for every car they sell over the quota. What is the
39、monthly sales quota at this dealership? (1) One salesperson exceeded the quota by 8 cars and received a total monthly commission of $7,500. (2) One salesperson achieved only half of the quota; he received a commission of $1,750 and a warning that he will be fired unless he meets the next months quot
40、a. 36 If ab, is ? (1) b2 a2 (2) a-b 1 37 The hold of a fishing boat contains only cod, haddock, and halibut. If a fish is selected at random from the hold, what is the probability that it will be a halibut or a haddock? (1)There are twice as many halibut as cod in the hold, and twice as many haddock
41、 as halibut. (2) Cod account for 1/7 of the fish by number in the hold. GMAT（ QUANTITATIVE）数学模拟试卷 5答案与解析 一、 QUANTITATIVE 1 【正确答案】 D 【试题解析】 For the average of four commissions to be $220, the total must be 2204=880. 880 minus the sum of the three listed commissions (385+70+190=645) equals $235. 2 【正确
42、答案】 B 【试题解析】 54 is 15 percent of the 360 in a circle; 15 percent of $20,000 is $3,000. 3 【正确答案】 C 【试题解析】 The equation 3(0.60.6)-1.8(0.6)+0.3=1.08- .08+0.3=0.3 4 【正确答案】 C 【试题解析】 At the end of the first week, the price was 1.25G= 1.25G. At the end of the second week, it was 0.81.25G= G. At the end of
43、the third week, the price was 1.05G = 1.05 G. 5 【正确答案】 C 【试题解析】 A cube has six sides, so if the total surface area is 96, then the surface area of a square side is 96/6=16. The area of a square is the square of the length of its sides, so the length of a side is . The volume of a cube is the cube of
44、 the length of its sides, so 444=64 6 【正确答案】 B 【试题解析】 To find the total number of students, you must separate them into nonoverlapping groups so that no one is counted twice. The students taking only Biology are the 50 students minus the 15 also taking Physics and the 10 also taking Calculus, so the
45、re are 25 students taking just Biology. Using this same method, the number of students taking just Physics is 35-15-12=8, and the number taking just Calculus is 40-10-12=18. The total number, then, is 25+8+18+10+15+12=88. 7 【正确答案】 E 【试题解析】 The people who answered “yes“ to both questions are 1/3 of 2
46、/5 P, so 2/15 P. Therefore, the people who did not answer “yes“ to both questions are P-2/15 P=13/15 P. 8 【正确答案】 D 【试题解析】 alone is sufficient, because if there are 12.4 ounces of vinegar, then there are 18.6-12.4=6.2 ounces of off; 6.2/12.4=1:2.(2) alone is sufficient because it tells you directly t
47、hat the ratio of oil to vinegar is 1:2. 9 【正确答案】 B 【试题解析】 alone is not sufficient, because there could have been 300 people who had 1 pancake and 300 people who had 3 pancakes, or 600 people who had 2 pancakes. (2) alone is sufficient, because you can directly infer from the statement that 100%-72%=
48、28% of attendees, or 168, had only 1 pancake. 10 【正确答案】 D 【 试题解析】 Both (1) and (2) independently allow you to infer both the length and the width of the rectangle, because ff the rectangle is equal in area to a square with sides of length 12, then its area=1212=144, and so the width is 144/16=9 and
49、the length is 144/9=16. By the Pythagorean theorem, we can determine that the diagonal is equal to the square root of 92+162=337. You do not have to determine the actual square root of 337 to determine that it is less than 20, because 2020=400. 11 【正确答案】 A 【试题解析】 alone is sufficient because it sets up a ratio between the colors and flavors; if 1/4 of the yellow pieces are sour, then 3/4 of the yellow pieces are sweet, and if 5/7 of the green pieces are sour, then 2/7 of th
