1、GMAT（ QUANTITATIVE）数学练习试卷 3及答案与解析 一、 QUANTITATIVE 1 Lottery balls numbered consecutively from 1 through 100 are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 1 on it exactly once? 2 Monthly rainfall was recorded for two towns over a five-mo
2、nth period using the chart above. If the median rainfall in Noahs Landing was equal to the average (arithmetic mean) rainfall in Bellaville, what is the value of x? （ A） 1 （ B） 8/5 （ C） 2 （ D） 3 （ E） 10 3 If x is a positive, single-digit integer such that 4x/3,2x, x, and x+2, and 3x-2 form a non-ord
3、ered list of consecutive integers, which of the following could be the median of that list? （ A） 3 （ B） 4 （ C） 5 （ D） 6 （ E） 8 4 If the sum of five consecutive odd integers is 5, which of the following could be true? . The average (arithmetic mean) of the list is equal to 5. . The median of the list
4、 is equal to 5. . The range of the list is equal to 5. （ A） None （ B） only （ C） only （ D） and （ E） and 5 A jar contains only red, yellow, and orange marbles. If there are 3 red, 5 yellow, and 4 orange marbles, and 3 marbles are chosen from the jar at random without replacing any of them, what is the
5、 probability that 2 yellow, 1 red, and no orange marbles will be chosen? 6 Closing prices for a certain stock were recorded each day for a week in the table above. If the monthly average (arithmetic mean) was 18.43 and the standard deviation was 0.27, how many days during this week did the closing p
6、rice fall within two standard deviations from the average? （ A） 1 （ B） 2 （ C） 3 （ D） 4 （ E） 5 7 A freight elevator can carry a maximum load of 1200 pounds. Sean, who weighs 200 pounds, is in the elevator with two packages weighing 150 pounds and 280 pounds. If he needs to fit three more packages in
7、the elevator that weigh as much as possible without exceeding the elevator limit, what is the difference between their average and the average of the two packages already in the elevator? （ A） 25 （ B） 85 （ C） 190 （ D） 215 （ E） 210 8 WINK, Inc. follows a certain procedure that requires two tasks to b
8、e finished independently in order for a job to be done. On any given day, there is a 7/8 probability that task 1 will be completed on time, and a 3/5 probability that task 2 will be completed on time. On a certain day, what is the probability that task 1 will be completed on time, but task 2 will no
9、t? 8 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 knowledg
10、e 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 sufficient. . BOT
11、H statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. . EACH statement ALONE is sufficient. . Statements (1) and (2) TOGETHER are NOT sufficient. 9 Kara attends a university where students study for an average (arithmetic mean) of 13.4 hours per week. How many hours per we
12、ek does Kara study? (1) The standard deviation of study time at Karas school is 2.8. (2) Karas study time is one standard deviation away from the mean. 10 The cards in a deck are numbered consecutively from 1 to 20. If some cards are red and some cards are black, what is the probability of drawing a
13、 red card? (1) The odd-numbered cards are all red. (2) The even-numbered cards are all black. GMAT（ QUANTITATIVE）数学练习试卷 3答案与解析 一、 QUANTITATIVE 1 【正确答案】 D 【试题解析】 The balls with the number 1 on them exactly once are 1, 10, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81, 91, and 100. Count
14、them up and we get 19 balls out of 100. 2 【正确 答案】 D 【试题解析】 Noahs Landing had a median rainfall of 2 inches, because if we put the numbers in an ordered list (0, 1, 2, 2, 3), the middle number is 2. That means Bellaville had a mean of 2 inches. Since the mean is just the total of the numbers divided
15、by the number of numbers, and there are five numbers in the list, the total of that list must be 10. When we subtract the existing values from 10, we get 10-2-0-4-1=3. 3 【正确答案】 C 【试题解析】 Since there are only nine single-digit, positive integers, and not all of them will yield integers when we use the
16、m in these algebraic expressions, lets start with trying to find a value for x that will give us a list of consecutive integers. I wont work, since 4/31 is not an integer. Same with 2. When we use 3, though, we get 4/33=4; thats an integer. The other expressions give us 23=6, 3, 3+2=5, and 33-2=7. S
17、o our group includes 4, 6, 3, 5, and 7. They arent in order, but they dont have to be according to the problem, and they are consecutive. But be careful! The problem asks for the median of the list, not the value of x. The median of the list 3, 4, 5, 6, 7 is 5. 4 【正确答案】 A 【试题解析】 Lets start by findin
18、g a list of consecutive odd integers that add up to 5. -3, -1, 1, 3, and 5 is one such list. In fact, can you think of another? There isnt one, so now we just have to see which of the Roman numerals is true in this case. isnt true-the mean is 1. is also untrue-the median is also 1. And the range is
19、8, so none of the Roman numerals are possible, and A is our answer. 5 【正确答案】 D 【试题解析】 It doesnt really matter in which order we draw the marbles since theyre really all drawn at once, but from a mathematical standpoint, its much easier to take these probabilities one at a time. Lets first take the p
20、robability of drawing a yellow marble from the jar. Since there are 5 yellow marbles out of 12 marbles total, the probability of drawing a yellow marble is 5/12 The probability of drawing a yellow marble after that is 4/11, since one yellow marble is missing and one marble is missing from the total.
21、 Finally, the probability of drawing a red marble is 3/10, So the probability of drawing the specified combination of marbles is . Once we reduce, we get 1/22 But since the order we draw in does not matter, we need to multiply this by the number of ways to arrange the three drawn marbles. It could b
22、e YYR, RYY, or YRY, for a total of 3 possible arrangements. So our total probability is 6 【正确答案】 C 【试题解析】 Since two standard deviations away from the mean works out to 18.43-0.272=17.89, there are 3 days during which the stock prices fell between 17.89 and 18.43: Monday, Tuesday, and Wednesday. We r
23、eally dont have to worry about prices above the mean, because there were none of them during this time frame. 7 【正确答案】 A 【试题解析】 Scan and the two packages in the elevator weigh 630 pounds together, so the three packages Scan wants to put into the elevator must weigh a maximum of 1,200-630, or 570. If
24、 we divide that by 3, we get the average weight of each package, 190. The two packages already in the elevator weigh a total of 430 together, so their average weight is 215. Subtract 190 from 215 and we get the difference in the averages, or 25. 8 【正确答案】 D 【试题解析】 Task 1 has a 7/8 probability of bein
25、g completed on time, and task 2 has a 3/5 probability of being completed on time, which can also be expressed as a 2/5 probability of not being completed on time, which is what the problem asked for. Multiply the probabilities and we get which reduces to 7/20. 9 【正确答案】 E 【试题解析】 Statement (1) alone t
26、ells us more about the student population, but nothing in particular about Kara, so it is not sufficient and we can cross off A and D. Statement (2) alone tells us nothing because we dont know what the standard deviation is, so we can eliminate B. Together, the statements tell us that Kara studies f
27、or either 16.2 hours or 10.6 hours, but because we dont know whether she studies more or less than the mean, the statements are not sufficient together and our answer is E. 10 【正确答案】 C 【试题解析】 This is a very deceptive problem. Statement (1) tells us that 10 of the 20 cards are red, but it doesnt say
28、that those are the only red cards in the deck, so its not sufficient on its own and we can eliminate A and D. The same thing applies to statement (2); it doesnt say that those are the only black cards in the deck. When we put the statements together, on the other hand, we see the whole picture and know that exactly 10 of the 20 cards are red. So our answer is C.
