【考研类试卷】工商管理硕士入学考试-GMAT+Geometry、Boolean+Problems+and+Combinatorics及答案解析.doc

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1、工商管理硕士入学考试-GMAT+Geometry、Boolean+Problems+and+Combinatorics 及答案解析(总分：64.98，做题时间：90 分钟)一、B单项选择题/B(总题数：1，分数：65.00)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 sta

2、tements 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

3、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.（分数：64.98）(1).In the figure a

4、bove, what is the area of the shaded region? （分数：7.22）A.B.C.D.(2).In the figure above, what is the value of x?（分数：7.22）A.B.C.D.(3).In the figure above, what is the length of RT? （分数：7.22）A.B.C.D.(4).An art gallery owner is hanging paintings for a new show. Of the six paintings she has to choose from

5、, she can only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings? A. 18 B. 30 C. 64 D. 120 E. 216（分数：7.22）A.B.C.D.(5).A composers guild is planning its spring concert, and ten pieces have been submitte

6、d for consideration. The director of the guild knows that they will only have time to present four of them. If the pieces can be played in any order, how many combinations of pieces are possible? A. 40 B. 210 C. 1,090 D. 5,040 E. 10,000（分数：7.22）A.B.C.D.(6).If x and y are odd integers, which of the f

7、ollowing must always be a non-integer? A. xy （分数：7.22）A.B.C.D.(7).Dan has a membership at a local gym that also gives classes three nights a week. On any given class night, Dan has the option of taking yoga, weight training, or kickboxing classes. If Dan decides to go to either one or two classes pe

8、r week, how many different combinations of classes are available? A. 3 B. 6 C. 7 D. 9 E. 12（分数：7.22）A.B.C.D.(8).Terry is having lunch at a salad bar. There are two types of lettuce to choose from, as well as three types of tomatoes, and four types of olives. He must also choose whether or not to hav

9、e one of the two types of soup on the side. If Terry has decided to have the salad and soup combo and he picks one type of lettuce, one type of tomato, and one type of olive for his salad, how many total options does he have for his lunch combo? A. 9 B. 11 C. 24 D. 48 E. 54（分数：7.22）A.B.C.D.(9).If r

10、is negative and s is positive, which of the following must be negative?C. r2+sD. r2s2（分数：7.22）A.B.C.D.工商管理硕士入学考试-GMAT+Geometry、Boolean+Problems+and+Combinatorics 答案解析(总分：64.98，做题时间：90 分钟)一、B单项选择题/B(总题数：1，分数：65.00)The following data sufficiency problems consist of a question and two statements, label

11、ed (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 knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of c

12、ounterclockwise), 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

13、ALONE is sufficient. Statements (1) and (2) TOGETHER are NOT sufficient.（分数：64.98）(1).In the figure above, what is the area of the shaded region? （分数：7.22）A.B.C. D.解析：Statement (1) alone lets us find the radius, which can tell us the area of the whole circle, but we still dont know what portion of t

14、he circle is made up by the shaded region, so we have to eliminate A and D. Statement (2) alone tells us what proportion of the circle is encompassed by the shaded region, but doesnt tell us the area of the whole circle, so we can eliminate B. Putting the statements together, we have both pieces of

15、information, which we can use to find the area of the shaded region, so statements (1) and (2) are sufficient together, and our answer is C.(2).In the figure above, what is the value of x?（分数：7.22）A.B.C. D.解析：Statement (1) is tempting, because the figure appears to be a parallelogram, but we dont re

16、ally know that it is without some indication that there are two sets of parallel lines. So statement (1) is actually not sufficient, and we can eliminate A and D. Remembering that we have to take statement (2) alone, and it is not sufficient by itself to solve for the value of x, we eliminate B. Put

17、ting both statements together, we have the information we need: If the figure is a parallelogram, then the angles add to 360. If 2y=100, then 2x=260 and x=130. So our answer is C.(3).In the figure above, what is the length of RT? （分数：7.22）A.B.C.D.解析：Statement (1) is not sufficient on its own, since

18、you can never solve for one side of a triangle given only one other side. Lets eliminate A and D. Statement (2) is not sufficient for the same reason, so we can eliminate B. Putting the statements together, it appears that we have enough information to solve for the diagonal of the rectangle (also k

19、nown as hypotenuse of a right triangle), except that we dont have any indication that the figure is actually a rectangle. So the statements are still not sufficient and the answer is E.(4).An art gallery owner is hanging paintings for a new show. Of the six paintings she has to choose from, she can

20、only hang three on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings? A. 18 B. 30 C. 64 D. 120 E. 216（分数：7.22）A.B.C.D. 解析：This problem asks for us to arrange the paintings, so it is a permutation. Using the * formul

21、a and using 6 as our n and 3 as our k, we get the following: *. When we cancel out, we get 654, which is 120.(5).A composers guild is planning its spring concert, and ten pieces have been submitted for consideration. The director of the guild knows that they will only have time to present four of th

22、em. If the pieces can be played in any order, how many combinations of pieces are possible? A. 40 B. 210 C. 1,090 D. 5,040 E. 10,000（分数：7.22）A.B. C.D.解析：This problem is a combination, so we would use the formula *. Since 10 is our n and 4 is our k; the equation works out to *. Simplifying and multip

23、lying gives us 210 combinations.(6).If x and y are odd integers, which of the following must always be a non-integer? A. xy （分数：7.22）A.B.C.D. 解析：Since we know that x and y are odd, xy must always be odd. Therefore, * will always be a non-integer. None of the other answer choices has this relationshi

24、p; in all of the other cases, it is possible to have values of x and y that would yield integer results.(7).Dan has a membership at a local gym that also gives classes three nights a week. On any given class night, Dan has the option of taking yoga, weight training, or kickboxing classes. If Dan dec

25、ides to go to either one or two classes per week, how many different combinations of classes are available? A. 3 B. 6 C. 7 D. 9 E. 12（分数：7.22）A.B.C.D. 解析：This problem is best done by brute force. First, we must establish that Dan has the option of taking one or two classes per week. If he only takes

26、 one class, the three possibilities are Y, W, and K. If he takes two classes per week, the six possibilities are YY, KK, WW, YK, YW, and WK (because the problem is looking for combinations, not arrangements). So that adds up to nine possible combinations.(8).Terry is having lunch at a salad bar. The

27、re are two types of lettuce to choose from, as well as three types of tomatoes, and four types of olives. He must also choose whether or not to have one of the two types of soup on the side. If Terry has decided to have the salad and soup combo and he picks one type of lettuce, one type of tomato, a

28、nd one type of olive for his salad, how many total options does he have for his lunch combo? A. 9 B. 11 C. 24 D. 48 E. 54（分数：7.22）A.B.C.D. 解析：This is a relatively simple problem if you know the process-and you read carefully. All you have to do is multiply the number of options: 2 types of lettuce,

29、3 types of tomatoes, 4 types of olives, and 2 soup options. (You did remember the soup, didnt you?) 2342=48, so 48 is our answer.(9).If r is negative and s is positive, which of the following must be negative?C. r2+sD. r2s2（分数：7.22）A.B. C.D.解析：Based on the rules of positive and negative numbers, the only answer choice that must be negative is B, since it takes a positive and divides it by a negative. All other manipulations end up positive.