GMAT考试PREP-MATH-PS2完整详解版-V1.0.doc

PP- Problem Solving2 (PS2) 完整詳解版 V1.0作者: yuma168 larry.tw Huang Hsin-Yi Penda Engedi mauricew pauline_chiou william0625 abc123 ruru.lu備註：本版權內容歸 作者 和 論壇共有，嚴禁任何未經允許的商業使用。Revised History由於這是眾人一起完成的,難免會有疏失,希望大家可以一起修正錯誤,讓這份詳解變得更完整!版本增加規則如下: 1) 修正算式錯誤or提出更好的算法, 請把版本小數+1 (Ex: V1.0 - V1.1)2) 增加or補齊題目,請把版本個位數+1 (Ex: V2.0 -V3.0)版本修正內容 (請標題號)作者日期V1.0新增全部詳解 (Q1Q197)yuma168larry.twHuang Hsin-Yi PendaEngedimauricewpauline_chiouwilliam0625abc123ruru.lu2008/7/17Practice Test #2 Problem Solving(197 Questions)1.246-!-item-!-187;#058&000117Tanya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelope with its correct address. If the 4 letters are to be put into the 4 envelopes at random, what is the probability that only 1 letter will be put into the envelope with its correct address?(A) (B) (C) (D) (E) 2.509-!-item-!-187;#058&000281For every order, a certain mail-order company charges a shipping fee of $3 plus an additional $2 if the value of the order is over $50 but not over $100 or an additional $3 if the value of the order is over $100. How much greater are the total shipping fees for 2 orders of $75 each than the total shipping fee for 1 order of $150 ?(A) $1(B) $2(C) $3(D) $4(E) $5-【答案】D【思路】2 orders of $75 each : 每件價值都75,所以要額外費用2元,且又兩件, 2(3+2)=101 order of $150: 1(3+3)=6依照題意相減可得4-3.827-!-item-!-187;#058&000411A copy service charges $0.05 per copy for the first 100 copies, $0.04 per copy for the next 100 copies, and $0.03 per copy for all copies thereafter. What would the copy service charge for 350 copies?(A) $10.50(B) $11.50(C) $12.00(D) $13.00(E) $13.50-【答案】E【思路】-4.1197-!-item-!-187;#058&000782If w, x, and y are consecutive odd positive integers and w x E-12.2238-!-item-!-187;#058&002618?If the two regions above have the same area, what is the ratio t : s ?(A) 2 : 3(B) 16 : 3(C) (D) (E) 13.2392-!-item-!-187;#058&002762?: line missed(A) A certain list of 100 data has an average (arithmetic mean) of 6 and a standard deviation of d, where d is positive. Which of the following pairs of data, when added to the list, must result in a list of 102 data with standard deviation less than d ?(B) 0 and 0(C) 0 and 6(D) 0 and 12(E) 6 and 614.2546-!-item-!-187;#058&002908If Sally drives at a constant speed of 50 miles per hour, how many minutes will be required for her to drive 10 miles?(A) 9(B) 10(C) 11(D) 12(E) 13-【答案】D【思路】距離/速度=時間 10/50=0.2 (hr) = 12(mins)-15.2647-!-item-!-187;#058&002944If a = 1 and ?, which of the following is NOT a possible value of b ?(A) -2(B) -1(C) 0(D) 1(E) 216.2698-!-item-!-187;#058&002953? All points (x, y) that lie below the line l, shown above, satisfy which of the following inequalities?(A) y 2x + 3(B) y -2x + 3(C) y -x + 3(D)(E)17.2747-!-item-!-187;#058&002959?On the number line above, what is the length of segment AB ?(A) 2.2(B) 0.38(C) 0.22(D) 0.038(E) 0.02218.2793-!-item-!-187;#058&002984After a fisherman sold ? of the fish he had caught and gave away ? of the remaining fish, he had 4 fish left. What was the total number of fish he had caught? (A) 8(B) 16(C) 20(D) 32(E) 4019.2896-!-item-!-187;#058&003100?For each country listed in the left column of the table, the number in the right column gives the number of units of Country X currency that is equivalent to 1 unit of the countrys currency. Which of the following is equivalent to the greatest number of units of Country X currency?(A) 4 units of Country A currency(B) 25 units of Country B currency(C) 98 units of Country C currency(D) 3 units of Country D currency(E) 7 units of Country E currency20.2942-!-item-!-187;#058&003104For any positive integer n, the length of n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75 = 3 ? 5 ? 5. How many two-digit positive integers have length 6 ?(A) None(B) One(C) Two(D) Three(E) Four21.2988-!-item-!-187;#058&003110A company wants to buy computers and printers for a new branch office, and the number of computers can be at most 3 times the number of printers. Computers cost $1,500 each, and printers cost $300 each. What is the greatest number of computers that the company can buy if it has a total of $9,100 to spend on computers and printers?(A) 2(B) 3(C) 4(D) 5(E) 6-【答案】D【思路】C=3P1500C + 300P 91001600C 9100C5.多 所以最多可買5台computers-22.3254-!-item-!-187;#058&003229If ?, then N is between(A) 0 and (B) and (C) and (D) and (E) and 223.3470-!-item-!-187;#058&003305240, 120, 60, 30, . . .In the sequence above, each term after the first is of the preceding term. What is the least term of the sequence that is greater than 1 ?(A) (B) (C) (D) (E) 24.3573-!-item-!-187;#058&003330A box contains 25 red blocks, 100 blue blocks, and 175 yellow blocks. What is the probability that a block picked at random from the box will be red?(A) (B) (C) (D) (E) 25.3619-!-item-!-187;#058&003382A fast-food company plans to build 4 new restaurants. If there are 12 sites that satisfy the companys criteria for location of new restaurants, in how many different ways can the company select the 4 sites needed for the new restaurants if the order of selection does not matter?(A) 48(B) 288(C) 495(D) 990(E) 11,880-【答案】C【思路】-26.3669-!-item-!-187;#058&003387If x is an even integer, which of the following must be an odd integer?(A) (B) (C) 3x2(D) (E) 27.3721-!-item-!-187;#058&003433?The figure shown represents a board with four rows of pegs, and at the bottom of the board are four cells numbered 1 to 4. Whenever the ball shown passes through the opening between two adjacent pegs in the same row, it will hit the peg directly beneath the opening. The ball then has probability of passing through the opening immediately to the left of that peg and probability of passing through the opening immediately to the right. What is the probability that when the ball passes through the first two pegs at the top it will end up in cell 2 ?(A) (B) (C) (D) (E) 28.3770-!-item-!-187;#058&003486What is the greatest possible area of a triangular region with one vertex at the center of a circle of radius 1 and the other two vertices on the circle?(A) (B) (C) (D) 1(E) 29.3873-!-item-!-187;#058&003594If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be(A) less than -10(B) between -1 and (C) between and 0(D) between 0 and (E) greater than 1030.4244-!-item-!-187;#058&003828An investor purchased 20 shares of a certain stock at a price of $45.75 per share. Later this investor purchased 30 more shares at a price of $46.25 per share. What was the average (arithmetic mean) price per share that this investor paid for the 50 shares?(A) $45.80(B) $45.95(C) $46.00(D) $46.05(E) $46.20-【答案】D【思路】-31.4295-!-item-!-187;#058&003848A certain basket contains 10 apples, 7 of which are red and 3 of which are green. If 3 different apples are to be selected at random from the basket, what is the probability that 2 of the apples selected will be red and 1 will be green?(A) (B) (C) (D) (E) 32.4504-!-item-!-187;#058&003922?When N is divided by T, the quotient is S and the remainder is V. Which of the following expressions is equal to N ?(A) ST(B) S + V(C) ST + V(D) T(S - V)(E)33.4550-!-item-!-187;#058&003924What is the number of different committees of 4 people that can be selected from a group of 10 people?(A) 20(B) 40(C) 80(D) 120(E) 210-【答案】E【思路】-34.4707-!-item-!-187;#058&003966?The table shows the numbers of greeting cards for various occasions sold at a certain store last year. According to the table, for which of the following occasions was the number of cards sold closest to ? of the number of birthday cards sold?(A) Valentines Day(B) Secretarys Day(C) Mothers Day(D) Fathers Day(E)35.4808-!-item-!-187;#058&003979If the operation is defined for all positive integers x and w by x w = ? , then (3 1) 3 =(A) 2(B) 4(C) 8(D) 16(E) 3236.5018-!-item-!-187;#058&004104If x = kc and y = kt, then y - x =(A) k(t - c)(B) k(c - t)(C) c(k - t)(D) t(k - c)(E) k(1 - t)-【答案】A【思路】kt-kc=k(t-c)-37.5174-!-item-!-187;#058&004144The function f is defined for all positive integers n by the following rule: f(n) is the number of positive integers each of which is less than n and has no positive factor in common with n other than 1. If p is any prime number then f(p) =(A) p - 1(B) p - 2(C) (D) (E) 238.5275-!-item-!-187;#058&004179A certain business produced x rakes each month from November through February and shipped 0.5x rakes at the beginning of each month from March through October. The business paid no storage costs for the rakes from November through February, but it paid storage costs of $0.10 per rake each month from March through October for the rakes that had not been shipped. In terms of x, what was the total storage cost, in dollars, that the business paid for the rakes for the 12 months from November through October?(A) 0.40x(B) 1.20x(C) 1.40x(D) 1.60x(E) 3.20x-【答案】C【思路】3-10每個月各運出0.5x所以每個月存貨為 3月(3.5) 4(3) 5(2.5) 6(2) 7(1.5) 8(1) 9(0.5) 10(0)-39.5378-!-item-!-187;#058&004220?The table shows the number of calls received by each of five operators during each of 4 one-hour periods. For which operator was the standard deviation of the numbers of calls received during these 4 periods the least?(A) Operator A(B) Operator B(C) Operator C(D) Operator D(E) Operator E40.5532-!-item-!-187;#058&004320A certain company sold 1,000 blenders at $100 each and 10 stoves at $1,000 each. If the companys total cost for the blenders and stoves was $50,000, what was the companys total gross profit on these items?(A) $10,000(B) $20,000(C) $30,000(D) $50,000(E) $60,000-【答案】E【思路】-41.5689-!-item-!-187;#058&004421In the infinite sequence a1, a2, a3, . . . , an, . . . , each term after the first is equal to twice the previous term. If a5 - a2 = 12, what is the value of a1 ?(A) 4(B) (C) 2(D) (E) 42.5737-!-item-!-187;#058&004537(-3)(-2) =(A) - 9(B) -6(C) (D) (E) 943.5837-!-item-!-187;#058&004612A college admissions officer predicts that 20 percent of the students who are accepted will not attend the college. According to this prediction, how many students should be accepted to achieve a planned enrollment of x students?(A) 1.05x(B) 1.1x(C) 1.2x(D) 1.25x(E) 1.8x-【答案】D【思路