英语考试gmat】gmat prep 数学 共（68页）

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1、PP- Data Sufficiency1 (DS1) 完整詳解版 V1.2作者: larry.tw Huang Hsin-Yi Penda Engedi mauricew charlie6989 abc123 sunnyblue13s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 -V

2、3.0)版本修正內容 (請標題號)作者日期V1.0新增全部詳解 (Q1Q218)larry.twHuang Hsin-Yi PendaEngedimauricewcharlie6989abc123sunnyblue13s2008/7/1V1.1修正DS1-156,DS1-158,DS1-213,DS1-214,DS1-215,DS1-210, DS1-217larry.tw2008/7/13V1.2Update Q122,Q201,Q205,Q206larry.twPhilosophia2008/08/29Practice Test #1 Data Sufficiency(218 Questi

3、ons)1.86-!-item-!-187;#058&000002A garden store purchased a number of shovels and a number of rakes. If the cost of each shovel was $14 and the cost of each rake was $9, what was the total cost of the shovels and rakes purchased by the store?(1) The ratio of the number of shovels to the number of ra

4、kes purchased by the store was 2 to 3.(2) The total number of shovels and rakes purchased by the store was 50.-【答案】C【思路】設Qs為shovels的數量設Qr為rakes的數量題目問: 14Qs + 9 Qr =?(1) Qs=2a, Qr=3a ,只知比例,不知各為多少,無法求得數量,不充分(2) Qs + Qr = 50,只知總和,不知各為多少,也無法求數total cost,不充分(1)+(2)將(1)代入(2)可得a=10 , 即Qs=20,Qr=30,所以total c

5、ost已經可以算出, 充分!-2.142-!-item-!-187;#058&000140Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student either likes or dislikes brussels sprouts. Of these students,dislike lima beans; and of those who dislike lima beans, also dislike brussels s

6、prouts. How many of the students like brussels sprouts but dislike lima beans?(1) 120 students eat in the cafeteria.(2) 40 of the students like lima beans.-【答案】D【思路】beans beanssproutsab sproutscdt註: 代表dislike 設t為total students 設like beans & like sprouts人數 為a 設dislike beans & like sprouts人數 為b 設like

7、beans & dislike sprouts人數 為c 設dislike beans & dislike sprouts人數 為d已知d= 題目問: b=?(1) t= 120, 得知b+d=80且d=50, 所以得出b=30, 充分(2) a+c = 40 = 得出t=120 同(1)也可以算出b, 充分-3.196-!-item-!-187;#058&000141How many different prime numbers are factors of the positive integer n ?(1) Four different prime numbers are facto

8、rs of 2n.(2) Four different prime numbers are factors of n2.-【答案】B【思路】(1) 如果2n=2.3.5.7的話 n的prime factor為3.5.7=三個 如果2n=.3.5.7的話 n的prime factor為2.3.5.7=四個 ,不充分(2) ,a,b,c,d不管是幾次方,都可以確定質數只有四個,充分-4.250-!-item-!-187;#058&000160Is the product of a certain pair of integers even? (1) The sum of the integers

9、is odd.(2) One of the integers is even and the other is odd.-【答案】D【思路】設2個整數為x,y題目問 xy = 2n?(1) x + y = 2n+1 ,即至少有一個為奇數;一個為偶數, 則xy相乘,一定為偶數,充分(2) 有一個為奇數;一個為偶數, 則xy相乘,一定為偶數,充分-5.304-!-item-!-187;#058&000163If k is an integer and 2 k 8, what is the value of k ?(1) k is a factor of 30.(2) k is a factor o

10、f 12.-【答案】E【思路】(1) 30因數有 2,3,5 ; 所以k=3 or 5 or 6,無法確定,不充分(2) 12因數有,3 ; 所以k=3 or 4 or 6,無法確定,不充分(1)+(2) 同樣有 3 or 6所以無法確定, 不充分-6.363-!-item-!-187;#058&000183On the number line above, is the product of w, x, y, and z negative?(1) z is positive.(2) The product of w and x is positive.-【答案】E【思路】題目問: wxyz

11、= 負?(1) z=負,不知 w,x,y是否為正負,所以不充分(2) wz=正,表示wz可能為+ +或 - -,不知x,z所以一樣不充分(1)+(2) 合起來不知y是否為正負,所以不充分-7.509-!-item-!-187;#058&000355If y and z are integers, is y(z + 1) odd?(1) y is odd(2) z is even.-【答案】C【思路】(1) y等於奇數,不知z,所以無法判斷,不充分(2) z等於偶數,不知y,所以無法判斷,不充分(1)+(2) y等於奇數, z等於偶數,可確定知道答案,充分-8.563-!-item-!-187;

12、#058&000364If n and m are positive integers, what is the remainder when 3(4n + 2 + m) is divided by 10 ?(1) n = 2(2) m = 1-【答案】B【思路】(1) n = 2 , 不知 m = ? m 的變化會影響到餘數的結果，餘數會不一樣，帶幾個不同數字進去，然後除10看看.不充份(2) m=1 的餘數都是7 因為 3的1次方個位數等於3 3的2次方個位數等於9 3的3次方個位數等於7 3的4次方個位數等於1 3的5次方個位數等於3 (又回到3了,所以4次一個循環) 所以4n是4的倍數

13、算出來餘數都是1 (4n+2) 的話餘數變9 (例如n=1時 , 4*1+2=6, 餘數是9, n=2時, 4*2+2=10, 餘數還是9) (4n+2+1) 的話餘數都變7, 充分-9.617-!-item-!-187;#058&000483If x is a positive integer, is x 16 ?(1) x is less than the average (arithmetic mean) of the first ten positive integers.(2) x is the square of an integer.-【答案】A【思路】(1) x 20250b2

14、0cdTotal:800設live off campus & old20人數 為b設live campus & old20人數 為c設live off campus & old20人數 為d題目問c=?(1) 250 + b= 640 可知 b,但無法知道c,不充分(2) d=60 c無從得知,不充分(1)+(2) 由(1)得知 250 + b= 640,所以可以算出 c+d= 160由(2)得知d = 60 代回c+d= 160,所以C可以算出答案,充分!-11.959-!-item-!-187;#058&000583If p is a positive odd integer, what

15、is the remainder when p is divided by 4 ?(1) When p is divided by 8, the remainder is 5.(2) p is the sum of the squares of two positive integers.-【答案】D【思路】(1) P=8n+5 =4(2n+1) + 1 得到餘數為1,充分(2) p=,餘1,充分Ps: P總和要為奇數, 兩數相加至少有一個數為奇數-12.1013-!-item-!-187;#058&000609Of the 25 cars sold at a certain dealersh

16、ip yesterday, some had automatic transmission and some had antilock brakes. How many of the cars had automatic transmission but not antilock brakes?(1) All of the cars that had antilock brakes also had automatic transmission.(2) 2 of the cars had neither automatic transmission nor antilock brakes.-【

17、答案】E【思路】transmission transmissionBrakeabBrakecdTotal:25設有transmission & 有 Brake車子數量 為a設沒有transmission & 有 Brake車子數量 為b設有transmission & 沒有 Brake車子數量 為c設沒有transmission & 沒有 Brake車子數量 為d題目問 c=?(1) 有brake汽車中也有transmission,表示 b=0, 但不知c為多少,不充分(2) d=2, 也不知c為多少,不充分(1)+(2) 可知b=0,d=2,但沒有其他算式可以算出c是多少,所以不充分!-13

18、.1067-!-item-!-187;#058&000618Is x to the right of -5 on the number line?(1) x is to the right of -7 on the number line.(2) x is between -4 and -3 on the number line.-【答案】B【思路】題目問: x在數線上位在-5的右邊嗎?(1) x位在-7的右邊,表示可能在-5的左邊or右邊,不充分(2) x在-4和-3的中間,確定在-5右邊,充分-14.1121-!-item-!-187;#058&000619Is y between -2

19、and 1 on the number line?(1) y is to the right of -1 on the number line.(2) y is to the left of 2 on the number line.-【答案】E【思路】題目問: 數線上,y在-2和1的中間嗎?(1) y位在-1的右邊,所以可能在-2和1的中間,也有可能在1的右邊,所以不充分(2) y位在2的左邊,所以可能在-2和1的中間,也有可能-2在的左邊,所以不充分(1)+(2) 取交集,一樣不充分-15.1175-!-item-!-187;#058&000621Is r to the right of

20、-6 on the number line?(1) r is between -4 and -1 on the number line.(2) r is between -3 and 1 on the number line.-【答案】D【思路】題目問: r在數線上位在-6的右邊嗎?(1) r位在-4和-1的中邊,表示確定在-6的右邊,充分(2) r在-3和1的中間,確定在-6右邊,充分-16.1275-!-item-!-187;#058&000656Lines n and p lie in the xy-plane. Is the slope of line n less than the

21、slope of line p ?(1) Lines n and p intersect at the point (5,1).(2) The y-intercept of line n is greater than the y-intercept of line p.-【答案】C【思路】(1)兩線同過一個點, 根本比較不出來, 所以不充份. (2) 兩線的與Y所截取的值N線比P線大, 也比較不出來, 因為不知兩線的各另外一點, 所以不充份 (1)+(2)合併即能算出, 因為條件一已經給了兩個線段的一點, 再加上條件二給了兩個線段分別在Y座標上點的相對位置, 畫個圖即能算出來, 線段較陡的斜

22、率一定比線段較平的斜率大, 所以選選項(C)-17.1329-!-item-!-187;#058&000662Six countries in a certain region sent a total of 75 representatives to an international congress, and no two countries sent the same number of representatives. Of the six countries, if Country A sent the second greatest number of representative

23、s, did Country A send at least 10 representatives?(1) One of the six countries sent 41 representatives to the congress.(2) Country A sent fewer than 12 representatives to the congress.-【答案】E【思路】(1)當有一個地區是41, 表示剩下的5個區域=75-41=34 故41的那個區域就會是greatest 當A=9時,這34可以分配給剩下的區域 EX: (9,8,7,6,4) 符合題目要求 但A小於10 當A=

24、11時,則可分配成(11,8,7,6,2) 符合題目要求 但A至少等於10 所以(1)不充分 (2)可由上面的舉例發現 A小於12不成立 因為等於9和等於11都可以 所以(2)不對(1)+(2) 沒有資料可以顯示其餘國家的人數比例,所以資料不充分-18.1383-!-item-!-187;#058&000675What is the hundredths digit of the decimal z ?(1) The tenths digit of 100z is 2.(2) The units digit of 1,000z is 2.-【答案】E【思路】(1) 100z=xx.2xx 除以

25、100 z= xx.xx2 ,可知千分之一位數是2,還是不知百分之一位,不充分(2) 1000z=2.xxx 除以1000 z= x.xx2, 可知千分之一位數是2,還是不知百分之一位,不充分(1)+(2) 還是不知百分之一位,不充分-19.1437-!-item-!-187;#058&000677Is z equal to the median of the three positive integers x, y, and z ?(1) x y + z(2) y = z-【答案】B【思路】代數字推法(1) 3 a+b ?(1) a=16, 不充分(2) ,已知,可算出,可得a+ca+b,充

26、分-24.1952-!-item-!-187;#058&002488At a certain restaurant, if each hamburger costs the same amount, what is the cost, excluding sales tax, of 1 hamburger?(1) The total cost, including a 6 percent sales tax, is $4.77 for 3 hamburgers.(2) The total cost, including a 6 percent sales tax, is less than $

27、6.50 for 4 hamburgers.-【答案】A【思路】設hamburger成本=h, 問 h=?(1) 3h(0.06) = 4.77,可得h,充分(2) 4h(0.06) 6.50 ,不知h多少,不充分-25.2055-!-item-!-187;#058&002563What is the value of n ?(1) n is between 0 and 1.(2) is more than n.-【答案】B【思路】(1) n=小數or分數,太多答案,不充分(2) =n + ,可得n,充分-26.2109-!-item-!-187;#058&002567In a certain conference room each ro