PP-DS1-4

150. 15103-!-item-!-187;#058&010253If a, b, k, and m are positive integers, is a k a factor of b m ?(1) a is a factor of b.(2) k m--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】問題是要問b m / a k 是否可以沒有餘數remainder(1) b/a 沒有餘數是不夠的例如b=ax (x being an positive integer)b m = (ax)m = a m x mb m/a k=(a m x m)/a k,a = 2 andb = 102 has one factor 2 and say k = 2 and m = 2In this case 22 = 4 is a factor of 100, However, if m = 1 then 4 is not a factor of 10.we don't know the value of k & m.(2) m-k≧0No information about a & b.(1)+(2)b m / a k = (a m x m)/a k = x m a (m-k)= (integer) × (integer≧1)-------------------------151. 15157-!-item-!-187;#058&010256Is x > 0.05 ?3(1) x >40(2) x is greater than 3 percent of 50.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】(1) 因為X>0.075 , 所以X>0.05 , 故條件充分(2) 因為X>0.06 , 所以X>0.05 , 故條件充分(1) (2) 皆充分-------------------------------------------------------------------------------------------------------------------------------152. 15303-!-item-!-187;#058&010299If xyz > 0, is x > 0 ?(1) xy > 0(2) xz > 0--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】(1) xy>0 , x= + or - , y=+ or - , if x= - , y= - , xy =+ , 故不充份(2) xz>0 , x= + or - , y=+ or - , if x= - , y= - , xz =+ , 故不充份xyz > 0 , 結合(1) (2) x>0 ,y >0 , z>0 , 則xyz >0--------------------------------------------------------------------------------------------------------------------------------------------------------153. 15354-!-item-!-187;#058&010304A wooden rod is cut into two pieces. What is the length of the longer piece?(1) One of the pieces is 20 inches longer than the other piece.1the length of the longer piece.(2) The length of the shorter piece is3--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】假設longer piece = x(1) longer piece = x , short piece = x – 20 , 無法得知length of the longer piece , 故不充份1x , , 故不充份(2) shorter piece =31x , x = 30 , 充份結合(1) (2) short piece = x – 20 =3--------------------------------------------------------------------------------------------------------------------------------------------------------154. 15408-!-item-!-187;#058&010332–The sum of positive integers x and y is 77. What is the value of xy ?(1) x = y + 1(2) x and y have the same tens digit.-------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】(1) 題目x + y = 77 , (1) x = y + 1 , x = 39 , y = 38 , xy =1482 , 充份(2) 題目x + y = 77 , x , y有共同的10位數, 只有38 , 39符合, 充份(1) (2)皆充份, 故選D--------------------------------------------------------------------------------------------------------------------------------------------------------155. 15462-!-item-!-187;#058&010358Did it take Pei more than 2 hours to walk a distance of 10 miles along a certain trail? (1 mile = 1.6 kilometers, rounded to the nearest tenth.)(1) Pei walked this distance at an average rate of less than 6.4 kilometers per hour.(2)On average, it took Pei more than 9 minutes per kilometer to walk this distance.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】10 miles = 16 kilometers(1) average rate <6.4 , 2小時所行走距離<12.8 , 所以12.8 < 16 ,則要超過兩個小時才能走16 kilometers ,充份(2) per kilometer花費9分鐘,16 kilometers花費144分,所以超過2小時,充份(1) (2)皆充份, 故選D--------------------------------------------------------------------------------------------------------------------------------------------------------156. 15516-!-item-!-187;#058&010359A store sells milk in cartons of two sizes, one-half gallon and one-quarter gallon. If the store sold a total of 300 cartons of milk yesterday, how many gallons of milk did it sell yesterday?(1) Yesterday the store sold 120 one-quarter-gallon cartons of milk.(2)Yesterday the store sold 90 gallons of milk in one-half-gallon cartons.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】題目問: h+q=300(i) q = 120Therefore, h=180. Total milk sold = 0.5*180+0.25*120 (SUFF)(ii) 這邊的題目要注意,有小變化(90 gallons of milk in one-half-gallon cartons)h = 90*2 = 180Therefore, q=120. Total milk sold = 0.5*180+0.25*120 (SUFF)--------------------------------------------------------------------------------------------------------------------------------------------------------157. 15663-!-item-!-187;#058&010465If n is a positive integer and r is the remainder when 4 + 7n is divided by 3, what is the value of r ?(1) n + 1 is divisible by 3.(2) n > 20--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】A【思路】(1) n + 1 是3的倍數, 則n=2,5,8……,帶入4+7n3,則r=0 ,故充份(2) n>20 , n=21,22,23…. ,帶入4+7n3,則r=3,6……,所以不充份--------------------------------------------------------------------------------------------------------------------------------------------------------158. 15810-!-item-!-187;#058&010518Each of the 25 balls in a certain box is either red, blue, or white and has a number from 1 to 10 painted on it. If one ball is to be selected at random from the box, what is the probability that the ball selected will either be white or have an even number painted on it?(1) The probability that the ball will both be white and have an even number painted on it is 0.(2)The probability that the ball will be white minus the probability that the ball will have an evennumber painted on it is 0.2.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】E【思路】問P (either white or even)= P (white)+P(even)- P(both)(1)只知P(both) ,不充分(2)只知P(white)-P(even) ,不充分(1)+(2)也不充分--------------------------------------------------------------------------------------------------------------------------------------------------------159. 15957-!-item-!-187;#058&010660If n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what is the value of r ?(1) n is not divisible by 2.(2) n is not divisible by 3.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】n-1()n+1()24=n2-124(1) n = 3 , 5 , 7 ,9…… ,則r=8 , 1 ……,不充份(2)n=1 , 2 , 4,….,r=2 ,3………,不充份(1) + (2) 不能被2 , 3整除,2 ,3 為24 的公因數,所以n排除為24因數後,r=0--------------------------------------------------------------------------------------------------------------------------------------------------------160. 16057-!-item-!-187;#058&010664If Company M ordered a total of 50 computers and printers and Company N ordered a total of 60 computers and printers, how many computers did Company M order?(1) Company M and Company N ordered the same number of computers.(2) Company N ordered 10 more printers than Company M.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】E【思路】(1) company M 和company N 訂購同樣數量的電腦,但題目並未告知companyM ,N 訂購computers和printers,不充份(2)假設訂購printers=x , x , x-10為M , N訂購printers , 總數量為110 ,但並不是printers總數,所以不充份(1) +(2)還是無法得知電腦或是printers的總數,故選E--------------------------------------------------------------------------------------------------------------------------------------------------------161. 16203-!-item-!-187;#058&010722If the average (arithmetic mean) of the five numbers x, 7, 2, 16, and 11 is equal to the median of the five numbers, what is the value of x ?(1) 7 < x < 11(2) x is the median of the five numbers.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】(1) 7 < x < 11 , 則數列為2 , 7 , x , 11 , 16 , m=36+x5, 中位數為x , x=36+x5,x=9 ,充份(2)x為中位數, 數列為2 , 7 , x , 11 , 16 , x=36+x5,x=9 ,充份(1) (2)皆充份,故選D--------------------------------------------------------------------------------------------------------------------------------------------------------162. 16257-!-item-!-187;#058&010730What fraction of this year's graduating students at a certain college are males?(1) Of this year's graduating students, 33 percent of the males and 20 percent of the females transferred from another college.(2) Of this year's graduating students, 25 percent transferred from another college.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】(1) 0.33M+0.2F=transfer 不充份(2) 0.25（M+F)=transfer 不充份(1)+ (2) M=5/8F 充份選E--------------------------------------------------------------------------------------------------------------------------------------------------------163. 16312-!-item-!-187;#058&010731Linda put an amount of money into each of two new investments, A and B, that pay simple annual interest. If the annual interest rate of investment B is 1.5 times that of investment A, what amount did Linda put into investment A ?(1) The interest for 1 year is $50 for investment A and $150 for investment B.(2) The amount that Linda put into investment B is twice the amount that she put into investment A. --------------------------------------------------------------------------------------------------------------------------------------------------------【答案】E【思路】假設investmentsA=X , investmentsB=y , interest rateA=X1, interest rateB=Y1 , 1.5X1=Y1(1) X(X1)=50 , Y(Y1)=150 , Y(1.5X1)=150 , 無法得investment ,不充份(2) Y=2X 無法得investment ,不充份(1)+(2) 2X(1,5X1)=150 , Y(1.5X1)=150 無法得investment 故選E--------------------------------------------------------------------------------------------------------------------------------------------------------164. 16412-!-item-!-187;#058&010774At a two-day seminar, 90 percent of those registered attended the seminar on the first day. What percent of those registered did not attend the seminar on either day?(1) A total of 1,000 people registered for the two-day seminar.(2) Of those registered, 80 percent attended the seminar on the second day.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】E【思路】(1)只知全部總數為1000, 90 percent參加第一天, 10 percent不知是否參加別天或是沒參加,故不充份(2)得知80 percent參加第2天,但有可能和第一天重複的人數或是只參加第二天的, 故不充份(1)＋(2) 全部人數為1000 ,可是沒資料得知重複人數,所以無法得知兩天都沒參加的人故選E--------------------------------------------------------------------------------------------------------------------------------------------------------165. 16466-!-item-!-187;#058&010795Of the 1,400 college teachers surveyed, 42 percent said that they considered engaging in research an essential goal. How many of the college teachers surveyed were women?(1) In the survey, 36 percent of the men and 50 percent of the women said that they considered engaging in research an essential goal.(2) In the survey, 288 men said that they considered engaging in research an essential goal.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】A【思路】(1) total（1400) x42100=588(參加人數）, 588 x women比例（50100)=參加女人的比例, 充份(2)原題問surveyed werer women , 包含engage 和not engage , so we only can get engage women , 不充份--------------------------------------------------------------------------------------------------------------------------------------------------------166. 16522-!-item-!-187;#058&010838In the xy-coordinate plane, the slope of line l is 3. Does line l pass through the point (-2,1)?(1) Line l passes through the point (4,4).(2) Line l passes through the point (-4,-2).--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】同斜率所通過的點相同, 所以帶入（Y2-Y1）/（X2-X1）, 得(1)(2)皆可通過(-2,1) ,故選D--------------------------------------------------------------------------------------------------------------------------------------------------------167. 16626-!-item-!-187;#058&010859If x, y, and z are integers and xy + z is an odd integer, is x an even integer?(1) xy + xz is an even integer.(2) y + xz is an odd integer.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】A【思路】xy + z = odd integer , xy(odd)+z(even)= odd integer , xy(even)+z(odd)=odd integer(1) xy + xz = even , xy(even)+xz(even)=even , so z 應該為odd , x為even , xz才為even ,xy(odd)+xz(odd)=even ,z 為even , xz不等於odd , 充份(2) y + xz = odd integer , y(odd)+xz(even)=odd , z=even ,x=even ,y(even)+xz(odd)=odd ,z=odd,x=odd , 所以不充份--------------------------------------------------------------------------------------------------------------------------------------------------------168. 16680-!-item-!-187;#058&010861On the number line, the distance between x and y is greater than the distance between x and z. Does z lie between x and y on the number line?(1) xyz < 0(2) xy < 0--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】E【思路】(1) xyz < 0 , 可能為+ - + , + + - , - + + , - - - , 所以不充份(2)xy < 0 , - + , + - , 不充份(1)＋(2) = - + + , + - + ,不充份選E--------------------------------------------------------------------------------------------------------------------------------------------------------169. 16735-!-item-!-187;#058&010875If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of a n, what is the value of a ?(1) a n = 64--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】B【思路】(1) 26= 64 , 43=64 , 82=64 , not sufficient(2) n = 6 , 26= 64 , sufficient--------------------------------------------------------------------------------------------------------------------------------------------------------170. 16927-!-item-!-187;#058&010946If n and t are positive integers, what is the greatest prime factor of the product nt ?(1) The greatest common factor of n and t is 5.(2) The least common multiple of n and t is 105.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】B【思路】(1)最大公因數為5 , 但其質因數有多組,不充份(2)105=(5)(3)(7) , 故其最質因數為7 , 充份--------------------------------------------------------------------------------------------------------------------------------------------------------171. 16981-!-item-!-187;#058&010960Is |x - y | > |x | - |y | ?(1) y < x(2) xy < 0--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】B【思路】(1) y < x , (y= - , x=+) , (y=+ , x=+) , (y=- , x=-) , 當x=+ - , y=- - , |x - y | > |x | - |y | , 當(y=+ , x=+)時, |x - y | = |x | - |y | ,所以不充份(2) xy < 0 , (y= - , x=+) or (y= + , x=- ) , |x - y | > |x | - |y | , 充份--------------------------------------------------------------------------------------------------------------------------------------------------------172. 17130-!-item-!-187;#058&011022If m, k, x, and y are positive numbers, is mx + ky > kx + my ?(1) m > k--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】(1) m > k , 另外兩變數x y 不知大小, 所以不充份(2) x > y , m, k 不知, 故不充份(1)＋(2)= m>k , x>y , m , x 兩個最大變數相乘,恆為最大,則mx + ky > kx + my 成立--------------------------------------------------------------------------------------------------------------------------------------------------------173. 17281-!-item-!-187;#058&011070If N is a positive integer, is the units digit of N equal to zero?(1) 14 and 35 are factors of N.(2) N = (25)(32)(57)(76)--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】(1)14和35為N的因數,70為最小公倍數,N為70倍數,充份(2) N = (25)(32)(57)(76) , 充份--------------------------------------------------------------------------------------------------------------------------------------------------------174. 17336-!-item-!-187;#058&011114In the xy-plane, what is the y-intercept of line l(1) The slope of line l is 3 times its y-intercept.(2) The x-intercept of line l is -31.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】E【思路】(1) 直線方程式為y=mx+b ,m為斜率,b為截距, 通過（0 ,Y1) , Y1=3b(x)+b , Y1=b, 不充份(2) y=mx+b , (-1/3, 0) 帶入,b=13m ,不充份(1)＋(2) 還是不充份故選E--------------------------------------------------------------------------------------------------------------------------------------------------------175. 17390-!-item-!-187;#058&011123The sum of the integers in list S is the same as the sum of the integers in list T. Does S contain more integers than T ?(1) The average (arithmetic mean) of the integers in S is less than the average of the integers in T.(2) The median of the integers in S is greater than the median of the integers in T.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】A【思路】(1) mean= sumn,當樣本越大,m越小,所以得知S的average小於T時,其樣本大於T ,充份(2) median of the integers 的大小不影響數列樣本的多少,不充份--------------------------------------------------------------------------------------------------------------------------------------------------------176. 17491-!-item-!-187;#058&011140If x and y are positive integers, is the product xy even?(1) 5x - 4y is even.(2) 6x + 7y is even.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】xy=even , 有三種情況,(x=even . y=even) ,(x=even ,y=odd) , (x=odd ,y=even)(1) 5x - 4y is even , even - even =even , 所以xy=even ,充份(2) 6x + 7y is even , even + even =even , 所以xy=even ,充份--------------------------------------------------------------------------------------------------------------------------------------------------------177. 17595-!-item-!-187;#058&011159If x and y are positive integers, what is the value of xy ?(1) The greatest common factor of x and y is 10.(2) The least common multiple of x and y is 180.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】(1) The greatest common factor of x and y is 10 ,其資料不充份(2) 若兩數互質, 則其最小公倍數為其兩者相乘,有許多組合,所以不充份(1)＋(2)=(a,b)[a,b]=ab 所以選C--------------------------------------------------------------------------------------------------------------------------------------------------------178. 17649-!-item-!-187;#058&011192If there are more than two numbers in a certain list, is each of the numbers in the list equal to 0 ?(1) The product of any two numbers in the list is equal to 0.(2) The sum of any two numbers in the list is equal to 0.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】B【思路】(1)任何數相乘只要數列有一個0,乘積為0,但不代表數列均為0,不充份(2)任何數相加為0,其必為兩個0,充份--------------------------------------------------------------------------------------------------------------------------------------------------------179. 17750-!-item-!-187;#058&011285A manufacturer conducted a survey to determine how many people buy products P and Q. What fraction of the people surveyed said that they buy neither product P nor product Q ?(1)1 of the people surveyed said that they buy product P but not product Q.(2) 21 of the people surveyed said that they buy product Q.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】(1)31買P 沒買Q , 資料不充份 (2)1買Q , 資料不充份 (1)+ (2) 1- 31-21 =no P no Q , 充份 故選C--------------------------------------------------------------------------------------------------------------------------------------------------------180. 17851-!-item-!-187;#058&011342Are x and y both positive?(1) 2x – 2y = 1(2) y x > 1--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】(1) 2x – 2y = 1 , x=+ ,y=- or x=+ , y=+ ,or x=- y=- ,不充份(2) y x > 1 , 則x= - , y= - ,x < y or x=+ ,y=+ , x>y ,不充份(1)＋(2)= x=+ ,y=+ , 選C--------------------------------------------------------------------------------------------------------------------------------------------------------181. 17908-!-item-!-187;#058&011358In the figure shown, what is the value of x ?(1) The length of line segment QR is equal to the length of line segment RS.(2) The length of line segment ST is equal to the length of line segment TU.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】(1) QR=RS 不能判斷x(2) ST=TU 不能判斷x(1)+(2) ∠RSQ=∠RQS && ∠TSU=∠SUT∠SUP=x+∠TSU∠SQP=x+∠RSQ∠SUP+∠SQP=180+x∠QPU+180+2x = 360 (四邊形內角和)2x=90, x=45--------------------------------------------------------------------------------------------------------------------------------------------------------182. 17963-!-item-!-187;#058&011379In a certain year, the difference between Mary's and Jim's annual salaries was twice the differencebetween Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year?(1) Jim's annual salary was $30,000 that year.(2) Kate's annual salary was $40,000 that year.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】Ｂ【思路】由題意得知M-J=2(M-K)M+J=2K 代入++3M J K =33K =K (1) 有2個未知(2) 代入上面簡化的算式得到.-------------------------183. 18017-!-item-!-187;#058&011390The positive integers x, y, and z are such that x is a factor of y and y is a factor of z. Is z even?(1) x is even.(2) y is even.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】由題意得知 y=m*x and z=n*y therefore z=n*m*x(1) z=(n*m)*x 偶數乘不等於0的整數=偶數(2) z=n*y 偶數乘不等於0的整數=偶數--------------------------------------------------------------------------------------------------------------------------------------------------------184. 18071-!-item-!-187;#058&011405Jack and Mark both received hourly wage increases of 6 percent. After the wage increases, Jack's hourly wage was how many dollars per hour more than Mark's?(1) Before the wage increases, Jack's hourly wage was $5.00 per hour more than Mark's.(2) Before the wage increases, the ratio of Jack's hourly wage to Mark's hourly wage was 4 to 3.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】A【思路】(1) J-M=5 1.06(J-M)=5.3(2) J:M=4:3 無法得知時薪增加多少--------------------------------------------------------------------------------------------------------------------------------------------------------185. 18511-!-item-!-187;#058&011604Is x between 0 and 1 ?(1) x is between -21 and 23 (2) 3 is 1 more than x.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】B【思路】 (1) -1< x <3x 可能小於0或大於0 (2) x = 43 -41= 2-------------------------186. 18566-!-item-!-187;#058&011610 If 0 < x < y, what is the value of)()(22y x y x -+?(1) x 2 + y 2 = 3xy(2) xy = 3--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】A【思路】 (1) ++-+222222x xy y x xy y =+-3232xy xy xy xy=5 (2) 226x y x y +++- 不知道x,y 的值 --------------------------------------------------------------------------------------------------------------------------------------------------------187. 18620-!-item-!-187;#058&011611If x, y, and z are integers greater than 1, what is the value of x + y + z ?(1) xyz = 70(2) yz x = 107--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】A【思路】(1) xyz = 70 = 1x2x5x7 or 1x7x10(不合題目條件)(x,y,z)={2,5,7} x+y+z=14(2) x 可以是7或14等..--------------------------------------------------------------------------------------------------------------------------------------------------------188. 18674-!-item-!-187;#058&011626Is p + pz = p ?(1) p = 0(2) z = 0--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】D【思路】p+pz = p(1+z)(1) 0x(1+z) = 0(2) p(1+0) = p--------------------------------------------------------------------------------------------------------------------------------------------------------189. 18728-!-item-!-187;#058&011689If the operation △is one of the four arithmetic operations addition, subtraction, multiplication, and division, is (6 △2) △4 = 6 △(2 △4) ?(1) 3 △2 > 3(2) 3 △1 = 3--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】A【思路】(6 △2) △4 = 6 △(2 △4) 乘或加,兩式相等. 除或減,兩式不相等(1) △可以是乘或加(2) △可以是乘或除--------------------------------------------------------------------------------------------------------------------------------------------------------190. 18785-!-item-!-187;#058&011838On the number line shown, is zero halfway between r and s ?(1) s is to the right of zero.(2) The distance between t and r is the same as the distance between t and -s.--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】C【思路】(1) r 可以是正或負數(2) s 可以是正或負數(1)+(2)t and s are positive. t+|r|= t+|-s|r=s or –s. r is not s (from graph), so r=-s--------------------------------------------------------------------------------------------------------------------------------------------------------191. 18839-!-item-!-187;#058&011851If the product of the three digits of the positive integer k is 14, what is the value of k ?(1) k is an odd integer.。