150. 15103-!-item-!-187;#058&010253
If a, b, k, and m are positive integers, is ak a factor of bm ?
(1) a is a factor of b. (2) k
? m
-------------------------------------------------------------------------------------------------------------------------------------------------------- 【答案】C 【思路】
問題是要問 bm / ak 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) bm = (ax)m = amxm bm/ak=(amxm)/ak, a = 2 and b = 10
2 has one factor 2 and say k = 2 and m = 2
In 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≧0
No information about a & b. (1)+(2)
bm / ak = (amxm)/ak = xm a (m-k) = (integer) × (integer≧ 1)
So ans = C 變形題（幾乎一模一樣） If a, b, k, and m are positive integers, is ak a factor of bm? (1) a is a factor of b. (2) k = m Answer: C --------------------------------------------------------------------------------------------------------------------------------------------------------
151. 15157-!-item-!-187;#058&010256 Is x > 0.05 ? (1) x >
(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
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152. 15303-!-item-!-187;#058&010299 If 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
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153. 15354-!-item-!-187;#058&010304
A 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.
(2) The length of the shorter piece is
13 the length of the longer piece.
-------------------------------------------------------------------------------------------------------------------------------------------------------- 【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 (2) shorter piece =
13x , , 故不充份
結合(1) (2) short piece = x – 20 =13x , x = 30 , 充份
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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.
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------------------------- 【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
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155. 15462-!-item-!-187;#058&010358
Did 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
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156. 15516-!-item-!-187;#058&010359
A 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 = 120
Therefore, 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 = 180
Therefore, q=120. Total milk sold = 0.5*180+0.25*120 (SUFF)
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157. 15663-!-item-!-187;#058&010465
If 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
4?7n【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-------------------------
158. 15810-!-item-!-187;#058&010518
3,則r=3,6……,所以不充份
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Each 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 even
number 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
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159. 15957-!-item-!-187;#058&010660
If 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.