100. 10681-!-item-!-187;#058&007619
2 + 2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^6 + 2^7 + 2^8 =
(A) 2^9 (B) 2^10 (C) 2^16 (D) 2^35 (E) 2^37
------------------------------------------------------------------------------------------------------------------------------------ 【答案】A 【思路】
此題最快的方式背等比級數求合sum of geometric progression的公式 等比級數求合公式: a0, a1, ... , an
where a0 × r = a1, a1 × r = a2, ..... then Sn = or Sn =
a0(1?rn) if r<1
(1-r)a0(rn?1) if r>1
(r-1)所以：
a(rn?1)
(r-1)a 首項 r 公比
2?2?22?23?24?25?26?27?28
2345678=2?[2?2?2?2?2?2?2?2]
=
2(28?1)= 2 +
(2-1)8=2?2(2?1)
9= 2?2?2
9= 2 此題商喀還有一個比較不正統的解法，可參考 有一點等比的概念 2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8=2^9 2+2=2^2 原式= 2^2+2^2+2^3+2^4+2^5+2^6+2^7+2^8=2^9 (2^2+2^2=2^3) 原式= 2^3+2^3+2^4+2^5+2^6+2^7+2^8=2^9 (2^3+2^3=2^4) ..依此類推 第N項=N-1項的總和 所以 2+2+2^2+2^3+2^4+2^5+2^6+2^7+2^8=2^9 ------------------------------------------------------------------------------------------------------------------------------------
101. 10730-!-item-!-187;#058&007650 [?]
The table above shows the amount of waste material, in tons, recycled by each of five counties in a single year and the amount of waste material, also in tons, that was disposed of in landfills by the five counties in that year. Which county had the lowest ratio of waste material disposed of to waste material recycled in the year reported in the table?
(A) A (B) B (C) C (D) D (E) E
102. 10776-!-item-!-187;#058&007653
A certain store found that last year the average (arithmetic mean) monthly sales from January through
October was $120,000. In November and December, the monthly sales were 3 and 5 times, respectively, the average for the other 10 months. What was the store's average monthly sales last year?
(A) $180,000 (B) $216,000 (C) $252,000 (D) $318,000 (E) $360,000
------------------------------------------------------------------------------------------------------------------------------------ 【答案】A
【思路】
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103. 10822-!-item-!-187;#058&007696
A certain meter records voltage between 0 volts and 10 volts, inclusive. If the average (arithmetic mean) value of 3 recordings on the meter was 8 volts, what was the smallest possible recording, in volts?
(A) 2 (B) 3 (C) 4 (D) 5 (E) 6
------------------------------------------------------------------------------------------------------------------------------------ 【答案】C 【思路】
total: 8x3=24
取最小的話, 另外兩個都要是最大的. 24-10-10=4
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104. 10868-!-item-!-187;#058&007697
The temperatures in degrees Celsius recorded at 6 in the morning in various parts of a certain country were 10, 5, -2, -1, -5, and 15. What is the median of these temperatures?
120000?10?3?120000?5?120000121200000?360000?600000 x?122160000??18000012x?
(A) -2 (B) -1 (C) 2 (D) 3 (E) 5
------------------------------------------------------------------------------------------------------------------------------------ 【答案】C 【思路】
從小到大排列
-5, -2, -1, 5, 10 15
(?1)?(5)?2
2------------------------------------------------------------------------------------------------------------------------------------
105. 10917-!-item-!-187;#058&007716 [?]
In the figure above, what is the value of x ?
(A) 55 (B) 60 (C) 65 (D) 70 (E) 75
106. 10964-!-item-!-187;#058&007770
Joshua and Jose work at an auto repair center with 4 other workers. For a survey on healthcare insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?
(A) (B) (C) (D) (E)
107. 11013-!-item-!-187;#058&007796 [?]
The table above shows the total sales recorded in July for the 5 salespeople at Acme Truck Sales. It was discovered that one of Cal's sales was incorrectly recorded as one of Ann's sales. After this error was corrected, Ann's total sales were still higher than Cal's total sales, and the median of the 5 sales totals was $330,000. What was the value of the incorrectly recorded sale?
(A) $30,000 (B) $48,000 (C) $90,000 (D) (E)
108. 11175-!-item-!-187;#058&007894 [?]
On the number line above, the segment from 0 to 1 has been divided into fifths, as indicated by the large tick marks, and also into sevenths, as indicated by the small tick marks. What is the least possible distance between any two of the tick marks?
(A) (B) (C) (D) (E)
109. 11276-!-item-!-187;#058&008007
What is the value of [?], to the nearest whole number?
(A) 8 (B) 11 (C) 12 (D) 15 (E) 32
110. 11325-!-item-!-187;#058&008034
During a trip on an expressway, Don drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had traveled at a constant rate of 60 miles per hour for the entire trip?
(A) 8.5% (B) 50% (C) (D) (E)
111. 11378-!-item-!-187;#058&008123 [?]
In the figures above, if the area of the triangle on the right is twice the area of the triangle on the left, then in terms of s, S =
(A) (B) (C) (D) (E) 2s
112. 11750-!-item-!-187;#058&008431
For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6 - n points whenever one of its members finished in nth place, where 1 <= n <= 5. There were no ties, disqualifications, or
withdrawals. If no team earned more than 6 points, what is the least possible score a team could have earned?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
------------------------------------------------------------------------------------------------------------------------------------ 【答案】D 【思路】
There are 9 individual members in total.
There were no ties, disqualifications or withdrawls, therefore all 9 members finished the race, and each one finished in a different place.
1st place = 5 points.
2nd place = 4 points. 3rd place = 3 points. 4th place = 2 points. 5th place = 1 point. 6th place = 0 points. 7th place = 0 points. 8th place = 0 points. 9th place = 0 points.
There are a total of 5 + 4 + 3 + 2 + 1 = 15 points to be awarded.; those points must be distributed in one way or another among the three teams.
None of the team earned more than 6 points, therefore when maximizing two of the teams in order to minimize the third, we cannot go over 6 points per team.
I gave one team 6 points and the other team 5 points since I took the \among individual members and no ties among the total score of each of the teams.
(However, \6 points).
If one team gets 5 + 1 = 6 points, and another team gets 4 + 2 = 6 points, they can get 6+6 =12. .third team got the the least possible 15-12 =3 pts. with the minimum.
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113. 11853-!-item-!-187;#058&008463 [?]
For the inequalities above, what is the maximum possible value of P + Q + R + S ?
(A) -2 (B) 0 (C) 2 (D) 4 (E) 6
114. 11899-!-item-!-187;#058&008467
If xy + k = k and x is not 0, which of the following must be true?
(A) x > y (B) x + y = 0 (C) y = 0
(D) |x - y | = 0 (E) xy = 1
------------------------------------------------------------------------------------------------------------------------------------ 【答案】C
x?0且 x>y, 假設x=3,y=2, 6?k?k
(B) X+Y=0, 且x?0,假設x=3, y=-3,?9?k?k (D) |x - y | = 0且x?0,假設x=3,y=3,9?k?k
1 (E) xy = 1且x?0,假設x=3,y= , 1?k?k
3 (C)y=0, 且x?0,則xy=0,thus xy + k = k must be true
【思路】(A)
------------------------------------------------------------------------------------------------------------------------------------ 115. 12001-!-item-!-187;#058&008506
A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster. If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?