能力傾向測試 - 平均值示例
答案 - A
解釋
Average of 20 numbers = 0. Therefore Sum of 20 numbers = (0 x 20) = 0 It is quite possible that 19 of these numbers may be positive and if their sum is a, then 20th number is (-a).
答案 - C
解釋
Average = (10 + 15 + 20 + 25 + 30)⁄5 = 100⁄5 = 20.
答案 - D
解釋
Average = 3(1 + 2 + 3 + 4 + 5)⁄5 = 45⁄5 = 9
答案 - B
解釋
Average = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23)⁄9 = 100⁄9 = 111⁄9
答案 - B
解釋
Clearly, we have (3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 + z)⁄12 = 12 or 137 + z = 144 or z = 144 - 137 = 7.
答案 - B
解釋
we have : (z + (z + 2) + (z + 4) + (z + 6) + (z + 8))⁄5 = 11 or 5z + 20 = 55 or z = 7. So the numbers are 7, 9, 11, 13, 15. therefore required mean = (11 + 13 + 15⁄3) = 39⁄3 = 13.
答案 - A
解釋
Average = (11 + 22 + 33 + 44 + 55 + 66 + 77 + 88 + 99⁄9) ((11 + 99) + (22 + 88) + (33 + 77) + (44 + 66) +55⁄9) (4 x 110 + 55⁄9) (495⁄9) = 55
答案 - A
解釋
Let the number be z. then, z + z 2⁄2 = 5z = z 2 - 9z = 0 z (z - 9) = 0 z = 0 or z = 9 so the number is 9.
答案 - C
解釋
Let the number be z, z + 1, z + 2, z + 3 ,z + 4, z + 5 ,z + 6. then, (z + (z + 1) + (z + 2) + (z + 3) + (z + 4) + (z + 5) + (z + 6))⁄7 = 20 7z + 21 = 140 or 7z = 119 or z = 17 Largest number = z + 6 = 17 + 6 = 23
答案 - B
解釋
Let the number be z, z + 2, z + 4, z + 6 and z + 8. then, (z + (z + 2) + (z + 4) + (z + 6) + (z + 8))⁄5 = 61 5z + 20 = 305 or z = 57 so the required number is = (57 + 8) - 57 = 8
答案 - A
解釋
Let the number be z, z + 2, and z + 4. then, (z + z + 2 + z + 4) - (z + z + 2 + z + 4)⁄3 = 38 2(3z + 6) = 114 or 6z = 102 or z = 17.
答案 - D
解釋
Clearly to find the average we ought to know the number of boys, girls or students in the class neither of which is given. So, data is inadequate.
題13 - 某些農業工人的平均年收入（單位：盧比）為S，其他工人的平均年收入為T。農業工人的數量是其他工人的11倍。則所有工人的平均月收入（單位：盧比）是多少？
答案 - B
解釋
Let the number of other workers be z. then, number of agricultural workers = 11z Total number of workers = 12z Therefore Average monthly salary = S x 11z + T x z⁄12z = 11S + T⁄12
題14 - 一個家庭由祖父母、父母和三個孫子組成。祖父母的平均年齡為67歲，父母的平均年齡為35歲，孫子的平均年齡為6歲。這個家庭的平均年齡是多少？
答案 - B
解釋
Required average = (67 x 2 + 35 x 2 + 6 x 3⁄2 + 2 + 3) = (134 + 70 + 18⁄7) = 222⁄7 = 315⁄7
答案 - C
解釋
Since the month begins with a sunday, so there will be five sundays in the month Therefore Required average = (510 x 5 + 240 x 25⁄30) = 8550⁄30 = 285
答案 - B
解釋
Required average = (55 x 50 + 60 x 55 + 45 x 60⁄55 + 60 + 45) (2750 + 3300 + 2700⁄160) = (8750⁄160) = 54.68
答案 - A
解釋
Required average = (50.25 x 16 + 45.15 x 8⁄16 + 8) (804 + 361.20⁄24) = (1165.20⁄24) = 48.55
題18 - 一位車主連續三年分別以每升7.50盧比、8盧比和8.50盧比的價格購買汽油。如果他每年花費4000盧比，那麼汽油的平均每升成本大約是多少？
答案 - A
解釋
Total quantity of petrol consumed in 3 years. = (4000⁄7.50 + 4000⁄8 + 4000⁄8.50) litres = 4000 2⁄15 + 1⁄8 2⁄17 = 76700⁄51 litres Total amount spent = Rs. (3 x 4000) = Rs 12000 Therefore Average cost = Rs. (12000 x 51⁄76700) = Rs. 6120⁄767 = Rs. 7.98.
題19 - 六個數的平均值為z，其中三個數的平均值為y。如果其餘三個數的平均值為w，則？
答案 - D
解釋
Clearly, we have: z = 3y + 3w⁄6 or 2z = y + w.
題20 - 在9個人中，8個人每人花了30盧比吃飯。第九個人比所有9個人的平均支出多花了20盧比。他們所有人一共花了多少錢？
答案 - C
解釋
Let the average expenditure be Rs z then, 9z = 8 x 30 + (z + 20) or 9z = z + 260 or 8z = 260 or z = 32.50. Therefore total money spent = 9z = Rs. (9 x 32.50) = Rs. 292.50.
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