[問題]OG 11th 新PP題 PS

[enim]

1. Last month 15 homes were sold in Town X. The average (arithmetic mean)
sale price of the homes was $150,000 and the median sale price was $130,000.
Which of the following statements must be true?

Ⅰ At least one of the homes was sold for more than $165,000.
Ⅱ At least one of the homes was sold for more than $130,000 ans less than $150,000.
Ⅲ At least one of the homes was sold for less than $130,000.

(A) Ⅰonly
(B) Ⅱonly
(C) Ⅲonly
(D) Ⅰand Ⅱ
(E) Ⅰand Ⅲ

ANS: A

2. Alice's take-home pay last year was the same each month, and she saved the
same fraction of her take-home pay each month. The total amount of money
that she had saved at the end of the year was 3 times the amount of that portion
of her monthly take-home pay that she did not save. If all the money that
she saved last year was from her take-home pay, what fraction of her take-home
pay did she save each month?

(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6

ANS:D


煩請版上大大解答一下 謝謝

[65kevin]

1. Last month 15 homes were sold in Town X. The average (arithmetic mean)
sale price of the homes was $150,000 and the median sale price was $130,000.
Which of the following statements must be true?

Ⅰ At least one of the homes was sold for more than $165,000.
Ⅱ At least one of the homes was sold for more than $130,000 ans less than $150,000.
Ⅲ At least one of the homes was sold for less than $130,000.

(A) Ⅰonly
(B) Ⅱonly
(C) Ⅲonly
(D) Ⅰand Ⅱ
(E) Ⅰand Ⅲ

ANS: A

2. Alice's take-home pay last year was the same each month, and she saved the
same fraction of her take-home pay each month. The total amount of money
that she had saved at the end of the year was 3 times the amount of that portion
of her monthly take-home pay that she did not save. If all the money that
she saved last year was from her take-home pay, what fraction of her take-home
pay did she save each month?

(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) 1/6

ANS:D


煩請版上大大解答一下 謝謝

1. 題目說15間房子售價的中位數為 130000, 平均數為150000
條件二 至少有一間房子售價介於 130000 到 150000 , 此條件錯誤, 有可能沒有一間房子介於 130000 到 150000
條件三 至少有一間房子售價小於 130000 , 此條件錯誤, 因為有可能八間房子都是 130000, 此仍滿足中位數為 130000
因此只有條件一必定為真, 因為平均數為 150000, 必定至少有一間房子售價大於等於 170000, 才能去補中位數 130000 和 平均數的差
答案選 A

2. 令每月實領薪資為 X, Y/100 為存款所佔比率, 根據題目可列出數學式: XY/100 * 12 = 3 * (100-Y)/100 * X
=> 5Y = 100
=> Y = 20, 所以存款所佔比率 = 20/100 = 1/5
答案選 D

[enim]

1. 題目說15間房子售價的中位數為 130000, 平均數為150000
條件二 至少有一間房子售價介於 130000 到 150000 , 此條件錯誤, 有可能沒有一間房子介於 130000 到 150000
條件三 至少有一間房子售價小於 130000 , 此條件錯誤, 因為有可能八間房子都是 130000, 此仍滿足中位數為 130000
因此只有條件一必定為真, 因為平均數為 150000, 必定至少有一間房子售價大於等於 170000, 才能去補中位數 130000 和 平均數的差
答案選 A

2. 令每月實領薪資為 X, Y/100 為存款所佔比率, 根據題目可列出數學式: XY/100 * 12 = 3 * (100-Y)/100 * X
=> 5Y = 100
=> Y = 20, 所以存款所佔比率 = 20/100 = 1/5
答案選 D

謝謝kevin 超級清楚的...

[汪汪北鼻]

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