推 ipas3:144. (1.08)^2=1.16 故(1.0r)^2>1.15 insufficient 08/22 09:36
兩題數學～沒有找到可以讓我瞭解的解法
請教大家.謝謝！
77. 9031-!-item-!-187;#058&006222
At a dinner party, 5 people are to be seated around a circular table.
Two seating arrangements are considered different only when the
positions of the people are different relative to each other.
What is the total number of different possible seating arrangements
for the group?
(A) 5
(B) 10
(C) 24
(D) 32
(E) 120
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【答案】C
【思路】
若為一直線排法 為5！
但此題目為圓形
五個人排圈圈...
ABCDE
BCDEA
CDEAB
DEABC
EABCD
都是一樣
故排圈圈時就是5!/5=4!
( 除以五是為了消除每次相鄰位置改變時都會有重複的情況)
-->不懂為何是除以5? 不是減5?
144. If $1,000 is deposited in a certain bank account and remains
in the account along with any accumulated interest, the dollar
amount of interest, I , earned by the deposit in the first n years
is given by the formula I =1000〔(1 + r/100 )^n - 1〕 , where r percent
is the annual interest rate paid by the bank.
Is the annual interest rate paid by the bank greater than 8 percent?
(1) The deposit earns a total of $210 in interest in the first two years.
(2) ( 1 + r/100 )^2 > 1.15
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【答案】A
【思路】
(1)
210 = 1000
0.21=1+ + -1
0.21= +
求得166.4….. The deposit earns a total of $210 in interest in the first two years.
是的…….sufficient
-->這個我的想法是,interest 有了,不用算出答案也充分.因為不管答案是大於還是小於
8%,都一定有一個唯一解～快速看下一個條件
(2)
>1.15
=1+2 + >1.15
=10000+200r+r2>11500
= >11500
=r+100>105(大約值)
所以 r 可能大於也可能小於 8……insufficient
--> 請問這個條件有更快的檢驗方式嗎？
這解法有點花時間
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