PP- T1-PS4

[小花]

粗體字是答案
不知道一個版面PO這麼多問題妥不妥當
請大家多多指教

4. 765-!-item-!-187;#058&000550
In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 16th board counting from the bottom of the stack. How many boards are in the stack?

(A) 38
(B) 36
(C) 35
(D) 34
(E) 32

19. 2463-!-item-!-187;#058&002761
For a finite sequence of nonzero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6 ?

(A) One
(B) Two
(C) Three
(D) Four
(E) Five

33. 4484-!-item-!-187;#058&004004
If x^4 + y^4 = 100, then the greatest possible value of x is between

(A) 0 and 3
(B) 3 and 6(C) 6 and 9
(D) 9 and 12
(E) 12 and 15

36. 4841-!-item-!-187;#058&004235
In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the cards could be

(A) 3 and 15
(B) 3 and 20
(C) 4 and 13(D) 4 and 14
(E) 5 and 14

[bibbyshiu]

4. 765-!-item-!-187;#058&000550
In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 16th board counting from the bottom of the stack. How many boards are in the stack?

上面數下來第20個剛好在下面數上去第16個下面 => 上面數下來第20個是下面數來第15個...下面有14個, 上面有19個, 加上那一個..答案是34個

19. 2463-!-item-!-187;#058&002761
For a finite sequence of nonzero numbers, the number of variations in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6 ?

variation : 當下一個數字的正負號與自己不同時, 算1次...1, -3......-3, 2..... 5, -4... 共3次

If x^4 + y^4 = 100, then the greatest possible value of x is between

當y^4=0時, x^4會是最大值, x= 100開4次方, 3的4次平方= 81, 6的4次平方是, 6x6x6x6..100在這兩個數之間

36. 4841-!-item-!-187;#058&004235
In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the cards could be

最小的product value會是 最小的數字x次小的數字必須大於15, 3x4=12, 4x5=20, 所以4是最小的數字
最大的product value會是最大的數字x次大的數字必須小於200, 12x13=156, 13x14=182, 14x15=210..
我算出來答案是 (D) 4 and 14, 跟你的答案不太依樣 :)

[小花]

感謝你的回答

36.答案的確給C
可能答案給錯了
題目和答案是從CD 上下載的

[bibbyshiu]

36. 4841-!-item-!-187;#058&004235
In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the cards could be

經過朋友提醒, 重新修正答案應該是(C)..
題意應該是抽一張牌就要乘上這張牌和其下一個號碼, 我前篇文章誤解題意
所以3x(3+1)=12. 4x(4+1)=20, 13x(13+1)=182, 14x(14+1)=210.
應該是3與13沒錯

[小花]

恩 謝謝 我懂了

[nemolee]

不好意思，想借問這一題，對於這一題的說明，看不懂 ><

If x^4 + y^4 = 100, then the greatest possible value of x is between

當y^4=0時, x^4會是最大值, x= 100開4次方, 3的4次平方= 81, 6的4次平方是, 6x6x6x6..100在這兩個數之間

----------------------------------------------------------------------

以上的 x = 100開4次方，這個地方看不了解
若 y^4 = 0 時，x^4 應該是 = 100 ==> x^4=100,
簡化兩邊同樣開4的根號 ==> x = 4根號 100,
繼續簡化 ==> x = 4根號 10^2 = 10^(2*1/4) ==> x = 根號10 = 3.16
這樣的話，我就會猜(B)的答案了，請問是這樣做的嗎???


我原先的錯誤的思路如下：錯誤的選到了(A)
讓y^4=0 , 則 x^4=100,
如果X代入3, 則3^4=81
如果 X代入 4, 則 4^4 = 256 已經大於 100了，如果繼續代到 5^4 的話，那一定也是大於100，所以我才會選 (A)這個答案。

請人指點指點~ 謝謝~~

[nemolee]

ding

[Huang Hsin-Yi]

我也頂一下

6^4明明是>100,怎會在範圍內

那個好心人可以告訴我們

[小花]

33. 4484-!-item-!-187;#058&004004
If x^4 + y^4 = 100, then the greatest possible value of x is between

(A) 0 and 3 =>四次方後 0~81
(B) 3 and 6 => 81~1296
(C) 6 and 9
(D) 9 and 12
(E) 12 and 15

取最大值100界於81~1296之間

題目問的是X的最大值在哪組範圍之內

[nemolee]

喔~ 原來是誤解題意哩... 謝謝小花大人

[Huang Hsin-Yi]

原來是這樣,肛溫~~~~~~~~~~~~~~~~