匿名使用者
匿名使用者 發問時間: 社會與文化語言 · 9 年前

Math Question

Math:

For any number W and Z, W.Z=W^3Z(8-W^2). If both Z and W.Z are positive numbers, which of the following could be a value of W?

1) 9

2) 3

3) 0

4) -2

5)-9

Thanks

* And, please tell me what "W.Z" mean mathematically.

已更新項目:

Thanks for your reply. And YES I can read Chinese. English is easier for me.

I have the same book you refer to and I also found it illogical in the book. (Answer key)

Well, I thought I misunderstood "W.Z" and that led me to the wrong answer.

But thanks anyway.

1 個解答

評分
  • 9 年前
    最佳解答

    書本上答案是(5),但是我認為這題有問題。

    我認為這題答案是以下皆非、或以上皆非。

    因為它說 If both Z and W.Z are positive numbers,

    中文意思是假如Z與W.Z兩者都是正數,

    如果Z與W.Z兩者都是正數的話,則W必然

    也是正數。但是書本上答案是(5),答案(5)是負數 -9,

    把-9代入W.Z,使W.Z是正數的話,則Z必然是個負數,才能負負得正使W.Z是正數,但是又與原定義Z與W.Z兩者都是正數的原則不符。

    另一方面,如果Z與W.Z兩者都是正數的話,則W必然

    也是正數。但是把答案選項中的 3或 9代入該等式裡,卻都不符,所以答案也不是 3或 9。

    原等式是W.Z=W^3Z(8-W^2)

    把兩邊的WZ消去,得 1=W^2(8-W^2)

    簡化,得 W^4 - 8W^2 +1 =0

    解此等式,W可得一正數值(也可得負數值,還有虛數)。

    2010-11-21 10:16:28 補充:

    McGraw-Hill's GMAT: graduate management admission test By James Hasik, Stacey Rudnick, Ryan Hackney

    page 412, 問題 24

    2010-11-21 10:18:00 補充:

    書本內之解法是把各個答案選項逐一代入等式中,看看哪一個符合。

    2010-11-21 13:29:23 補充:

    Can you read Chinese?

    2010-11-21 13:32:40 補充:

    You may find online the answer and explanation of this question in the book McGraw-Hill's GMAT: graduate management admission test. By James Hasik, Stacey Rudnick, Ryan Hackney

    page 412, No.24

    2010-11-21 13:39:57 補充:

    * And, please tell me what mathematically.

    In mathematics, "W.Z" means "W multiply Z" .

    2010-11-21 14:02:36 補充:

    You are welcome.

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