GMAT/留學申請專業顧問 Donz 之資訊交流園地

Is n odd?

(1) n is divisible by 3

(2) 2n is divisible by twice as many positive integers as n

Solution:

    (1) 不足, n = 3k, k could be even or odd, then n could be even or odd

    (2) 牽扯到因數個數的問題
        假設 n = (X^a)(Y^b)(Z^c).........
        n 的因數個數為 (a+1)(b+1)(c+1)..........

        現在探討 2n 所以我們假設 n = (2^a)(Y^b)(Z^c).........
        n 的因數個數為 (a+1)(b+1)(c+1)..........

        2n = (2^(a+1))(Y^b)(Z^c).........
        2n 的因數個數為 (a+2)(b+1)(c+1)..........

        由於兩者因數個數差了兩倍
        2(a+1)(b+1)(c+1)..........
        =(a+2)(b+1)(c+1)..........

        顯然的 a = 0, 也就是 n 沒有 2 這個因數
        n is odd

        Answer (B)