prep DS2 184, nn help pls

shanefeng · 发表于 2010-1-3 08:15:34

184. 17933-!-item-!-187;#058&011666
If k is an integer greater than 1, is k equal to 2r for some positive integer r ?

(1) k is divisible by 2^6.

(2) k is not divisible by any odd integer greater than 1.

the key is B.

but I think 1 is also sufficient.

since k is divisible by 2^6, k=n 2^6, when n=1, then k=2^6. so r=6 ->sufficiently support that k equal to 2^r for some positive integer r

what's wrong with my process?

大荣 · 发表于 2010-1-3 12:06:09

184. 17933-!-item-!-187;#058&011666
If k is an integer greater than 1, is k equal to 2r for some positive integer r ?

(1) k is divisible by 2^6.

(2) k is not divisible by any odd integer greater than 1.

the key is B.

but I think 1 is also sufficient.

since k is divisible by 2^6, k=n 2^6, when n=1, then k=2^6. so r=6 ->sufficiently support that k equal to 2^r for some positive integer r

what's wrong with my process?

-- by 会员 shanefeng (2010/1/3 8:15:34)

注意问题是“equal to”。你给的解法中，k还有一个因子n，这个n不确定，所以条件1可能满足也可能不满足。

realric · 发表于 2010-1-3 14:24:31

184. 17933-!-item-!-187;#058&011666
If k is an integer greater than 1, is k equal to 2r for some positive integer r ?

(1) k is divisible by 2^6.

(2) k is not divisible by any odd integer greater than 1.

the key is B.

but I think 1 is also sufficient.

since k is divisible by 2^6, k=n 2^6, when n=1, then k=2^6. so r=6 ->sufficiently support that k equal to 2^r for some positive integer r

what's wrong with my process?

-- by 会员 shanefeng (2010/1/3 8:15:34)

注意问题是“equal to”。你给的解法中，k还有一个因子n，这个n不确定，所以条件1可能满足也可能不满足。

-- by 会员大荣 (2010/1/3 12:06:09)

我来补充一点~其实楼主把n取-1就明白了

snail007 · 发表于 2010-1-3 14:38:30

可是不是说了K>1吗

184. 17933-!-item-!-187;#058&011666
If k is an integer greater than 1, is k equal to 2r for some positive integer r ?

(1) k is divisible by 2^6.

(2) k is not divisible by any odd integer greater than 1.

the key is B.

but I think 1 is also sufficient.

since k is divisible by 2^6, k=n 2^6, when n=1, then k=2^6. so r=6 ->sufficiently support that k equal to 2^r for some positive integer r

what's wrong with my process?

-- by 会员 shanefeng (2010/1/3 8:15:34)

注意问题是“equal to”。你给的解法中，k还有一个因子n，这个n不确定，所以条件1可能满足也可能不满足。

-- by 会员大荣 (2010/1/3 12:06:09)

我来补充一点~其实楼主把n取-1就明白了

-- by 会员 realric (2010/1/3 14:24:31)

snail007 · 发表于 2010-1-3 14:50:55

楼主你的问题问错了

184. 17933-!-item-!-187;#058&011666

If k is an integergreater than 1, is k equal to 2^r for some positive integer r ?

(1) k is divisibleby 2⁶.

(2) k is notdivisible by any odd integer greater than 1.

--------------------------------------------------------------------------------------------------------------------------------------------------------【答案】B

【思路】

k=2^r

(1) 2⁶ x n = k, n可以是任何數不限於2的次方。

(2) k 只可被偶數除,所以只有是2的次方的factors.

[另解]
題目應該就是問 K能不能等於2^r ?
(1)的條件k/(2^6)=整數(設X)
所以k=(2^6)X當X等於2的倍數則條件成立
反之不成立因此條件一不充分
(2)的條件 K不能被大於一的任何奇數整除
換句話說 K只能被2的倍數整除也就是說K一定是2的倍數且只有1和2的因數

shanefeng · 发表于 2010-1-3 22:16:18

got it. thanks.

prep DS2 184, nn help pls

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