求PREP-DS-2-122 解

jesuisdesole

122.
                12685-!-item-!-187;#058&009461

If n is a positive integer and r is the remainder when (n - 1)(n + 1) is divided by 24, what is the value of r ?

 

(1)  2 is not a factor of n.

 

(2)  3 is not a factor of n.

答案:C

求思路,谢谢

bellamama

这个题我之前做过，用的是举例法。

题目就是说(n - 1)(n + 1)=24A+r (A是整数）
 
不能被2和3整除最小可能就是5了，然后(n - 1)(n + 1)就等于24 , R=0  
然后试了7，算出来R还是等于0 ,(n - 1)和(n + 1)一定一个能被4整除一个能被6整除,那么它们相乘肯定能被24整除,所以余数就是0,则r=0.

嗬嗬，别的方法不会了，我就是用这个方法做的，仅供参考。。。。

xinxian

Neither statement alone is sufficient. With statement 1, (n - 1)(n + 1) can, for example, be 8 or 24, which yield two different remainders when divided by 24. With statement 2, (n - 1)(n + 1) can, for example, be 3 or 15, which yield two different remainders when divided by 24.

Considering the two statements together...

Statement 1 tells us that n is not even; therefore (n - 1) and (n + 1) are both even. And furthermore, because (n - 1) and (n + 1) are two consecutive even numbers, one of them is a multiple of 4. Therefore (n - 1)(n + 1) will be a multiple of 8.

Statement 2 tells us that n is not a multiple of 3; therefore either (n - 1) or (n + 1) must be a multiple of 3. Therefore (n - 1)(n + 1) will be a multiple of 3.

The two statements together, then, tell us that (n - 1)(n + 1) is a multiple of 8*3 = 24. So the remainder when divided by 24 will always be 0. Sufficient. The correct response is C.

jesuisdesole

以下是引用xinxian在2008-8-17 2:32:00的发言：
Neither statement alone is sufficient. With statement 1, (n - 1)(n + 1) can, for example, be 8 or 24, which yield two different remainders when divided by 24. With statement 2, (n - 1)(n + 1) can, for example, be 3 or 15, which yield two different remainders when divided by 24.

Considering the two statements together...

Statement 1 tells us that n is not even; therefore (n - 1) and (n + 1) are both even. And furthermore, because (n - 1) and (n + 1) are two consecutive even numbers, one of them is a multiple of 4. Therefore (n - 1)(n + 1) will be a multiple of 8.

Statement 2 tells us that n is not a multiple of 3; therefore either (n - 1) or (n + 1) must be a multiple of 3. Therefore (n - 1)(n + 1) will be a multiple of 3.

The two statements together, then, tell us that (n - 1)(n + 1) is a multiple of 8*3 = 24. So the remainder when divided by 24 will always be 0. Sufficient. The correct response is C.

....超COOL~~~

小女子谢过先!!!