【OG20-P293-451题】Are all of the numbers in a certain list of 15 num_OG16

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【OG20-P293-451题】

Are all of the numbers in a certain list of 15 numbers equal?

(1) The sum of all the numbers in the list is 60.

(2) The sum of any 3 numbers in the list is 12.

A

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
分析A选项
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B

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
分析B选项
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C

BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
分析C选项
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D

EACH statement ALONE is sufficient.
分析D选项
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E

Statements (1) and (2) TOGETHER are NOT sufficient.
分析E选项
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暂无雷哥网文字解析

当前版本由 bella 更新于2015-06-30 10:24:46 感谢由 bella 对此题目的解答所做出的贡献。

（1）15个数之和等于60不能保证15个数相等，可能性很多；
（2）任意3个数字之和等于12，经试验只有当所有的数字都等于4时才能满足条件；
所以选B。

提交

贾思敏

条件一: 15个数之和等于60，不一定是15个数都相等，可能性很多，不充分。条件二: 运用字母表达法将这15个数设为a,b,c,d.... a+b+c=12① a+b+d=12② ①-②得出c-d=0，也就是c=d 同理可得a=b=c=...这15个数都相等，充分错题反思:好有毒，我就是错在第二个条件的分析上

0 0 回复 2021-10-05 00:41:58
purity

OK. Let's name the 15 numbers by letters, a, b, c, d, ... Consider a, b, and c, three arbitrary numbers from the list; we know from (2) that a + b + c= 12 (I) Now consider a, b and d; we know from (2) that a + b + d= 12 (II) From (I) and (II) we have: a + b + c = a+ b + d ---> c=d We can again consider a + b + d, a + b + e , ... and prove that d=e and hence c = d = e In the similar way it can be proved that a = b = c = d = e = f = ...

2 0 回复 2021-02-22 04:45:36
勇敢的狗勾

经试验只有当所有的数字都等于4时才能满足条件？？有谁有更好的方法吗。。。。

2 0 回复 2020-12-13 12:38:42
268265zgqp回复勇敢的狗勾

可以证明：a+b+c=x，b+c+d=x，相减得a=d，以此类推

0 0 回复 2021-06-24 12:58:18