请教一道prep2的题目关于集合的中值

eeyore0827 · 发表于 2011-4-1 12:19:01

Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T ?

(1) The median of the numbers in set S is 0.

(2) The sum of the numbers in set S is equal to the sum of the numbers in set T.

答案是C，为什么2单独不成立呢？求点拨啊求点拨

sdcar2010 · 发表于 2011-4-1 12:32:06

Example 1:
-2, -1, 0, 1, 2
-3, -2, -1, 0, 1, 2, 3

Example 2:
5, 6, 7, 8, 9
2, 3, 4, 5, 6, 7, 8

eeyore0827 · 发表于 2011-4-1 12:42:04

thank u sdcar2010!!!! 我怎么就没想出反例呢

sdcar2010 · 发表于 2011-4-1 12:47:51

For set S, the sum = (s1+s1+4)*5/2

For set T, the sum = (t1+t1+6)*7/2

We want to have s1+2 = t1+3 or (1) s1 = t1 + 1

Condition 2: If (s1+s1+4)*5/2 = (t1+t1+6)*7/2, then 5*s1 + 10 = 7*t1 + 21 or (2) 5*s1 = 7*t1 + 11 Thus there will be many pairs of s1 and t1 which statisfy condition (2). But can any of the pairs satisfies equation (1)? Well, now you have two equations with two unknowns, great!
The answers are: t1 = -3; and s1 = -2. That's the only solution!

eeyore0827 · 发表于 2011-4-1 13:00:35

好清晰的思路！懂了~~

请教一道prep2的题目关于集合的中值

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