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今天考试碰到一道诡异输血让人很惊奇。现在有1 2 3 4 5 五个数,随意组合成三个相加,得出的数x能有1 2 3 4 5 表示。 比如: 12+34 +5=51 DS题, 下面什么情况下能保证所加之和x为偶数。 (1)X是3位数 (2)有一个 加号在1 2中间, 如 31+42。。。
For this question, it is important to realize that the one's digit of the three numbers has to be chosen from two setups of (2, 4, 5) and (3, 4, 5) because the one's digit of x has to be chosen from 1-5, more like only 1 or 2. Any if only one setup works under the condition, that condition is sufficient.
1) insufficient. 123 +4 +5=132, 132 +4 +5= 141 2) inufficient. 32 +14 + 5 = 51, 23 + 14 + 5 = 42
1) and 2) together: Since 1 and 2 has to be separated and X is a 3-digit number, then we have to go with the (2,4,5) setup. The reason is that for the (3, 4, 5) setup, 1 and 2 have to be together in order to have x greater than 100. But this is not alowed in condition (2). So we have to go with (2, 4, 5).
One possible example is 2 + 314 + 5 = 321
So 1) and 2) together will give an odd number.
Choose E since none of the conditions can make sure x is an even number. But 1) and 2) can give x an odd number!
But if the question ask you that which condition can tell you whether x is an even number, choose C since you know x will be odd when combining 1) and 2).
That's one of the reasons why I prefer working on original English questions! The Chinese translation might bring in uncertainties. |
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