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题库 / GMATAdvanced-DS-70
Given a positive number N, when N is rounded by a certain method (for convenience, call it Method Y), the result is 10n if and only if n is an integer and 5×10n-1≤N<5×10n. In a certain gas sample, there are, when rounded by Method Y, 1021molecules of H2 and also 1021 molecules of O2. When rounded by Method Y, what is the combined number of H2 and O2 molecules in the gas sample?
(1)The number of H2 molecules and the number of O2 molecules are each less than 3 X1021.
(2)The number of H2 molecules is more than twice the number of O2 molecules.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
一开始我也没看懂题目，以为是题目错了。后来我想明白了，其实就是能不能把这团气体的近似值限定在5*10^n里。
先把氢分子和氧分子后面的10^21不管，就是看二者气体加起来会不会超过5，例如，条件一说两者都小于3，但是两者之和还是可能会超过5，比如说相加等于5.5，那用Y方法得到的结果是5*10^21<=5.5*10^21<5*10^22，如果相加等于4.5，那用Y 方法得到的就是5*10^20<=4.5*10^21<5*10^21。所以n就可以等于21或者22，这样就不能用Y方法得出准确结果了，
加上条件2的话，氢分子和氧分子之和肯定小于5，这样用Y方法得出的结果一定是n等于21
嗯嗯 简化比较好看一些， 若设氢分子数量为a，氧分子数量为b，题目给出了a和b大小在0.5~5的范围，问a+b还在不在0.5~5的范围？初步可以知道a+b下限至少等于1；条件1可以得出氢分子和氧分子都各自小于3，两者之和小于6（有大于5的部分），即a<3, b<3, a+b＜6；条件2可以得出氢分子＞两倍的氧分子，即a＞2b；两个条件结合起来就是 3b < a+b < 6则易得b<2，结合a<3可以进一步缩小为1≤a+b<5
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