2. 外语
  3. Given a positive number N, when N is rounded by a certain method (for convenience, call it Method Y), the result is 10" if and o

Given a positive number N, when N is rounded by a certain method (for convenience, call it Method Y), the result is 10" if and o

admin2022-10-18  67
问题 Given a positive number N, when N is rounded by a certain method (for convenience, call it Method Y), the result is 10" if and only if n is an integer and 5×10n-1≤N<5x10n. In a certain gas sample, there are, when rounded by Method Y, 1021 molecules of H2 and also 1021 molecules of 02. When rounded by Method Y, what is the combined number of H2 and 02 molecules in the gas sample?
(1) The number of H2 molecules and the number of 02 molecules are each less than 3 x 1021.
(2) The number of H2 molecules is more than twice the number of 02 molecules.
选项 A、Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B、Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C、BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D、EACH statement ALONE is sufficient.
E、Statements (1) and (2) TOGETHER are NOT sufficient.
答案C
解析 Let H be the number of H2 molecules and let O be the number of O2 molecules. We are given that 0.5 ×1021 < H < 5 × 1021 and 0.5 × 1021 < 0 < 5 × 1021. When rounded by Method Y, what is the value of H+ O ?
(1)     If H= 2 × 1021 and O = 2 × 1021, then each of H and O equals 1021 when rounded by Method Y, each of H and O is less than 3 × 1021, and H+ O = 4 × 1021, which equals 1021 when rounded by Method Y. However, if H= 2.6 × 1021 and O = 2.6 × 1021, then each of H and O equals 1021 when rounded by Method Y, each of H and O is less than 3 × 1021, and H+ O = 5.2 × 1021, which equals 1022 when rounded by Method Y; NOT sufficient.
(2)     If H= 2 × 1021 and O= 0.8 × 1021, then each of H and O equals 1027 when rounded by Method Y, H > 2 × O, and H+ O = 2.8 × 1021, which equals 1021 when rounded by Method Y. However, if H= 4.5 × 1021 and O = 2 × 1021, then each of H and O equals 1021 when rounded by Method Y, H > 2 × O, and H+ O = 6.5 × 1021, which equals 1022 when rounded by Method Y; NOT sufficient.
Given (1) and (2), since O > 0.5 × 1021 (given information), it follows from statement (2) that H > 1 × 1021. Also, since H < (statement (1)), it follows from statement (2) that O < 1.5 × 1021.Thus, 1 × 1021 < H < 3 × 1021 and 0.5 × 1021 ≤ O < 1.5 × 1021, and hence 1.5 × 1021 < H+ O < 4.5 × 1021. Therefore, the value of H+ O equals 1021 when rounded by Method Y.
The correct answer is C;
both statements together are sufficient.
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