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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
admin
2022-10-18
22
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 5×10
n-1
≤N<5x10
n
. In a certain gas sample, there are, when rounded by Method Y, 10
21
molecules of H
2
and also 10
21
molecules of 0
2
. When rounded by Method Y, what is the combined number of H
2
and 0
2
molecules in the gas sample?
(1) The number of H
2
molecules and the number of 0
2
molecules are each less than 3 x 10
21
.
(2) The number of H
2
molecules is more than twice the number of 0
2
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 H
2
molecules and let O be the number of O
2
molecules. We are given that 0.5 ×10
21
< H < 5 × 10
21
and 0.5 × 10
21
< 0 < 5 × 10
21
. When rounded by Method Y, what is the value of H+ O ?
(1) If H= 2 × 10
21
and O = 2 × 10
21
, then each of H and O equals 10
21
when rounded by Method Y, each of H and O is less than 3 × 10
21
, and H+ O = 4 × 10
21
, which equals 10
21
when rounded by Method Y. However, if H= 2.6 × 10
21
and O = 2.6 × 10
21
, then each of H and O equals 10
21
when rounded by Method Y, each of H and O is less than 3 × 10
21
, and H+ O = 5.2 × 10
21
, which equals 10
22
when rounded by Method Y; NOT sufficient.
(2) If H= 2 × 10
21
and O= 0.8 × 10
21
, then each of H and O equals 10
27
when rounded by Method Y, H > 2 × O, and H+ O = 2.8 × 10
21
, which equals 10
21
when rounded by Method Y. However, if H= 4.5 × 10
21
and O = 2 × 10
21
, then each of H and O equals 10
21
when rounded by Method Y, H > 2 × O, and H+ O = 6.5 × 10
21
, which equals 10
22
when rounded by Method Y; NOT sufficient.
Given (1) and (2), since O > 0.5 × 10
21
(given information), it follows from statement (2) that H > 1 × 10
21
. Also, since H < (statement (1)), it follows from statement (2) that O < 1.5 × 10
21
.Thus, 1 × 10
21
< H < 3 × 10
21
and 0.5 × 10
21
≤ O < 1.5 × 10
21
, and hence 1.5 × 10
21
< H+ O < 4.5 × 10
21
. Therefore, the value of H+ O equals 10
21
when rounded by Method Y.
The correct answer is C;
both statements together are sufficient.
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本试题收录于:
GMAT QUANTITATIVE题库GMAT分类
0
GMAT QUANTITATIVE
GMAT
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