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31 May 2025, 15:58
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C
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In a gas sample, there are, rounded to the nearest order of magnitude (that is, to the nearest power of 10), approximately \(10^{21}\) molecules of \(H_2\) and also \(10^{21}\) molecules of \(O_2\). What is the combined number of \(H_2\) and \(O_2\) molecules in the gas sample, rounded to the nearest order of magnitude?
(1) The number of \(H_2\) molecules and the number of \(O_2\) molecules are each less than \(3 × 10^{21}\).
(2) The number of \(H_2\) molecules is more than twice the number of \(O_2\) molecules.
(1) The number of \(H_2\) molecules and the number of \(O_2\) molecules are each less than \(3 × 10^{21}\).
(2) The number of \(H_2\) molecules is more than twice the number of \(O_2\) molecules.
102060
31 May 2025, 16:15
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In a gas sample, there are, rounded to the nearest order of magnitude (that is, to the nearest power of 10), approximately \(10^{21}\) molecules of \(H_2\) and also \(10^{21}\) molecules of \(O_2\). What is the combined number of \(H_2\) and \(O_2\) molecules in the gas sample, rounded to the nearest order of magnitude?
Since rounded to the nearest power of 10, the number of \(H_2\) and \(O_2\) is both \(10^{21}\), then:
Summing the above we get:
If \(H_2 + O_2 < 5 * 10^{21}\), then rounded to the nearest power of 10, the combined number of \(H_2\) and \(O_2\) molecules will be \(10^{21}\).
If \(5 * 10^{21} < H_2 + O_2\), then rounded to the nearest power of 10, the combined number of \(H_2\) and \(O_2\) molecules will be \(10^{22}\).
(1) The number of \(H_2\) molecules and the number of \(O_2\) molecules are each less than \(3 × 10^{21}\).
If both are \(6 * 10^{20}\), then \(H_2 + O_2 = 1.2 * 10^{21}\), which rounds to \(10^{21}\).
If both are \(2.75 * 10^{21}\), then \(H_2 + O_2 = 5.5 * 10^{21}\), which rounds to \(10^{22}\).
Not sufficient.
(2) The number of \(H_2\) molecules is more than twice the number of \(O_2\) molecules.
If \(O_2 = 10^{21}\) and \(H_2 = 3 * 10^{21}\), then \(H_2 + O_2 = 4 * 10^{21}\), which rounds to \(10^{21}\).
If \(O_2 = 10^{21}\) and \(H_2 = 4.5 * 10^{21}\), then \(H_2 + O_2 = 5.5 * 10^{21}\), which rounds to \(10^{22}\).
Not sufficient.
(1)+(2) Since from (1) \(H_2 < 3 * 10^{21} \), then from (2) \(O_2 < 1.5 * 10^{21} \). Thus, \(H_2 + O_2 < 4.5 * 10^{21}\), which rounds to \(10^{21}\). Sufficient.
Answer: C.
Since rounded to the nearest power of 10, the number of \(H_2\) and \(O_2\) is both \(10^{21}\), then:
\(5 * 10^{20} < H_2 < 5 * 10^{21}\)
\(5 * 10^{20} < O_2 < 5 * 10^{21}\)
\(5 * 10^{20} < O_2 < 5 * 10^{21}\)
Summing the above we get:
\(10^{21} < H_2 + O_2 < 10^{22}\)
If \(H_2 + O_2 < 5 * 10^{21}\), then rounded to the nearest power of 10, the combined number of \(H_2\) and \(O_2\) molecules will be \(10^{21}\).
If \(5 * 10^{21} < H_2 + O_2\), then rounded to the nearest power of 10, the combined number of \(H_2\) and \(O_2\) molecules will be \(10^{22}\).
(1) The number of \(H_2\) molecules and the number of \(O_2\) molecules are each less than \(3 × 10^{21}\).
If both are \(6 * 10^{20}\), then \(H_2 + O_2 = 1.2 * 10^{21}\), which rounds to \(10^{21}\).
If both are \(2.75 * 10^{21}\), then \(H_2 + O_2 = 5.5 * 10^{21}\), which rounds to \(10^{22}\).
Not sufficient.
(2) The number of \(H_2\) molecules is more than twice the number of \(O_2\) molecules.
If \(O_2 = 10^{21}\) and \(H_2 = 3 * 10^{21}\), then \(H_2 + O_2 = 4 * 10^{21}\), which rounds to \(10^{21}\).
If \(O_2 = 10^{21}\) and \(H_2 = 4.5 * 10^{21}\), then \(H_2 + O_2 = 5.5 * 10^{21}\), which rounds to \(10^{22}\).
Not sufficient.
(1)+(2) Since from (1) \(H_2 < 3 * 10^{21} \), then from (2) \(O_2 < 1.5 * 10^{21} \). Thus, \(H_2 + O_2 < 4.5 * 10^{21}\), which rounds to \(10^{21}\). Sufficient.
Answer: C.
General Discussion
09 Jun 2025, 09:54
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Fairly tricky, but its about whether the coefficients add up and carry over to be more that 5 (round up) or not (round down):
