The given sentences are related to the topic of Mars and its water history. Four sentences can be logically grouped to form a coherent paragraph discussing how water was lost and where it might still exist, while one sentence directly states that ancient water was lost. The sentences can be analyzed as follows:
Sentence 1: Most of the planet's remaining water is now frozen or buried, but clues over the past decade suggested that some liquid water, a presumed necessity for life, might survive in underground aquifers.
Sentence 2: Data from NASA's MAVEN orbiter show that solar storms stripped away most of Mars's once-thick atmosphere.
Sentence 3: Particles from the Sun collided with molecules in the atmosphere, knocking them into space or giving them an electric charge that caused them to be swept away by the solar wind.
Sentence 4: A recent study reveals how Mars lost much of its early water, while another indicates that some liquid water remains.
Sentence 5: The water that made up ancient lakes and perhaps an ocean was lost.
Sentences 1, 2, 3, and 4 collectively describe the mechanisms for water loss and hint at remaining water, suggesting causes and potential reservoirs. Sentence 5 merely states water loss, without connecting it to a detailed explanation or current state. Hence, Sentence 5 is the odd one out.
The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In investigating memory-beliefs, there are certain points which must be borne in mind. In the first place, everything constituting a memory-belief is happening now, not in that past time to which the belief is said to refer. It is not logically necessary to the existence of a memory-belief that the event remembered should have occurred, or even that the past should have existed at all. There is no logical impossibility in the hypothesis that the world sprang into being five minutes ago, exactly as it then was, with a population that "remembered" a wholly unreal past. There is no logically necessary connection between events at different times; therefore nothing that is happening now or will happen in the future can disprove the hypothesis that the world began five minutes ago. Hence the occurrences which are CALLED knowledge of the past are logically independent of the past; they are wholly analysable into present contents, which might, theoretically, be just what they are even if no past had existed.
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: