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14 Oct 2021, 05:58
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
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78% (01:27) correct
22%
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wrong
based on 118
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Team A and Team B will combine into a new team called Team C. If Team A and Team B do not have any common members, does Team A have larger membership than Team B?
1. The average (arithmetic mean) height of the members of Team A is 68.3 inches and the average height of Team B is 71.4 inches.
2. The average (arithmetic mean) height of the members of Team C is 69.4 inches.
1. The average (arithmetic mean) height of the members of Team A is 68.3 inches and the average height of Team B is 71.4 inches.
2. The average (arithmetic mean) height of the members of Team C is 69.4 inches.
14 Oct 2021, 14:57
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Raisakatyal
We know from the question stem that Team C is going to contain all the members of Team A and Team B, and (conveniently) we know that there's no overlap between the two teams A and B, saving us from any complications regarding overlapping sets. All we really need to know to be able to answer the question is the relative sizes of the two individual teams.
Statement (1) gives us the average heights of the two teams individually. This sort of setup suggests that a weighted-average issue may be on the way, but as of now, we're given nothing to relate those two average heights to one another. It's easy to imagine a scenario in which Team A has 100 people and Team B has 10 people, and it's just as easy to imagine the reverse scenario (in which Team A has 10 people and Team B has a hundred people)--the individual averages don't do anything to constrain the numbers on each team. Therefore, statement (1) is insufficient, and answers (A) and (D) should be eliminated.
Statement (2) gives us the average height of Team C. If you were expecting a weighted-average setup after reading statement (1), this seems like the fulfillment of that expectation. However, it's important to explicitly remind yourself at this juncture that the information provided in statement (1) is currently not in play, meaning that we have no notion at the moment of the average heights of Teams A and B individually. As such, you can envision a scenario in which perhaps the average height of Team A and the average height of Team B are each 69.4 inches; in this case, there'd be absolutely no way to tell how many members each team had relative to one another, as the average height of Team C would be 69.4 inches no matter what. Eliminate answer (B).
Now that we're down to answers (C) and (E), we must combine the two statements and see where we stand. Here's where things get interesting. If we know that the average height of Team A is 68.3 inches and the average height of Team B is 71.4 inches, then we also know that the average height of Team C is somewhere between those two heights (overall averages are always somewhere between their individual components). Moreover, knowing where the overall average (Team C's average) falls with respect to those two individual averages tells us a lot about the composition of the team. If Team A and Team B were the same size, for instance, the average height of Team C would be exactly in the middle of the two individual averages (that is, it would be 69.85 inches, the exact average of 68.3 and 71.4). The fact that the actual average height of Team C is smaller than 69.85 inches and is thus closer to the average height of Team A tells us that rather than being equally balanced between members of Team A and Team B, Team C must have more members from Team A than from Team B. Thus, the answer to the original question is a definitive yes, the two statements together are sufficient, and the answer is (C).
09 Aug 2025, 12:37
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