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15 Aug 2019, 01:40
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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:
35%
(medium)
Question Stats:
62% (01:21) correct
38%
(01:16)
wrong
based on 61
sessions
History
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In each of two rows, a series of statues is ordered by height. On the bottom row, the shortest statue is 14.1 centimeters tall. On the top row, the tallest statue is 14.01 centimeters tall. What is the median height of all the statues in both rows?
(1) There are 14 statues in the lower row.
(2) There are 15 statues in the upper row.
(1) There are 14 statues in the lower row.
(2) There are 15 statues in the upper row.
19 Aug 2019, 04:29
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Bunuel
Given: In each of two rows, a series of statues is ordered by height. On the bottom row, the shortest statue is 14.1 centimeters tall. On the top row, the tallest statue is 14.01 centimeters tall.
Asked: What is the median height of all the statues in both rows?
(1) There are 14 statues in the lower row.
Since number of statues in upper row is unknown
NOT SUFFICIENT
(2) There are 15 statues in the upper row.
Since number of statues in lower row is unknown
NOT SUFFICIENT
Combining (1) & (2)
(1) There are 14 statues in the lower row.
(2) There are 15 statues in the upper row.
Total number of statues in both rows = 29
Median height of all statues = 15th term = 14.1 cm
SUFFICIENT
IMO C
17 Sep 2019, 03:38
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Bunuel
Official Explanation
This question is confusing because we have different heights: statues of various heights, and we have an upper shelf and a lower shelf, but they are not necessarily related in the way that we expect. The key is to focus on the word "median" and work backwards from what we know about that concept. To determine the median of a set, we can order it, put it in a line, and see what's in the middle. That gives us this:
... ... ... ... 14.01) (14.1 ... ... ... ... ...
Where the parentheses delineate the statues on one shelf and those on the other. We have some useful information, it turns out. For example, if the set on the left had a grand total of two statues and the one on the right had a grand total of three statues, we would know that the median is 14.1 Let's move to the data statements, separately first.
Statement (1) gives useful information, but not enough. In one case, there could be a similar number of statues on the other row, putting the median near the middle of our diagram. Or, in another case, there could be just a couple statues in the other part, pushing the median away from the middle of our diagram. Insufficient.
Statement (2) is insufficient for identical reasons.
Combined, we know that the median is 14.01, so the statements are sufficient together.
The correct answer is (C).
