Bunuel wrote:
Cassandra sets her watch to the correct time at noon. At the actual time of 1:00 PM, she notices that her watch reads 12:57 and 36 seconds. Assuming that her watch loses time at a constant rate, what will be the actual time when her watch first reads 10:00 PM?
(A) 10:22 PM and 24 seconds
(B) 10:24 PM
(C) 10:25 PM
(D) 10:27 PM
(E) 10:30 PM
We see that Cassandra’s watch loses 2 minutes and 24 seconds each hour or 144 seconds per hour. So if the correct time is 10 PM, her watch will lose 1440 seconds or 1440/60 = 24 minutes and the time on her watch would read 9:36 PM. Therefore, when her watch reads 10:00 PM (“24 minutes” later), the correct time should be slightly over 10:24 PM. Of the answer choices, we can eliminate A and B. Let’s guess that correct answer should be 10:25 PM, that is, for the correct time to elapse 25 minutes, the time on her watch only elapses 24 minutes. In other words, her watch loses 1 minute for every 25 minutes. Let’s verify that is indeed the case. We know that her watch losses 144 seconds every hour (i.e., every 60 minutes). So we can set up the proportion:
144 sec/60 min = x sec/25 min
60x = 144(25)
60x = 3600
x = 60
We see that her watch indeed losses 60 seconds (i.e., 1 minute) for every 25 minutes. So when her watch reads 10:00 PM, the correct time should be 10:25 PM.
Answer: C
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