Question 15. In my office, there are two clocks. One clock gains one minute every hour, and the other loses two minutes every hour. Yesterday, I set them both to the correct time, but when I looked at them today, I saw that the time shown on one was 11 a.m. and shown on the other was 12 noon. What time was it when I set the two clocks? We can start off by looking at option A, 11 p.m. We know that after one hour passes, one clock will display 12.01 a.m., and the other clock will display 11.58 p.m. After another hour passes, one of the clocks will display 1.02 a.m., and the other clock will display 12.56 a.m. Since we know that every time one clock gains one minute every hour and the other loses two minutes every hour, this will continue on like so. Once we get to 11 a.m., we see that one of the clocks says 11.11 a.m., and the other clock says 10.36 a.m. So the option A is incorrect. We can cross it out. Next, we can look at the next option, 7.40 p.m. Again, after one hour passes, one clock would say 8.41 p.m., and the other would say 8.38 p.m. If we keep adding like so, once we get to 11.44 p.m., it is safe to cross this option out, since after 12 more hours, the clocks would not line up correctly. Next, we can look at option C, 3.40 p.m., doing the same thing as previously, adding one hour. Once we get to 3.51 a.m. and 3.16 a.m., we need a little bit more space. So let's start counting up this time. 4.52 a.m. and 4.14 a.m. Add another hour, after another hour, after another hour, and then we are at 10.59 a.m. and 10.02 a.m. One more hour, and we are at 12 p.m. and 11 a.m. So we get our correct answer, which will be C, 3.40 p.m.

clocks

time discrepancy

gain and lose

correct time

3:40 p.m.