Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 10 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 10 minute mark.) Answers:
A) 41  B) 42  C) 43  D) 44  E) 45
10 minutes is 600 seconds.   Lamp A and Lamp B will flash together every 24 seconds.   600/24= 
<gadget id="calculator">600/24</gadget>
<output>25</output>
25.   In the time period, Lamp A and Lamp B will flash together 25 times.   Lamp A and Lamp C will flash together every 30 seconds.   600/30= 
<gadget id="calculator">600/30</gadget>
<output>20</output>
20.   In the time period, Lamp A and Lamp C will flash together 20 times.   Lamp B and Lamp C will flash together every 40 seconds.   600/40= 
<gadget id="calculator">600/40</gadget>
<output>15</output>
15.   In the time period, Lamp B and Lamp C will flash together 15 times.   All three lights will flash together every  2*2*2*3*5= 
<gadget id="calculator"> 2*2*2*3*5</gadget>
<output>120</output>
120 seconds.   600/120= 
<gadget id="calculator">600/120</gadget>
<output>5</output>
5.   We have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together.   The number of times that exactly two lights flash together is   25+20+15-15= 
<gadget id="calculator">  25+20+15-15</gadget>
<output>45</output>
45 times.   The answer is 45.
<result>E</result>
Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 10 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 10 minute mark.)