There are five bells which start ringing together at intervals of 3, 6

Question

There are five bells which start ringing together at intervals of 3, 6, 9, 12 and 15 seconds respectively. In 36 minutes, how many times will the bells ring simultaneously?

(A) 13 
(B) 12
(C) 6 
(D) 5
(E) 4

sj296 · Answer

LCM of 3,6,9,12,18=180 Sec

So Bell Rings =(36x60/180) +1 =13

OA should be A

MathRevolution · Answer

LCM ( 3, 6, 9, 12, 15) = 180 seconds (3 mins)

In 36 minutes =  \frac{36}{3} = 12 + 1 =  13 times

Answer A

IanStewart · Answer

I agree with the method in the solutions above until the last step, but there's no logical justification for adding 1 at the end. The answer should be 12, not 13. For one thing, the question doesn't even tell us when the 36-minute time interval begins, and if it begins, say, one minute after all five bells chime together, the answer is clearly 12 and not 13.

But even if the bells all chime together at the exact beginning of the 36-minute interval, it still does not make sense to add 1 -- that is, it doesn't make sense to count the chimes both at the exact beginning and at the exact ending of the interval. It's easier to see why with a simpler example: say my alarm beeps once a minute. How many times does it beep in the first minute, if it beeps at the very beginning of that minute? If we think the answer to that question is 2, then surely the answer to the question "how many times does my alarm beep in the second minute?" is also 2. But those two one-minute intervals don't overlap; if the alarm beeps 2 times in the first minute and 2 in the second minute, it must beep 4 times in the first two minutes. But it clearly doesn't, no matter how you count things, so we've done something wrong: it can't be correct that it beeps 2 times in the first minute.

The same principle applies in this question, and the only reasonable answer is 12, but the GMAT would never present such a logically ambiguous situation.

kingcrimson282 · Answer

Hello!

I got all the steps right, but could you kindly explain the +1 at the end?

Thank you

There are five bells which start ringing together at intervals of 3, 6

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