Is this a Work Rate or LCM question?

GRE Quant Problem Solving
1

Marie has two electronic beepers: one beeps 5 times in every 90 seconds and the other one beeps 6 times in every 96 seconds. If both the beepers are started simultaneously, how many times will they beep together in next 3 hours 35 mins and 16 seconds?

Could someone solve the above problem and explain why my approach is wrong? The correct answer is 89.

My Approach:

I treated this as a work rate problem because I saw that the rates for the 2 beepers were given.

work = rate * time

Since the beepers are working simultaneously, I counted the final rate as = rate of beeper 1 + rate of beeper 2.

so rate = 5/90 + 6/96 = 110/864 beeps per second

now time would be = (3 * 60 * 60)+(35 * 60)=16 = 12916 seconds

so work = (110 * 12916)/864 = 1644 beeps

My answer is obviously wrong but is it because it is incorrect to look at this problem as a work rate question because the beepers aren’t “working together”? I saw another answer somewhere online regarding LCM but I don’t understand how do we know that we need to find LCM.

2

Hey,

I guess the keyword in the question is “together,” which should trigger you to use LCM.
Here’s the solution:

5\frac{beep}{90\ sec} = \frac{5}{90}\frac{beep}{sec}

So the first beeper takes \frac{90}{5}=18 seconds to beep.
Similarly, the second beeper takes \frac{96}{6} = 16 seconds to beep.

LCM(18, 16) = 144

So these two beepers beep simultaneously every 144 seconds.
3 hours 35 minutes and 16 seconds is equal to 12916 seconds.

\frac{12916}{144} = 89.69444\dots

Now the question is, do they beep at the moment we start them? If so, we will have 1+89 simultaneous beeps. Otherwise, 89.

1 Like
3

Thank you for the reply! This might be a stupid question but why is the work rate approach wrong? I’m trying to understand what I misunderstood/did wrong so I can work on it.

4

I suppose that the work rate approach would be useful when we’re looking at some kind of work being done collectively by multiple agents. But in this case, there’s no “work” per se, just two beepers working independently, and the fact that beeper B starts simultaneously with beeper A, doesn’t affect beeper A’s speed or progress, or vice versa.

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5

Thank you for your explanation! :slight_smile: