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07 Jan 2019, 03:45
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (01:17) correct
29%
(01:12)
wrong
based on 214
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A lighthouse blinks regularly 5 times a minute. A neighboring lighthouse blinks regularly 4 times a minute. If they blink simultaneously, after how many seconds will they blink together again?
A. 20
B. 24
C. 30
D. 60
E. 300
A. 20
B. 24
C. 30
D. 60
E. 300
07 Jan 2019, 04:03
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The LCM of 4 and 5 is 20 . So 20 seconds.
Posted from my mobile device
Posted from my mobile device
Updated on: 08 Jan 2019, 01:15
Originally posted by Archit3110 on 07 Jan 2019, 04:13.
Last edited by Archit3110 on 08 Jan 2019, 01:15, edited 1 time in total.
Last edited by Archit3110 on 08 Jan 2019, 01:15, edited 1 time in total.
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Bunuel
Starting at 0 where they both blink together
for 1st it would be 1 blink every 12 seconds; 60/5
and 2nd 1 blink every 15 seconds; 60/4
so together they would second blink together at 60 seconds ; later at 120,180,240,300
IMO D..
07 Jan 2019, 10:14
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Bunuel
Assume that they both blink at 0 seconds. It turns out that 0 must be the start time.*
The number of seconds after which they blink together again?
Lighthouse #1 blinks 5 times per minute
1 minute = 60 seconds
L #1 blinks: \(\frac{60secs}{5}=12\), i.e., every 12 seconds
Lighthouse #2 blinks 4 times a minute
L #2 blinks: \(\frac{60secs}{4}=\) every 15 seconds
LCM of 12 and 15 is 60
AND there are only 60 seconds in one minute
We have to start at 0 in order to satisfy both conditions (that #1 and #2 blink 5 and 4 times per 1 minute AND that they blink again simultaneously).
The LCM = 60 seconds = 1 minute
= start time 0, end time 60
The next time that #1 and #2 blink together again is after 60 seconds.
Answer D
Write it out
In about 30 seconds this problem can be solved with a little brute force.
List the times at which each light blinks. Find the match.
L #1 blinks every 12 seconds at
12, 24, 36, 48, 60
(Stop there to check. L #2's rate of every 15 seconds has a units digit of 5;
it will hit only numbers that end with 5 or 0)
L #2 blinks every 15 seconds at 15, 30, 45, 60
They blink together again 60 seconds later.
Answer D
**1) #1 and #2 must coincide a second time. Each must blink 5 and 4 times respectively within a minute
2) the LCM of 12 and 15 is 60
3) but there are only 60 seconds in one minute
-- The LCM (when they will strike together again) and
-- the time in seconds in which each must strike a certain number of times
-- are the same.
0 is a multiple of 60.
From second 1 to second 60 of one minute, there is exactly one number at which both lights can blink together again: 60
4) we are stuck.
We must make the first simultaneous blink at 0 in order to "fit in" a multiple of 60 before the clock resets.
