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# A lighthouse blinks regularly 5 times a minute. A neighboring lighthou

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A lighthouse blinks regularly 5 times a minute. A neighboring lighthou  [#permalink]

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07 Jan 2019, 03:45
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Difficulty:

35% (medium)

Question Stats:

48% (01:02) correct 52% (01:33) wrong based on 46 sessions

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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

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Re: A lighthouse blinks regularly 5 times a minute. A neighboring lighthou  [#permalink]

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07 Jan 2019, 04:03
The LCM of 4 and 5 is 20 . So 20 seconds.

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A lighthouse blinks regularly 5 times a minute. A neighboring lighthou  [#permalink]

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Updated on: 08 Jan 2019, 01:15
1
Bunuel wrote:
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

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..
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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.
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A lighthouse blinks regularly 5 times a minute. A neighboring lighthou  [#permalink]

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07 Jan 2019, 10:14
Bunuel wrote:
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

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.

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.

**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.

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Re: A lighthouse blinks regularly 5 times a minute. A neighboring lighthou  [#permalink]

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07 Jan 2019, 10:17
generis wrote:
Bunuel wrote:
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

Assume that they both blink at 0 seconds. The number of seconds after which they blink together again will be the same because the rates are fixed after the first blink.

Lighthouse #1 blinks 5 times per minute
1 minute = 60 seconds
$$\frac{60}{5}=12$$: every 12 seconds

Lighthouse #2 blinks 4 times a minute: $$\frac{60secs}{4}=$$ every 15 seconds

LCM of 12 and 15 is 60.

The next time #1 and #2 blink together again is after 60 seconds.

Write it out
In about 30 seconds this problem can be solved with a little brute force.

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.

generis
I agree that the two lights blink together at 60 seconds; but the question is asking if they blink simultaneously, after how many seconds will they blink together again?

it would be a multiple of 60 which I think would be 300.. from the given set of options..
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A lighthouse blinks regularly 5 times a minute. A neighboring lighthou  [#permalink]

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07 Jan 2019, 21:37
Archit3110 wrote:
generis wrote:
Bunuel wrote:
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

Assume that they both blink at 0 seconds. The number of seconds after which they blink together again will be the same because the rates are fixed after the first blink.

Lighthouse #1 blinks 5 times per minute
1 minute = 60 seconds
$$\frac{60}{5}=12$$: every 12 seconds

Lighthouse #2 blinks 4 times a minute: $$\frac{60secs}{4}=$$ every 15 seconds

LCM of 12 and 15 is 60.

The next time #1 and #2 blink together again is after 60 seconds.

generis
I agree that the two lights blink together at 60 seconds; but the question is asking if they blink simultaneously, after how many seconds will they blink together again?

it would be a multiple of 60 which I think would be 300.. from the given set of options..

Archit3110 , I should have said that the 60-second interval in which the lights must blink is the same as the LCM of 12 and 15. We are stuck. They must first strike together at 0 in order to "hit" together on a multiple of 60.

5 cycles (300 seconds) is random. Suppose #1 and 2 strike first at 12.
#1:
12, 24, 36, 48, 60 (cycle 1)
12, 24, 36, 48, 60 (cycle 2 ..)
12, 24, 36, 48, 60 (cycle 5)

#2
12, 27, 42, 57 (cycle 1)
12, 27, 42, 57 (cycle 2)
12, 27, 42, 57 (cycle 5)
They never meet. They will meet if we mark off the start time at 0 (a multiple of 60). The second simultaneous blink at 60. I'll amend.
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A lighthouse blinks regularly 5 times a minute. A neighboring lighthou   [#permalink] 07 Jan 2019, 21:37
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