Lamp A flashes every 6 seconds, lamp B flashes every 8 seconds, lamp

Question

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 2 minutes after that how many times will exactly two lamps flash?

A) 5

B) 6

C) 9

D) 12

E) 15

I've found different answer than an official one. What do you think, guys? What would be your answer?

A) 5

B) 6

C) 9

D) 12

E) 15

I've found different answer than an official one. What do you think, guys? What would be your answer?

KarishmaB · Accepted Answer

You can easily enumerate this since 120 secs is a small time frame.

Exactly two lamps can flash in three ways:

Lamps A and B but not C: LCM of 6 and 8 is 24. It shouldn't be divisible by 10
 24, 48, 72, 96 , 120 (ignore - divisible by 10)

Lamps B and C but not A: LCM of 8 and 10 is 40. It shouldn't be divisible by 6
 40, 80 , 120 (ignore - divisible by 6)

Lamps A and C but not B: LCM of 6 and 10 is 30. It shouldn't be divisible by 8
 30, 60, 90 , 120 (ignore - divisible by 8)

There are total 9 cases.

Answer (C)

Psiva00734 · Answer

lamp A flashes every 6 secs,
b flashes every 8 secs,
c flashes every 10 secs.
At certain time three flashes simultaneously.
after that calculate when the three lamps flashes simultaneously in 2 minutes.

take a L.C.M of three 6,8,10 sec then it is 120 secs.

so exactly after 2 minutes it flashes simultaneoulsy.

question stem asks exactly two lamps falshes .

take lcm of a and b .6 and 8 is 24 secs. so two lamp flashes 5times in 2minutes.

lcm of b and c . 8 and 10 secs is 40 secs. so both flashes 3times in 2minutes.
lcm of c and a ,6 and 10 secs is 30 secs . pair flashes 4times..

all three pairs flashes simultaenoulsy at 2 minutes. we have to minus one from all three pairs.

then 12-3=9.
so option C is correct.

EMPOWERgmatRichC · Answer

Hi TeymurHajiyev,

Since you mentioned coming across at least one DIFFERENT answer, what was THAT answer? Did it include an explanation?

GMAT assassins aren't born, they're made,
Rich

chetan2u · Answer

Hi,
since 120 secs is too small a time, one can work out each time two lights are on...
lets see the way/procedure incase the time frame is much more..

we will solve this Q by that procedure..
we have three different time at which the bulbs are on.. 6,8,10..
 the solution is based on LCM concept..

1) we will get the entire time in same units, that is minutes..

2) take LCM of all three, this along with its multiples till the total time, will be the time all three will be on simulatenously..

to find how many times all three are on simultaneously, divide the TOTAL TIME by LCM, the INTEGER value will give us the number, say A..

3) Next would be to take LCM of each pair of time and divide total time by each of these three LCMs. Again the integer value will give us the time two blink together..

4) Since we are asked exactly 2 of them blink together, we subtract A, all three blinking together, from each of the three answers we get from (3) above.

5) Add all three new values and we have the answer....
 
lets use this in this Q..

1) total time=120 secs..
2) LCM of 6,8,10=120.. times=120/120=1... so all three will switch on together only once , A=1..
3) three pairs..
 6,8.. LCM=24...times=120/24=5
6,10.. LCM=30..times=120/30=4
8,10.. LCM=40..times=120/40=3 
4) three sets of two blinking together
 5-1=4
4-1=3
3-1=2 
5) total times= 4+3+2=9

TeymurHajiyev · Answer

Thank you guys: Psiva00734, VeritasPrepKarishma and chetan2u, now it's much clearer for me.

Dear Rich, I had answer 5, which was based on wrong LCM of 20, 15 and 12 (60 times). I messed up with "seconds" and "times", but now I feel better ;-)

minustark · Answer

This 3 lamps will flash simultaneously flash every 2 minutes. Lamp A and B will flash together at every 24 seconds, Lamp B and C will flash together at every 40 seconds, and Lamp A and C will do at every 30 seconds. So, total number of times during the period of 2 minutes when 2 lamps will flash together is (120/24) + (120/30)+(120/40) - 3 (at 120 second 3 lamps will flash simultaneously, as this is counted in each of the 3 cases, we have to deduct it) = 5 + 4 +3 - 3= 9.

CAMANISHPARMAR · Answer

What is the source of this question? It does not seem like a GMAT official question.

ScottTargetTestPrep · Answer

Since the LCM of 6, 8, and 10 is 120, the lamps will flash at the same time every 120 seconds, or every 2 minutes. Furthermore, the LCM of 6 and 8 is 24, that of 8 and 10 is 40, and that of 6 and 10 is 30. Therefore, lamps A and B will flash every 24 seconds, B and C every 40 seconds, and A and C every 30 seconds.

In the 120-second, or 2-minute, period, A and B will flash 5 times, at 24, 48, 72, 96, and 120 seconds; B and C will flash 3 times, at 40, 80, and 120 seconds; and A and C will flash 4 times, at 30, 60, 90, and 120 seconds.

Thus, in the 2-minute period, two lamps will flash 5 + 3 + 4 = 12 times, but we cannot count the flashing of all three lights at 120 seconds, as this does not satisfy the event “EXACTLY TWO lamps flash.” Since this event was counted 3 times, our final answer must be 12 - 3 = 9.

Answer: C

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Lamp A flashes every 6 seconds, lamp B flashes every 8 seconds, lamp

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Lamp A flashes every 6 seconds, lamp B flashes every 8 seconds, lamp

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