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Comet A is seen near the Earth every 12 years while comet B every 20 years. If both comets were observed in 1979, for how many years do we have to wait to see the two comets together again? (Assume now is 2004)

Again the wording is very bad, are you asking in how many years does it take both of them to appear that is 60 years, however if you want to know, how long from NOW do we have to wait to see the comets reappear together?? is better wording

Hi, the corrent answer is E ie after 35 years. Comet A is seen after 12 years and B after 20 years. So they will be seen together after LCM(12,20) = 60 years. After every 60 years they will be seen together. They were seen together in 1979, so 60 years after 1979 ie 2039. So number of years 2039-2004(2004 is current year) = 35 years.

For people who dont know what LCM stands for it is Least Common Multiple. LCM of two numbers can be found out as below: 12 = 2*2*3 (Find the prime factors) 20 = 2*2*5 (Find the prime factors) LCM(12, 20) = Common * Uncommon = 2*2*3*5 = 60

Comet A is seen near the Earth every 12 years while comet B every 20 years. If both comets were observed in 1979, for how many years do we have to wait to see the two comets together again? (Assume now is 2004)

Comet " B " will appear once in 20 years... 20 * 1 = 20th year 20 * 2 = 40th year 20 * 3 = 60th year

Comet " A " will appear once in 12 years.. 12 * 1 = 12th year 12 * 2 = 24th year 12 * 3 = 36th year 12 * 4 = 48th year 12 * 5 = 60th year

When we compare above table, Both the comet will appear again in 60th year from 1979 = 1979+60 =2039th year current year is 2004 therefore 2039-2004 = 35 years..

Comet A is seen near the Earth every 12 years while comet B every 20 years. If both comets were observed in 1979, for how many years do we have to wait to see the two comets together again? (Assume now is 2004)

* 16 * 20 * 25 * 32 * 35

Again the wording is very bad, are you asking in how many years does it take both of them to appear that is 60 years, however if you want to know, how long from NOW do we have to wait to see the comets reappear together?? is better wording

C. 25

NOPE..

so it takes 60 years..so from 1979--60 years is 2039..so when we see it next will be 2039-2004 or 35 yrs from now..

Hi, the corrent answer is E ie after 35 years. Comet A is seen after 12 years and B after 20 years. So they will be seen together after LCM(12,20) = 60 years. After every 60 years they will be seen together. They were seen together in 1979, so 60 years after 1979 ie 2039. So number of years 2039-2004(2004 is current year) = 35 years.

For people who dont know what LCM stands for it is Least Common Multiple. LCM of two numbers can be found out as below: 12 = 2*2*3 (Find the prime factors) 20 = 2*2*5 (Find the prime factors) LCM(12, 20) = Common * Uncommon = 2*2*3*5 = 60

Send me kudos if you like my post.

Kudos.

This is how I calculated mine although I don't think I would be able to explain it as well as you.

Thanks a lot. +1. We'll edit the wording of this one.

fresinha12 wrote:

Comet A is seen near the Earth every 12 years while comet B every 20 years. If both comets were observed in 1979, for how many years do we have to wait to see the two comets together again? (Assume now is 2004)

* 16 * 20 * 25 * 32 * 35

Again the wording is very bad, are you asking in how many years does it take both of them to appear that is 60 years, however if you want to know, how long from NOW do we have to wait to see the comets reappear together?? is better wording

So... I get that 2039 - 1979 equals 35 but how do you recognize the multiplication of 3 * 2 * 2* 5 to give you the years.

I did separate the 12 and 20 yrs in Greatest Common Factor and Least Common Multiple (4)*(15) but I don´t understand why the multiplication of both will give me the answer of when both comets will see each other again.

LCM of 12 and 20 is 60 hence they would meet in 2029.i.e. 2029-2004 = 35

Why LCM......Lcm can also be explained as occurrence of different digits after some interval so that the result is same.
_________________

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Comet A is seen near the Earth every 12 years while comet B every 20 years. If both comets were observed in 1979, for how many years do we have to wait to see the two comets together again? (Assume now is 2004)

Again the wording is very bad, are you asking in how many years does it take both of them to appear that is 60 years, however if you want to know, how long from NOW do we have to wait to see the comets reappear together?? is better wording

LCM of 12 and 20 is 60. Hence 60 years after 1979 these will be seen again. Now it is 2004. So it is alrady 25 years since 1979. So additional 60-25 = 35 Years will be needed. Hence "E"

Hi, the corrent answer is E ie after 35 years. Comet A is seen after 12 years and B after 20 years. So they will be seen together after LCM(12,20) = 60 years. After every 60 years they will be seen together. They were seen together in 1979, so 60 years after 1979 ie 2039. So number of years 2039-2004(2004 is current year) = 35 years.

For people who dont know what LCM stands for it is Least Common Multiple. LCM of two numbers can be found out as below: 12 = 2*2*3 (Find the prime factors) 20 = 2*2*5 (Find the prime factors) LCM(12, 20) = Common * Uncommon = 2*2*3*5 = 60

Send me kudos if you like my post.

I got E as well. But, it took a while to arrive at the answer.

I know LCM, but didn't know that we can use it for this problem. Can you please explain any other problem scnerios where LCM can used to solve a problem.

Waiting for the day when I will be able to approach and solve maths the way you guys do it! truly commendable!

Both comets have different frequencies i.e. 12 yrs and 20 yrs. If B covers 20 yrs A will be covering 12 yrs At the end of B's 20 yrs , A's 24 yrs .... ....... in 60 yrs they will be visible together !!!

OR

LCM 12, 20 = 60 MEANS that both are visible together at every 60 years. In 1979 both appeared together, so 60 yrs after again they will be visible together, i.e in 2039. Now it is 2004 so in another 35 years it will be seen together again.

(E) Wins
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" Make more efforts " Press Kudos if you liked my post

Comet A is seen every 12 years and Comet B is seen every 20 years. So minimum after 60 years (smallest number to be divisible by both 12 and 20) both comets will be seen together.

Last observed together in 1979. So will be observed together again in 1979+60 = 2039 As current year is given as 2004, we have to wait 2039-2004=35 years more to see both comets together again.