Bunuel wrote:
Five satellites monitor a certain region during different times, as part of a study. Alpha1 orbits the region every 6 days, Beta1 orbits every 4 days, Gamma1 orbits every 9 days, Delta1 orbits every 12 days and Epsilon1 orbits every 18 days. There are certain readings to be collected about the region from the satellites when all the five monitor the region together. The readings have been collected for a 292 day period. If there has to be a minimum of a dozen readings collected, for how many more days will the satellites have to monitor the region together?
(A) 36 days
(B) 90 days days
(C) 140 days
(D) 204 days
(E) 432 days
So the satellites orbit together every \(36 \) days which is LCM of \(6,4,9,12,18\)
For the past \(292 \) days :
\(292 = 36*8 + 4\)
Above eqn. means that in the last \(292\) days they have come together \(8\) times already and since their last reunion \(4\) days have passed.
For them to come together at least \(12\) times ( dozen ) we need \(4\) more reunions.
For \(4\) more reunions we need \(36*4 = 144\) more days since their last reunion.
But since \(4 \) days have already passed since their last reunion we need \(140\) more days to complete \(12\) reunions-
Ans-C
Hope it's clear.
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