In a particular machine, there are 2 gears that interlock; One gear is larger in circumference than the other. The manufacturer of the gears guarantees that each gear will last for atleast 6,000,000,000 revolutions. Assuming that there is no slippage between the 2 gears and that when one gear rotates the other gear also rotates, the larger gear is guaranteed to last how many days longer than the smaller gear.

(1) The diameter of the larger gear is twice the diameter of smaller gear.
(2) The smaller gear revolves 600 times per minute.

Please put your reasoning across and then I will ask my doubt. I want to see if I am assuming much in this question.

Thanks
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Eva above is pretty much spot-on. Note that the larger gear having a diameter twice as long as the smaller gear's means that the larger will turn once for every 4 times the smaller does, but the logical process remains sound. Do also note that as Eva mentioned, you should not bother working out the "complete" answer to the question; once you figure out that you need both the ratio of circumferences (or diameters/radii) and the turn speed of one gear, you can answer the question.
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+1 C

Beautiful question. When the small gear rotates one time, the big gear rotates 1/2 its diameter. Therefore, the big gear rotates 300 times in 1 minute.
With that information, we can calculate the time for both gears when they make 6 x 10^9 times.
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the larger gear is guaranteed to last how many days longer than the smaller gear.

The question is about the guaranteed number of days and not about possible scenarios.
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Each gear has life to 6,000,000,000 revolutions. As both gears are interlocked, smaller gear will have more revolutions and will wear out before the larger one.

(1) The diameter of the larger gear is twice the diameter of smaller gear.
INSUFFICIENT: This means - the circumference of the larger gear is twice that of smaller gear. I.e. 1 revolution of larger gear = smaller gear rotates two times.
Even if we know relative ratio for diameters, we don’t know what rate at they are revolving per minute.
- If the gears are rotating at extreme high speed, they will wear out soon -> hence difference of their life (in minutes) will be smaller.
- If the gears are rotating at extreme slow speed, they will last lot longer -> hence difference of their life (in minutes) will be much larger.
Hence we cannot conclude how many days the gears will last long.

(2) The smaller gear revolves 600 times per minute.
INSUFFICIENT: This information is clearly insufficient. This tells the revolution rate only for smaller gear. No info about larger gear (speed or relative diameter ratio)

Combining (1) & (2)
SUFFICIENT: As we know smaller gear has 600 RPM and 1/2 the diameter than larger one -> the larger gear rotate at half the speed i.e. 300 RPM and hence we can find out how many days they can last long.

We can stop at this point (no need to calculate further during actual exam) but just for sake of curiosity lets calculate further:
No of days larger gear lasts longer than smaller gear = \frac{6,000,000,000}{24*60*60 minutes} * (\frac{1}{300}-\frac{1}{600}) = 115.74 days.

Hence choice(C) is the answer.
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