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16 Aug 2012, 08:32
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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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.
(1) The diameter of the larger gear is twice the diameter of smaller gear.
(2) The smaller gear revolves 600 times per minute.
16 Aug 2012, 10:32
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imhimanshu
(1) We can deduce that the smaller gear makes two rotations while the larger gear makes just one rotation. No information about the speed of revolution, so we cannot establish any connection with time.
Not sufficient.
(2) No information about the larger gear.
Not sufficient.
(1) and (2): The larger gear makes 300 rotations per minute and the smaller gear 600 per minute. So, we can calculate how long it takes in minutes each one to do 6,000,000,000 rotations, take the difference and convert to days...really messy. But being a DS question, you shouldn't spend time on working out the final answer.
Choose Answer C, and move on.
PrashantPonde
Joined: 27 Jun 2012
Last visit: 29 Jan 2025
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Concentration: Strategy, Finance
Schools: Haas EWMBA '17
17 Jan 2013, 01:06
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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.
(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.
