Solutions

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Question

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 at least 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.

I. The diameter of the larger gear is twice the diameter of smaller gear.

II. The smaller gear revolves 600 times per minute.


 

Option A:

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

Option B:

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Option C:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Option D:

EACH statement ALONE is sufficient to answer the question asked.

Option E:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Difficulty Level

Easy

Solution

Option C is the correct answer.


Option Analysis

Statement I is insufficient: The diameter of the larger gear is twice the diameter of the 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 the relative ratio for diameters, we don’t know what rate at they are revolving per minute.

– If the gears are rotating at extremely high speed, they will wear out soon -> hence the difference in their life (in minutes) will be smaller.

– If the gears are rotating at extremely slow speed, they will last a 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.

Statement II is insufficient: 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)

Together I and II, Sufficient:

As we know smaller gear has 600 RPM and 1/2 the diameter than the 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 longer.

No of days larger gear lasts longer than smaller gear = 6,000,000,000/24∗60∗60minutes∗((1/300)−(1/600))=115.74days.