Since a speedometer measures speed, we're looking for an answer choice in which the first word measures what the second word represents. While "binoculars are to sight" might seem like a good answer, because binoculars are a device that enhance your sight, it doesn't represent the "measuring device is to measured quantity" relationship that we're looking for.  "Odometer is to distance," however, does represent that relationship, as an odometer measures distance, so "odometer is to distance" is the right answer.

The best choice is "odometer is to distance." The relationship between "clock" and "time" is that a clock measures time. Likewise, an odometer is a device in a car which measures distance traveled. Considering the other options, "length is to ruler" is the only other choice with the correct relationship, but it is not in the right order as it is worded what is being measured to measuring device instead of measuring device to what is being measured as it is in the question. "Meter is to yard" is incorrect because a meter and a yard are both two different units that measure length. "Degree is to temperature" is incorrect because a degree is a unit of measurement for temperature (not a device that measures temperature) and temperature is the thing being measured. "Volume is to gram" cannot be correct as volume is what is being measured while a gram is a unit of measurement (albeit the incorrect one for volume).

A grotto is a small cave, often an artificial one and a cavern is a large cave or part of a cave, so the comparison between the two terms is one of size. We thus need to pick out an answer choice that represents something that could be thought of as a very large ditch. Since a gorge is a narrow valley with a stream at the bottom, "canyon," which means a deep gorge, is the best answer, because just like a cavern can be thought of as a very large grotto, a canyon can be thought of as a large gorge.

A “metropolis” is defined as a large city, while a “village” is a small settlement in the countryside. A metropolis is a large-scale version of a village, and we need to pick out an answer choice that describes something of which the larger-scale version would be an ocean. While “puddle” and “storm” might each look like a potentially correct answer because like an ocean, they both involve water, a larger-scale storm would not be an ocean, so “storm” cannot be the correct answer. One could think of a large-scale puddle as an ocean however, as both are bodies of water, so “puddle” is the correct answer.

A semicolon is "half" of a colon, and a hemisphere is half of a sphere. 

A rivulet is a small river, so to solve this analogy you have to determine which of the answer choices is a larger version of a hamlet. A hamlet is a small town so the correct answer is “town.”

A pittance is a very small amount of money, so to solve this analogy you have to determine what a tidbit is a small amount of. A tidbit is used to describe a small piece of gossip or information.

The diameter of a circle is twice the size of the radius. A quadrant refers to a one-fourth section of something, so twice one-fourth is a half. 

A "stopwatch" is the device that is used to measure the time that is taken for a given event. For example, a coach or physical education instructor will use a stopwatch to clock the time taken to run a race. Thus, the analogy could be represented as, “Just as a stopwatch measures time, so a yardstick measures X.” Note that the options “yards” and “inches” are not as appropriate as “distance.” If the first half of the analogy had used (e.g.) “seconds” instead of “time,” those other options would be more acceptable. However, as things stand, the analogy indicates the general type of measure done by the device (time and distance respectively).

"Luminosity" is how bright something is, a measure of "brightness." So, to solve this analogy you need to determine what it is that "viscosity" measures. Well, "viscosity" is a measure of how thick something is, a measure of "thickness."