CSET: Math Question: A record player rotates at a constant, unchanging speed....

[adp5025]

Hello, I'm a bit confused on the following math question:

A record player rotates at a constant, unchanging speed. With a given record size, a point on the record’s outer edge revolves at a speed of 3 miles per hour. What change to the record’s dimensions would cause a point on the record’s outer edge to revolve at a speed of 1.5 miles per hour?

A. The record’s area is doubled.

B. The record’s area is halved.

C. The record’s circumference is doubled.

[FONT=arial, sans-serif]D. The record’s circumference is halved.[/FONT]

[FONT=arial, sans-serif]I know if we halve the circumference or area we would would have less linear distance with a circle but, in this question, how would you quickly determine what the correct answer is. I tried using C as 3.5miles (2xPixr) and keeping the rotation 1 round per hour. The correct answer is D. Can someone explain this to me a logical way without doing calculations? The question is based on logic. [/FONT]

 

[stapel]

A record player rotates at a constant, unchanging speed. With a given record size, a point on the record’s outer edge revolves at a speed of 3 miles per hour. What change to the record’s dimensions would cause a point on the record’s outer edge to revolve at a speed of 1.5 miles per hour?

A. The record’s area is doubled.

B. The record’s area is halved.

C. The record’s circumference is doubled.

D. The record’s circumference is halved.

I know if we halve the circumference or area we would would have less linear distance with a circle but, in this question, how would you quickly determine what the correct answer is. I tried using C as 3.5miles (2xPixr) and keeping the rotation 1 round per hour. The correct answer is D. Can someone explain this to me a logical way without doing calculations? The question is based on logic.

You know that the speed of the point on the edge derives from the movement of that point on the circumference. As such, probably one of the "circumference" options is going to be the expected answer.

You know (from having watched things spin, or having ridden on a schoolyard merry-go-round) that points move faster (that is, cover more distance in the same amount of time) the further these points are from the center of rotation; at the very center, the point would spin but would not have any "speed" because it isn't moving across distance.

Using this background knowledge, the most likely option is quickly apparent.