1. How much more light does one collect with a 4-meter diameter telescope in 0.5 minutes than with a 0.5-meter diameter telescope in 4 minutes?

A. The same amount
B. Twice as much
C. Four times as much
D. Eight times as much
E. Sixteen times as much

EXAMPLE: How much more light does one collect with a 2-meter diameter telescope in 1 minute than with a 1-meter diameter telescope in 2 minutes?

C. Twice as much
answer explanation: Since light collected is proportional to telescopes area × exposure time (t) and telescope area is proportional to telescope diameter (D) squared, light collected is proportional to D2t. Hence, light collected1st / light collected2nd = (D1st / D2nd)2 × (t1st / t2nd) = (2 m / 1 m)2 × (1 minute / 2 minutes) = 2.

2. One sixteenth of a radioactive elements atoms remain in a lunar rock sample. How many half lives old is the rock?
A. 1
B. 2
C. 4
D. 8
E. 16

3. Consider a planet with half the surface gravity of Earth. The maximum height to which shield volcanoes could grow is how many times that on Earth?
A. 0.5
B. 1
C. 2
D. 4