percent of the rest of the population of Transitania. The population of Norson is what percent of the entire population of Transitania?
(A) 
(B) 
(C) 
(D) 
(E) 
2.If 2^a = 4^b, which of the following expresses a in terms of b?
Answer Choices
(A) b over 2
(B) b
(C) 2 times b
(D) 4 times b
(E) 2^b
3.In the figure above, 
and 
. If the dashed lines bisect the angles with measures of 
and 
, what is the value of 
?
(A) 
(B) 
(C) 
(D) 
(E) 
4.A mechanic can install carburetors in 3 cars every 4 hours. At that rate, how long will it take the mechanic to install carburetors in 5 cars?
(A) 6 hr 20 min
(B) 6 hr 40 min
(C) 7 hr 15 min
(D) 7 hr 30 min
(E) 7 hr 45 min
Explanation
1.The correct answer is D
Let 
equal the population of Norson, and let 
equal the entire population of Transitania. Then 
is the population of the rest of Transitania. 
is 
of 
.
, or 
.
This gives 
, or 
.
So the population of Norson is one third, or 
, of the entire population of Transitania.
2.The correct answer is C
Choice (C) is correct. Since 4 = 2^2, it follows that 4^b = (2^2)^b = 2^(2 times b). Therefore, 2^a = 4^b = 2^(2 times b), from which it follows that a = 2 times b.
3.The correct answer is E
First, add the labeled points 
, 
, 
, 
, 
, and 
to the figure, as shown above. Then segment 
bisects 
, so 
, and 
. Thus, 
. Similarly, 
, because 
and 
are of equal measure and the sum of their measures is 
. From the figure, it follows that 
. Therefore, 
.
4.The correct answer is B
From the information given, you can write the proportion 3 cars is to 4 hours as 5 cars is to x hours, where x represents the number of hours the mechanic will take to install carburetors in 5 cars. This gives 3 cars over 4 hours = 5 cars over x hours, which simplifies to 3 times x = 4 times 5 = 20. Therefore, x = 20 over 3 = 6 and (2 over 3) hours. Since 2 over 3 hour is 40 minutes, x is 6 hours 40 minutes.