Sat practice Test #8 Answer Explanations

Choice B is correct. Let the measure of the third angle in the smaller 
triangle be a°. Since lines 
ℓ and m are parallel and cut by transversals, 
it follows that the corresponding angles formed are congruent.
So a° = y° = 20°. The sum of the measures of the interior angles of a 
triangle is 180°, which for the interior angles in the smaller triangle 
yields a + x + z = 180. Given that z = 60 and a = 20, it follows that 
20 + x + 60 = 180. Solving for x gives x = 180 − 60 − 20, or x = 100.
Choice A is incorrect and may result from incorrectly assuming 
that angles x + z = 180. Choice C is incorrect and may result from 
incorrectly assuming that the smaller triangle is a right triangle, 
with x as the right angle. Choice D is incorrect and may result from 
a misunderstanding of the exterior angle theorem and incorrectly 
assuming that x = y + z.
QUESTION 6
Choice D is correct. Since only two types of tickets were sold and a 
total of 350 tickets were sold, the sum of the numbers of both types of 
ticket sold must be 350. Therefore, B + L = 350. Since the bench tickets 
were $75 each, the income from B bench tickets was 75B. Similarly, 
since the lawn tickets were $40 each, the income from L lawn tickets 
sold was 40L. The total income from all tickets was $19,250. So the 
sum of the income from bench tickets and lawn tickets sold must equal 
19,250. Therefore, 75B + 40L = 19,250. Only choice D has both correct 
equations.
Choice A is incorrect and may result from incorrectly multiplying 
the income from each type of ticket instead of adding them. It also 
incorrectly uses 1,950 instead of 19,250. Choice B is incorrect and may 
result from confusing the cost of bench tickets with the cost of lawn 
tickets. Choice C is incorrect and may result from confusing the total 
number of tickets sold with the total amount raised.
QUESTION 7