Sat practice Test #8 Answer Explanations

Choice A is correct. Multiplying both sides of the equation by 6 
results in 6E = O + 4M + P. Then, subtracting O + 4M from both sides of 
6E = O + 4M + P gives P = 6E − O – 4M.
Choice B is incorrect. This choice may result from solving for −P 
instead of for P. Choice C is incorrect and may result from transposing 
P with E in the given equation rather than solving for P. Choice D is 
incorrect and may result from transposing P with E and changing the 
sign of E rather than solving for P.
QUESTION 4
Choice C is correct. Since RT = TU, it follows that ∆RTU is an 
isosceles triangle with base RU. Therefore, 
∠TRU and ∠TUR are 
the base angles of an isosceles triangle and are congruent. Let the 
measures of both 
∠TRU and ∠TUR be t °. According to the triangle sum 
theorem, the sum of the measures of the three angles of a triangle is 
180°. Therefore, 114° + 2t ° = 180°, so t = 33.
Note that 
∠TUR is the same angle as ∠SUV. Thus, the measure of 
∠SUV is 33°. According to the triangle exterior angle theorem, an 
external angle of a triangle is equal to the sum of the opposite interior 
angles. Therefore, x° is equal to the sum of the measures of 
∠VSU and 
∠SUV; that is, 31° + 33° = 64°. Thus, the value of x is 64.
Choice B is incorrect. This is the measure of 
∠STR, but ∠STR is not 
congruent to 
∠SVR. Choices A and D are incorrect and may result from 
a calculation error.
QUESTION 5
Choice B is correct. It is given that the width of the dance floor is 
w feet. The length is 6 feet longer than the width; therefore, the length 
of the dance floor is w + 6. So the perimeter is w + w + (w + 6) + (w + 6) = 
4w + 12.
Choice A is incorrect because it is the sum of one length and one 
width, which is only half the perimeter. Choice C is incorrect and may 
result from using the formula for the area instead of the formula for 
the perimeter and making a calculation error. Choice D is incorrect 
because this is the area, not the perimeter, of the dance floor.
QUESTION 6