12.Practice.Tests.for.the.SAT_2015-2016_1128p

12 Practice Tests for t h e SAT
Practice Test Seven Answers and Explanations I
647
17. A
Difficulty: Hig h
Strategic Advice: T h e interior ang l es of any triang l e sum to
1 80°, so a + b + c = 1 80.
Getting to the Answer:
T h at gives you d 3 ifferent equations containing t h e 3
unknowns a, b, an d c-you can so l ve t h ese for b. One way
to d o t h is is to combine t h e equations: a + b = 80 an d
b + C= 140.
T h en:
a + b + b + c = 80 + 140
a+ 2b + c=220
Now subtract t h e t h ir d equation:
a+ 2b + c -(a + b + c) = 220 - 180
a+ 2b + c - a -b - c = 220 - 180
a - a + 2b - b + c - c = 40
b=40
18. c
Difficulty: Hig h
Strategic Advice: If you know t h e s l ope of RS, you can fin
t h ey-coor d inate of d
R using t h e s l ope formu l a. T h s l ope of
a l ine is t h e c h ange in y-coor d inates d ivi d e d by t h e c h ange
in x-coor d inates.
Getting to the Answer:
Since t h e l ine a l so passes t h roug h t h e origin, (0, 0), t h e
s l ope of RS = t h e s l ope of SO = 1..
6 - 0 = .§. =
9 3·
P l ug t h is into your s l ope-intercept equation to so l ve for y
w h en x = -6, given t h ey-intercept= 0.
y= 1.. (-6) + 0
3
y=-4
9-0
19. D
Difficulty: Hig h
Strategic Advice: Since t h e ra d io station can be receive d in
a ll d irections, its region of reception is a circ l e wit h t h e ra d io
station at t h e center.
Getting to the Answer:
Before t h e c h ange, t h e signa l cou l d be receive d for 60
mi es, so t h e area of reception was a circ l e wit ra d ius 60
mi l es. Now it can be receive d for 40 mi l es furt h er, or for a
tota l of 60 + 40, or 100 mi l es. T h e area is now a circ l e wit
ra d ius h
l 00 mi l es:
New region of reception
Ra d io station
O l d region of reception
T e increase is just t h e d ifference in t h ese areas; t h at is, t h e
s h a d e d region on t h e above d iagram.
Increase New area - O l d area
7t(l 00) 2 - 7t(60) 2
l 0,0007t - 3,6007t
= 6,4007t
T e va l ue of 7t is a bit more t h an 3, s o 6,4007t is a bit more
t h an 3 x 6,400, or just over 1 9,200. T h e on l y c h oice c l ose
to t h is is (0), 20,000.
20. A
Difficulty: Hig h
Strategic Advice: T h e tota l number of wor d s in t h e paper is
e number of wor d s per page times t h e number of pages,
t h at is, wp .
Getting to the Answer:
If Bi ll types atx wor d s per minute, h e can type wp wor d s in
wp -+-x minutes, or an average rate of .!'Y.e. minutes. Now to x