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

12 Practice Tests for the SAT
Practice Test Two Answers an d Exp l anations 221
I
Getting to t h e Answer:
To more easily visualize the scenario, pick numbers. The
easiest scenario is to pick 4 coins, 2 G and 2 S. If the last
two coins are G, then the display is SSGG, and (E) is true.
If there are 6 coins and the last two are G, you could have
GSSSGG, SGSSGG, or SSGSGG. No matter what you do,
there will be at least 2 adjacent S coins. So (E) is true.
Choices (A), (B), and (C) are not true: to return to the
4-coin example, you could have GSSG, ruling out choices
(A) and (B), or SGSG, ruling out (C). Choice (D) is a bit
trickier, but if you put two S coins together in the middle and
alternate the others, you do not have to have 2 adjacent G
coins. With 4 coins, GSSG does this. With 6, GSSGSG works
as well, and so on. Therefore, (D) is incorrect as well.
12. D
Difficu l ty: Medium
Strategic A d vice: Substitute the values given in the initial
setup of the problem. Work carefully to avoid mistakes, and
be sure not to stop too soon.
Getting to t h e Answer:
IV'XY-rl
IV' -3 x IV'=27 - 9 I
l -3 -9 1
= l -12 1 =12
9 - 9 I
13. B
Difficu l ty: Medium
Strategic A d vice: Just remember the rules for
transformations of functions; the graph of g(x - n) is the
graph of g(x) shifted n units to the right.
Getting to t h e Answer:
Only (B) is shifted to the right; (A), (C), and (D) are shifted
in different directions, and (E) is identical to the graph in the
question.
14. B
Difficu l ty: Medium
This is a great problem to practice your English-to-math
translation skills. Translate each part of the word problem
into an equation and then solve.
Getting to t h e Answer:
x+6-2=2x
4=x
15. c
Difficu l ty: Medium
Strategic A d vice: The SAT presents some word problems
that are not what they seem. This question appears to test
probability, but in reality, algebra is all that is necessary.
Backsolving also works well because there are numbers in
the answer choices.
Getting to t h e Answer:
Algebraically, if x represents the total number of coins, you
can solve for x -} using the equation x + ± x + t x + 6 =x.
4
ux+ ux+ 3 TIX+ 2 6=x
12 x+6=x
6= l 12 x
X=24
Using Backsolving, start with (C):
-} C24) + t (24) + t (24) + 6 =x
8 + 6 + 4 + 6 = 24, so (C) is correct.
16. D
Difficu l ty: Medium
Strategic A d vice: Remember that (x°) b = x° b and solve the
original equation for 23, or simplify each answer choice to
see which one equals 23.
Getting to t h e Answer:
= (y)4 (2 r
y4=23