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

12 Practice Tests for t h e SAT I
Practice Test Four Answers and Explanations
395
Getting to the Answer:
Triang l e BCD is a 45-45-90 triang l e, w h ic h means eac h of
t h e l egs h as l engt h 2. So BC = 2. T h en, since h ypotenuse
BC is twice l eg AB for t h e l eft triang l e, t h is must b e a
30-60-90 triang l e; y = 30°, so z = 60°.
10. c
Difficulty: Medium
Strategic Advice: Since t h ey are percentages of t h e same
num b er, you can forget a b out t h e "positive num b er." Just t h in k ,
20 percent of 30 percent is t h e same as 15 percent of w h at?
Getting to the Answer:
200/o of 300/o = 1 50/o of h
0.2(0.3) = 0.15 h
0.06=0.15 h h = 0.4 = 400/o
11. B
Difficulty: Medium
Strategic Advice: Eac h time t h e square is sp l it, eac h sma l l er
square is t t h e size of t h e origina l square. How many suc h
sp l its did we make?
Getting to the Answer: We made 4 sp l its, so the sma ll est
squares are eac h t oft oft oft of t h e l argest square,
w h ic h is t x t x t x t = 26 of t h e l argest square. Since
two of t h e sma l l est squares are s h a ded, t h ey are 2;6 = 1 is
of t h e l argest square.
12. E
Difficulty: Medium
Strategic Advice: Varia b l es in t h e answer c h oices ma ke t h is
a great time to Pick Num b ers.
Getting to the answer:
Try x = - 1 and y = 2 so t h at -3 < 0 < 2, as required.
(A) 0
(B) y = 2 ( l arger t h an (A))
(C) -3x = -3(-1) = 3 ( l arger t h an (8))
(D) -(3x + y) =-(3(-1) + 2) =-(-3 + 2) =-(-1) = 1
(sma l l er t h an (C))
(E) -(3x-y) = -(3(-1) - 2) = -(-3 -2) = - (-5) = 5
( l arger t h an (C))
So (E) is t h e l argest.
13. D
Difficulty: Medium
Strategic Advice: Write an expression for eac h d ay's p h ysics
pro bl ems, t h en find t h e average.
Getting to the Answer:
Monday=m
Tuesday= 3m
Wedesday = 2m 3
Average = m + (3m) + (2m + 3) = 6m +
3 3
3 = 2m + 1
A l so notice you cou l d Pick Num b ers for t h is pro bl em.
Picking somet h ing l ike 2 or 3 form makes t h is very quick to
so l ve.
14. D
Difficulty: Hig h
Strategic Advice: In t h e question, t h e reciproca l of t h e
expression is equa l to itse l f. W h at num b ers can you t h ink of
t h at h ave t h ose properties?
Getting to the Answer:
Don't l et fractions in t h e exponents t h row you off. T h e first
step of any pro bl em l ike t h is is to cross-mu l tip l y.
l
(a+ br2
(a+ b)- 1 1
i =(a+ br 1 x (a+ br 1 =(a+ b)-1 = (a b)
Since t h is fraction is equa l to 1, we know t h e reciproca l is
a l so equa l to 1.
1 =(a+b),or (D).
Even t h oug h t h ere are answer c h oices wit h varia bl es, t h is is
not a good question to try to so l ve b y Picking Num b ers, as it
invo l ves comp l icated a l ge b ra.
15. E
Difficulty: Hig h
Strategic Advice: W h at is t h e x-coordinate at 07 W h at do
you know a b out t h e functions at t h at va l ue?