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

12 Practice Tests for t h e SAT
652 Practice Test Seven Answers and Explanations
Getting to the Answer:
To so l ve in terms of b , divide bot h sides of t h e equation
a b c= b2 by b :
a b c b2
_
b-b
ac= b
2. D
Difficulty: Low
Strategic Advice: Try to e l iminate one of your variabl es.
Getting to the Answer: Add t h e two equations to cance l
out b : 5a- b =9
30 +b = 15
8a=24
a=3
If a= 3, t h en b = 15 -3a = 15 -9 = 6.
So a + b = 3 + 6 = 9.
3. E
Difficulty: Low
Strategic Advice: Simp l ify t h is a l gebraic fraction by
cance l ing common factors from t h e numerator and t h e
denominator.
Getting to the Answer: x 2 means 2 factors of x; x 6 means
6 factors of x. Cance l ing, you're l eft wit h 4 factors of x,
or x4 in t h e denominator. T h e y's cance l out. Cance l ing
t h e common factors of z, you're l eft wit h z in t h e
numerator. Combining t h e terms in t h e numerator 4
4 and t h e
denominator gives you !..___, (E).
x4
4. c
Difficulty: Medium
Strategic Advice: Since you are asked w h ic h statements
must be true, try to find a case w h ere t h e conditions in t h e
question h o l d but t h e statement does not. If you can find
suc h an examp l e, you can discard any answer c h oice t h at
inc l udes t h at statement.
Getting to the Answer:
Statement I: Let x = 3 and y = -1. T h en y < O and x + y >
0, but x is not l ess t h an 0, so Statement I is not a l ways true.
Discard (A) and (D).
Statement II: If x = 3 and y -1, t h en = y < 0 and x + y > 0,
butx is not l ess t h an -y. So Statement II is not a l ways true.
Discard (B) and (E).
T h ere is no need to c h eck Statement Ill. Since (C) is t h e
on l y one remaining, it must be correct.
5. E
Difficulty: Medium
Strategic Advice: Notice t h at a and b are two of t h e four
ang l es in a quadri l atera l .
Getting to the Answer:
T h e sum of t h e measures of t h e interior ang l es of any
quadri l atera l a l ways equa l s 360, so a + b +t h e ot h er two
angles= 360. Note t h at t h e ot h er two ang l es are a l so t h e
base ang l es of an equi l atera l triang l e, so eac h measures 60
degrees. So,
+ 60 + 60 = 360
a + b = 240
6. c
Difficulty: Medium
Strategic Advice: T h e vo l ume of a rectangu l ar so l id is given
by t h is re l ations h ip:
vo l ume = l engt h x widt h h x eig h t
Getting to the Answer:
In t h is case, t h e h eig h t is equiva l ent to t h e given dept h , so
8640 = 60 x 6 x widt
8640 h
60 widt h
x 6
24 =widt h
So t h e widt h of t h e swimming poo l is 24 feet.
7. D
Difficulty: Medium
Strategic Advice: For t h is Function question, first find t h e
va l ue of f(2) and g(2). T h en find t h e difference between
t h em. Be sure you've answered t h e rig h t question before
you fi ll in your answer-t h is question h as l ots of tempting
p l aces to stop before you've actua ll y found w h at t h e
question asks for.