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

1 2 Practice Tests for t h e SAT
Practice Test Seven Answers and Explanations I
645
q ands. T h erefore, Statement II is not necessari l y true,
and (D) can be e l iminated. Since s cou l d be l ess t h an q, s
cou l d be l ess t h an p. So Statement I is not necessari l y true,
and (B) can be e l iminated. Since none of t h e statements
are necessari l y true, (A) is correct.
7. c
Difficulty: Medium
Strategic Advice: Looking at t h e pie c h art, you s h ou l d see
t h at Housing and Uti l ities represents about± of t h e Newton's
mont hl y expenses.
Getting to the Answer:
Since t h eir tota l mont hl y income is $1,800, t h e amount spent
on Housing and Uti l ities is approximate l y± x $1,800, or $600.
8. E
Difficulty: Medium
Strategic Advice:
l You' ll need to uti l ize t h e positive/negative
aws an d your know l edge about powers to so l ve t h is
probl em. Pic k Numbers for x and y.
Getting to the Answer:
Let x = 2, so x 2 = 4. T h erefore, y must equa l -4 in order for
t h e equation to remain true. So p l ug in 2 for x and -4 for y
into eac h of t h e answer c h oices to see w h ic h one is true:
C h oice (A): Is (2) 2 = -4? No; e l iminate
C h oice (B): Is (2)(-4) = -4? No; e l iminate
C h oice (C): Is 2 = -? No; e l iminate
C h oice (D): Is (2) 3 = (-4) 2 ? No; e l iminate
C h oice (E): Is (2)4= (-4) 2 ? Yes
9. E
Difficulty: Medium
Strategic Advice: If e product of t h ree positive integers
is an even number, t h en at l east one of t h e t h ree integers
must be even. Pick Numbers to make t h is c l earer.
Getting to the Answer:
2 x 3 x 5 = 30 Even
7 x 6 x 9 =378
11x13 x 4 = 572
So (E) is correct.
Even
Even
10. E
Difficulty: Medium
a mu l tip l e of bot h 12
Strategic Advice: You're given t h at r is
and 18. So l ist t h e first few mu l tip l es of eac h to find
r
Mu l tip l es of 12: 12, 24, 36, 48, 60
Mu l tip l es of 1 8: 18, 36, 54, 72, 90
Getting to the Answer:
Since 36 is bot h a mu l tip l e of 12 and 18, r cou l d equa l
36. Scanning t h e answer c h oices, you s h ou l d see t h at t h e
on l y factor of 36 among t h e c h oices is 36 itse l f. So (E) is
correct.
11. D
Difficulty: Medium
Strategic Advice: To be abl e to mu l tip l y 4x an d 8x, t h ey
must be expressed as powers wit h t h e same base. W h en
you mu l tip l y powers wit h t h e same base, you add t h e
exponents and keep t h e base.
Getting to the Answer:
Since 4 and 8 are powers of 2, 4x and 8x can be written as
powers of 2.
4 = 2 2 , so 4x = (2 2 Y
W h en you raise a power to a power, you mu l tip l y t h e powers:
so (2 2 )X = 2 2 x
And 8 = 2 3 , so 8x = (2 3 Y = 2 3 x
So ( 4x)(8x) = 2 2 x 2 3 x = 2 2 x+ 3 x = 2sx
12. D
Difficulty: Medium
Strategic Advice: Remember t h at
average_ sum of terms . In t h is case 6
number of terms = sum of terms
6
or sum of terms= 6 x 6 = 36.
Getting to the Answer:
Now t h e sum of t h e terms is c h anged: 3 is subtracted from
4 of t h e numbers. T h e new sum of t h e terms wi ll b e 3 x 4,
or 12 l ess t h an e origina l sum; t h at is, 36 - 12 = 24. T h e
new average is t h en
new
number
sum
of
of
terms
terms = 24 = 4· 6
: