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

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12 Practice <strong>Tests</strong> <strong>for</strong> <strong>the</strong> <strong>SAT</strong><br />

578 Practice Test Six Answers and Explanations<br />

14. 85<br />

Difficulty: Medium<br />

Strategic Advice: To solve this problem, you only need<br />

to remember two pieces of in<strong>for</strong>mation-<strong>the</strong> number of<br />

degrees in a quadrilateral and <strong>the</strong> number of degrees in a<br />

straight line. Once you have <strong>the</strong>se facts in mind, <strong>the</strong> solution<br />

is fairly straight<strong>for</strong>ward.<br />

Getting to <strong>the</strong> Answer:<br />

The 75° angle and <strong>the</strong> unlabeled angle of <strong>the</strong> quadrilateral<br />

<strong>for</strong>m a straight line, so <strong>the</strong>ir measures must sum to 180.<br />

Thus, <strong>the</strong> unlabeled angle must be:<br />

180 - 75 = 105°<br />

The angles of a quadrilateral sum to 360°, so:<br />

15. 6.1<br />

130 + 40 + 105 + x = 360<br />

x = 360 - 130 - 40 - 105 = 85<br />

Difficulty: Medium<br />

Strategic Advice: Don't <strong>for</strong>get to use <strong>the</strong> distributive<br />

property when you have a sum of values multiplied by<br />

one number.<br />

Getting to <strong>the</strong> Answer:<br />

- 1 -(30x3 + 20x2 + 1 Ox + 1) = 3x3 + 2x2 + lx + - 1 10<br />

10<br />

1<br />

So a = 3 ' b = 2 '<br />

c = 1 ' d = -.<br />

10<br />

Then, 3 + 2 + 1 + 0. 1 = 6. 1 .<br />

16. 4<br />

Difficulty: Medium<br />

Strategic Advice: Don't get confused if a diagram gives you<br />

too much in<strong>for</strong>mation.<br />

Getting to <strong>the</strong> Answer:<br />

The area of any quadrilateral is base times height, so use<br />

<strong>the</strong> coordinates to find <strong>the</strong> base and height:<br />

A=bh<br />

b=r+ 2<br />

h=r<br />

Now substitute and solve:<br />

r(r + 2) = 24<br />

r2 + 2r = 24<br />

r2 + 2r -24=0<br />

(r + 6)(r - 4) = 0<br />

r=-6 or r= 4<br />

Since r has to be positive according to <strong>the</strong> diagram, only 4<br />

works.<br />

17. 19<br />

Difficulty: High<br />

Strategic Advice: Don't let yourself get psyched out by <strong>the</strong><br />

fact that a question is phrased to sound difficult and occurs<br />

late in a section. All this is asking is what number divides<br />

into 23 with a remainder of 4?<br />

Getting to <strong>the</strong> Answer:<br />

If <strong>the</strong> remainder is 4, that means w divides with no<br />

remainder into 23 - 4 = 19. Only one number divides 19,<br />

itself. So w = 19. This makes sense, since 23 + 19 = 1<br />

remainder 4.<br />

18. 320<br />

Difficulty: High<br />

Strategic Advice: Take a complicated problem like this one<br />

step at a time. Keep <strong>the</strong> ultimate end point in your head<br />

and work toward it carefully.<br />

Getting to <strong>the</strong> Answer:<br />

From <strong>the</strong> problem, we know that it costs an extra $45 to go<br />

200 miles when compared to 50 miles. Thus, it costs $45<br />

to travel an extra 150 miles, and <strong>the</strong> additional charge is<br />

$1 5 <strong>for</strong> every 50 miles.<br />

To travel 450 miles, one needs to go 400 miles more than<br />

in <strong>the</strong> first journey.<br />

0 ° = 8, and 8 x $ 15 = $120, and $200 + $120 = $320<br />

0<br />

SECTION 7<br />

1. c<br />

Difficulty: Low<br />

The words Be<strong>for</strong>e he could even hope to sell indicate that<br />

because <strong>the</strong> furniture was faded and dirty, or essentially<br />

unattractive, it would be difficult to sell. Thus, <strong>the</strong> blank must<br />

describe an action that would eliminate those unattractive<br />

qualities, such as restoration.

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