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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 />

Practice Test One Answers and Explanations I<br />

l09<br />

SECTION 3<br />

1. A<br />

Difficulty: Low<br />

Strategic Advice: The algebra here isn't too difficult; you<br />

just need to be careful about dealing with values outside<br />

<strong>the</strong> radical. Isolate <strong>the</strong> radical expression on one side of <strong>the</strong><br />

equation, <strong>the</strong>n take <strong>the</strong> square root. Backsolving, or plugging<br />

<strong>the</strong> answers into <strong>the</strong> question, would also work well.<br />

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

2\!4()2 + 7 = 39<br />

2\!4()2 = 32<br />

2. D<br />

\!4()2 = 16<br />

2n = 16<br />

n=8<br />

Difficulty: Low<br />

Strategic Advice: An integer is any positive or negative<br />

whole number. Make sure you understand <strong>the</strong> definition of<br />

an integer on Test Day.<br />

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

Since x must be an integer, k must be a perfect square.<br />

Eliminate (A), (B), (C), and (E) because <strong>the</strong>y are not perfect<br />

squares. If you're not sure which answer choices are perfect<br />

squares, take <strong>the</strong> square root of each answer choice to see<br />

if it is an integer.<br />

3. D<br />

Difficulty: Low<br />

Strategic Advice: Convert <strong>the</strong> improper fractions to<br />

decimals or mixed fractions. Notice that in this question <strong>the</strong><br />

answer choices are not ordered from least to greatest or<br />

greatest to least.<br />

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

(A) ]_ < 1<br />

9<br />

(B) ]_ = 2J_ > 2<br />

3 3<br />

(C) 2. = 2l > 2<br />

4 4<br />

(D)<br />

1 7 ° = 1 %· This is between 1 and 2, so (D) is correct.<br />

(E) J1. = 21- > 2<br />

5 5<br />

4. c<br />

Difficulty: Low<br />

Strategic Advice: When a problem asks about an<br />

expression, look <strong>for</strong> a shortcut. You could solve <strong>the</strong> first<br />

equation <strong>for</strong> x in terms of b, <strong>the</strong>n plug that into <strong>the</strong> second<br />

equation, but you'll solve <strong>the</strong> problem faster if you can find<br />

a way to relate 2x + 4 and 6x + 12 directly.<br />

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

2x +4=b<br />

3(2x + 4) = 3(b)<br />

6x+ 12 =3b<br />

5. B<br />

Difficulty: Low<br />

Strategic Advice: Look <strong>for</strong> a pattern in <strong>the</strong> figure. What will<br />

help you figure out where <strong>the</strong> numbers need to go?<br />

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

In <strong>the</strong> figure, <strong>the</strong> larger numbers are on <strong>the</strong> side of <strong>the</strong><br />

line with <strong>the</strong> arrowhead. Look <strong>for</strong> this in your answer.<br />

Only (B) fits.<br />

6. D<br />

Difficulty: Low<br />

Strategic Advice: Do not be intimidated by <strong>the</strong> multiple<br />

variables. If you don't see how to turn <strong>the</strong> word problem<br />

into an equation, try picking your own values <strong>for</strong> x and y.<br />

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

Remember, John has to pay <strong>the</strong> $19 first be<strong>for</strong>e spending<br />

any leftover money on CDs, so he has y - 19 dollars to<br />

buy CDs with. Since each CD costs x dollars, he can buy<br />

CDs.<br />

x<br />

7. B<br />

Difficulty: Medium<br />

Strategic Advice: Make this abstract problem more<br />

concrete by picking simple numbers. You'll find that this<br />

problem isn't so difficult with real numbers in place of <strong>the</strong><br />

variables. You can also solve it by applying your knowledge<br />

of number properties.<br />

You can eliminate (A), (C), (D), and (E) by noticing that<br />

<strong>the</strong>y contain even exponents, which will produce positive<br />

numbers no matter what x is. The only answer choice that<br />

will always be negative is (B).

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