SECTION 2
1. A Answer this question in bite-sized pieces. The first step is to use your calculator to
compute the sum of the subscriptions: $68.80. The down payment was half that
amount, leaving $34.40 to be paid in 4 installments of $8.60 each. If you answered D
or E, you may have misread the question.
2. C Try Plugging In The Answers. Starting with C, put in
Cross-multiply:
for x:
. So C is correct. Another way would be to cross-
multiply first to get 2x2 + 4x = 2x2 + 2. Subtract 2x2 from both sides to get 4x = 2.
Divide by 4 to get x =
.
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3. C This is an excellent time to turn on your calculator. If 48,000 people live in
Town X and each household has 3.2 people, you can determine the number of
households: 48,000 ÷ 3.2 = 15,000. And since each household has 1.2 televisions,
you can now determine the number of televisions: 15,000 × 1.2 = 18,000.
4. B From the statement, you know that flour is necessary to make the cookies. You
don’t know that flour is the only thing necessary to make the cookies. For
example, you may also need sugar and eggs. You cannot conclude A or E, because
there may be other reasons for not making the cookies (maybe you didn’t feel like
it, or maybe you were out of sugar). Choice C is not necessarily true because there
may be other things necessary besides flour. Answer choice D contradicts the
original statement. Choice B must be true because you couldn’t have made the
cookies without the flour.
5. B Start by plugging in what you know into the function given. If f(x) = x2 – c, and f(–2)
= 6, then plug in –2 for x in the function: f(–2) = (–2)2 – c. Solve and replace f(–2)
with 6: 6 = 4 – c; 2 = –c; and c = –2. If you picked answer choice A, you forgot that
(–2)2 is positive 4, and if you picked answer choice E then you forgot about the
minus sign in the original function.
6. A First solve for b. If 9b = 81, then b must equal 9. Insert 9 for b into
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:
7. A The formula for the circumference of a circle is C = 2πr or C = dπ. (If you forget the
formula, you can look it up at the beginning of the section.) The circumference of
the circle is 5, so 5 = πd. Now, just solve for d, which equals
.
8. D If you got this question wrong, you either misread it or forgot the correct order of
operations. Remember to do parentheses first. Translating the information to an
equation, you’d get the following:
9. E Approach the problem in bite-sized pieces.
get x = 16.
= 23, so
= 4. Square both sides to
10. B We’re solving for shirts and pants, which constitute 60% of total sales. Because
shoes ($12,000) account for 15%, shirts and pants would be four times that amount,
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or $48,000. Another way to solve this is to find out the total value of sales and find
60% of that. If $20,000 represents 25% (or ) of sales, then the total must be
$80,000. Using translation, you’ll find that
× $80,000 = $48,000.
11. D You should have noticed several things about this question. First, the figure was not
drawn to scale. So a good first step would be to redraw the figure to comply with
the condition (
>
). Second, the question asks which of the following must be
true. Must is an important word—if it were which of the following could be
true, you’d change your analysis completely. So, redrawing the figure, you’d get
something like this:
In this figure,
is clearly larger than
. Because plugging in numbers makes the
distance more concrete, you might have made AB = 3 and CD = 2, for example.
Because you don’t know the length of BD, however, you’d have to leave it alone.
Now, let’s check the conditions. Option I: Well, this could be true, but it doesn’t
have to be. So, option I is out. This allows you to eliminate A and E. Option II: If you
let AB = 3 and CD = 2, AC = 3 + BC while BD = BC + 2. No matter
what BC is, AC > BD. Option II is true. This allows you to eliminate C, which does not
include Option II. We still need to check one more. Option III: If AB > CD,
and AC > AB, then AC > CD. Option III is true; therefore, D is the answer.
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12. D Absolute value, a number’s distance from zero on a number line, is always
expressed as a positive number. Cross out A and B since both are negative. Solve the
function with x = 1: f(1) = |(|1| − 3)| = 2.
13. D This geometric sequence can be expressed as 6 × 2x, where x is the number of
hours. So, after 9 hours, there will be 6 × 29 = 6 × 512 = 3,072. Alternatively, you
could just work out the problem each hour by doubling. So, after the first hour,
there are 6 × 2 = 12. Then, after the second hour, there are 12 × 2 = 24, and so on,
until you get to the ninth hour.
14. E Because any value squared must be 0 or positive, the least possible value for x2 is 0.
This means the least possible value of x2 + 2 is 2. So, A, B, C, and D are not possible
values for f(x). Only E is a possible value because when x = 0, f(x) = 2.
15. E Once again, the way not to solve an SAT question is to reason algebraically. Instead,
use your calculator to start cubing integers and stop when you find an integer
cubed that is greater than 200. 13, 23, 33, 43, and 53 are all less than 200. 63 is 216, so
that’s too large. Thus there are 5 numbers.
16. B Plug in! Because the values you choose for x and y must satisfy the equation,
let x equal 6 and y equal 9. The perimeter p would then equal 6 + 6 + 9 + 9, or 30.
The target is y, which is equal to 9. Plugging in 30 for p in each of the choices,
you’d get B as the answer. Although some of you might have answered this
question correctly by using algebra, doing so might have caused you to make a
mistake without realizing it. Trust us. Plugging In is always the safer method for this
type of problem. The Joe Bloggs choice, by the way, was C.
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17. C And yet again, the slow way to solve a word problem like this is to set up equations.
Letting w and l represent the number of wins and losses, respectively, the slow
method of setting up equations would yield the following:
Then you’d have to substitute
for
in the second equation and solve for l and
then go back to solve for w.
We can also plug in the answer choices, starting in the middle, C, and see which one
works:
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Bingo! We found the answer on the first try! If C didn’t work, you’d move up or
down depending on whether the result was too small or too big.
18. A This is a great opportunity to plug in. Make up a value for x—let’s say 40. Then
name the two other angles created by the lines that meet at vertex P— let’s call
the one to the left of x (within the same triangle as the angle labeled a°) angle y and
the one to the right of x (within the same triangle as the angle labeled b°) angle z.
Now make up values for these two angles so the sum of x, y, and z is 90. Let’s say
that y = 30 and z = 20. Because both of these triangles are right triangles, a = 180 –
90 – 30 = 60, and b = 180 – 90 – 20 = 70. Thus a + b = 130, which becomes our
target. Only A yields this answer.
19. C First a little error avoidance: Because 5 is one of the numbers you see, 52, or 25, is
not going to be the answer. It’s a Joe Bloggs answer. So, eliminate A. Next, let’s
estimate the area before you try to solve directly. The length of the square’s side is
a little more than 5, so the area is going to be a little more than 52, or 25. E is too
large, so before solving the problem, you’ve eliminated A and E. If you couldn’t
calculate the area exactly, you could guess from among the remaining choices. To
determine the area, let’s begin by assigning the variable s to indicate the length of
the square’s sides. The area is given by this formula: A = s2. Notice the triangle
formed by side
and the x- and y-axes. The base of that triangle is 1 and the
height is 5, so you can use the Pythagorean theorem to find the length of side
or s:
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20. B Probability is the chance of something happening. In this case, to find the
probability, find the area that is in the circle but not the square, divided by the area
of the circle (which represents all possibilities). Plug in for the radius of the circle.
Let’s say r = 5. So, the area of the circle is π × 52 = 25π. The area that is in the
circle but not the square is the area of the circle minus the area of the square. Find
the area of the square. The diagonal of the square is equal to the diameter of the
circle: 2 × 5 = 10. The diameter creates a 45°-45°-90° triangle from the square. So,
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the side of the square is
. That means the area of the square is
.
Therefore, the area within the circle but not the square is 25π – 50. That means the
probability is
. This is the target. Only B matches. After you’ve
plugged in and realized that the probability is
, you can also solve
algebraically:
Another, even more complicated, approach would be to call the area of the circle
πr2, the diameter 2r, and the area of the square
would be
. This is simplified:
. The probability
. It’s much more confusing
when you don’t plug in numbers!
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