264 MCGRAW-HILL’S SAT
Check the Question
Always quickly reread the question before
marking your answer to make sure that you’ve
answered the rightquestion and to make sure
that your solution makes sense in the context
of the question.A bin contains 20 basketballs and soccer balls. If there
are 8 more basketballs than soccer balls in the bin,
how many soccer balls are in the bin?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Many students think that since there are 8 more
basketballs than soccer balls, they should just subtract
8 from the total to get the number of soccer balls, get-
ting 20 – 8 = 12 soccer balls. The answer is (E), right?
Wrong. If there are 12 soccer balls, then there
must be 8 basketballs, for a total of 20. But the ques-
tion says that there are 8 morebasketballs than soc-
cer balls, and 8 sure isn’t more than 12! So now what?
Eliminate choice (E) first of all. Since there are fewer
basketballs than soccer balls, soccer balls must make
up fewer than half the balls, so there must be fewer
than 10 soccer balls, eliminating choice (D). Checking
the remaining choices shows (B) 6 works because if
there are 6 soccer balls, there are 14 basketballs, and
14 is 8 greater than 6!
The “direct” method for solving is to subtract 8
from 20 and then divide the result by 2to get the num-
ber of soccer balls.
Check Your Algebra
When solving an equation, check two things:
first your answer,and then your steps. If the
answer works when you plug it back into the
equation, there’s no need to check the steps. If
it doesn’t, then check your steps. When solving
equations, write out every step, and make sure
that each one is logical. You’re likely to make
mistakes if you skip steps or do them too
quickly in your head.If , then what is the value of x?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
You might notice that since both fractions have
the same numerator, the equation can be simplified
and solved without much trouble.Multiply by x– 2: 2 x= x^2
Divide by x:2 = x
Piece of cake. The answer is (C), right? Wrong. Notice
that substituting x= 2 into the original equation gives you
4/0 = 4/0. Although this seems true at first, it’s not, be-
cause 4/0 isn’t a number! (Just ask your calculator.) What
now? The check suggests a solution: you can just test the
choices. Plugging in the other choices for xshows that
only (A) 0 produces a true equation: 0/–2 = 0/–2.
What went wrong the first time? Check the steps.
Our second step was to divide by x. We’re allowed to
divide both sides of an equation by any number except
0 because division by 0 is undefined. That’s where we
went wrong: We didn’t check division by 0. Notice that
division by 0 also explains why x= 2 doesn’t work in
the original equation.Check by EstimatingEstimation is one of the simplest and most ef-
fective checking strategies you can use on the
SAT. Getting an approximateanswer can help
you to narrow down the choices quickly.If Carla drives at 40 miles per hour for nmiles and then
drives at 60 miles per hour for another nmiles, what is
her average speed, in miles per hour, for the entire trip?
(A) 42
(B) 48
(C) 50
(D) 52
(E) 54
Many students average 40 and 60 and get 50. But
this is wrong because Carla is not spending equal times
at 40 and 60 miles an hour. Since 40 mph is slower than
60 mph,she spends more timeat that speed. So her av-
erage speed is closer to 40 than 60. This eliminates
choices (C), (D), and (E). The correct answer is (B). (For
more on rate problems, see Chapter 9, Lesson 4.)2
22
x^2
xx
− x=
−
2
22
x^2
xx
− x=
−
Lesson 8:CheckingYour Work