CHAPTER 6 / WHAT THE SAT MATH IS REALLYTESTING 267
Concept Review 8
- Check your answer by plugging it back into the
original equation and checking your steps.
Write out each step, one beneath the other, so
that checking your logic and arithmetic is
easier. - Estimate only when it is easy to do. If the answer
choices are numerically far apart, estimation can
help you to eliminate obviously wrong answers. - If you can quickly “ballpark” a numerical answer
and rule out those choices that are “out of the ball-
park,” you can often avoid doing complicated cal-
culations or algebra.- Reread the question and make sure that you’ve
answered the right question, and make sure that
your answer makes sense in the context of the
question. - Dividing by 0 and taking the square root of an ex-
pression that can be negative are not allowed be-
cause they are undefined.
Answer Key 8:CheckingYour Work
SAT Review 8- 30 The simplest way to solve this problem is to
add 10 to both sides of the equation, which gives
3 x+ 5 = 30. However, many students do the
“knee-jerk” of solving for xand become prone to
silly arithmetic mistakes. If you didsolve for x,
you should have checked your answer by plug-
ging it back in to the original equation. - D Did you say (C)? Then you misread the question.
Always reread before marking your answer. It
asks for the value of s^2 , not s.Although scan be 0
or 2, s^2 is either 0 or 4. Did you say (A) or (B)?
Then you may have made this common mistake:
s^2 – 1 = 2s– 1
Add 1: s^2 = 2s
Divide by s: s= 2What went wrong? In the second step, we divided
by s without checking whether it could equal 0.
(Remember that division by 0 is undefined and
usually causes trouble.) Indeed, plugging in
shows that s= 0 is in fact a solution. The correct
method iss^2 – 1 = 2s– 1
Add 1: s^2 = 2s
Subtract 2s: s^2 – 2s= 0
Factor: s(s– 2) = 0
Use 0 product property: s= 0 or 2- E You might start by approximating. Since
the sum of their ages is about 60, and since
Tom is about twice as old as Julio, Tom is about
40 and Julio is about 20. This rules out (A) and
(B). From here, you may just want to “test” the
remaining choices until you find what works. If
you prefer algebra, you may want to let tequal
Tom’s age now and jequal Julio’s age now. You
are told that t+ j= 65 and that 2(j– 1) = t– 1.
Since you only need the value of t, solve the
first equation for j,getting j= 65 – t, and sub-
stitute this into the second equation. This gives
2(65 – t– 1) = t– 1
Simplify: 2(64 – t) = t – 1
Distribute: 128 – 2t= t– 1
Add 2tand 1: 129 = 3t
Divide by 3: 43 = tTherefore, Tom is now 43 and Julio is now 65 – 43 =- Notice that last year they were 42 and 21, respec-
tively, and 42 is twice as old as 21. - E Since more students averaged 80% than 70%, the
overall average should be closer to 80%. This rules out
(A) and (B). To get the precise answer, let xbe the
overall average. There are two ways to calculate the