Sat math Essentials

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T E C H N I Q U E S A N D S T R AT E G I E S
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3 3

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8
12
4
7
a
10
8
12
4
7
a
4 
10 
4
8 
12 
7 
a
40
27 
a
40
27 
a
– 27 
40 – 27
a
13
However, you can also solve this problem without
algebra. You can write the expression 
8
12
4
7
a
and
just substitute each answer choice for 
a
until you find
one that makes the expression equal to 10.
Tip:
When you substitute an answer choice,
always start with answer choice 
c
. Answer choices are
ordered from least to greatest, so answer choice 
c
will
be the middle number. Then you can adjust the out-
come to the problem as needed by choosing answer
choice 
b
or 
d
next, depending on whether you need a
larger or smaller answer.
Let’s see how it works:
Answer choice 
c
:
8
12
4
7
19
4
4
5
, which is greater
than 10. Therefore, we need a small answer choice.
Try choice 
b
next:
Answer choice 
b
:
8
12
4
7
13
4
4
0
10
There! You found the answer. The variable 
a
must be
13. Therefore answer choice 
b
is correct.
Of course, solving this problem with algebra is
fine, too. But you may find that substitution is quicker
and/or easier. So if a question asks you to solve for a
variable, consider using substitution.