Approaching Math IC Questions
Though there are four types of questions on the Math IC,
there is a standard procedure that you should use to approach all
Read the question without looking at the answers.
Determine what the question is asking and come to some conclusion
about how to solve it. Do not look at the answers unless you decide
that using the process of elimination is the best way to go.
you think you can solve the problem, go ahead. Once you’ve derived
an answer, only then see if your answer matches one of the choices.
you’ve decided on an answer, test it quickly to make sure it’s correct, then
Working Backward: The Process of Elimination
If you run into difficulty while trying to solve a multiple-choice
problem, you might want to try the process of elimination. For every
question, the answer is right in front of you, hidden among five
answer choices. So if you can’t solve the problem directly, you
might be able to plug each answer into the question to see which
Not only can this process help you when you can’t figure
out a question, there are times when it can actually be faster than
setting up an equation, especially if you work strategically. Take
the following example:
classroom contains 31 chairs, some of which have arms and some of
which do not. If the room contains 5 more armchairs than chairs
without arms, how many armchairs does it contain?
Given this question, you could build the equations:
Then, since y = x –
5 you can make the equation:
There are 18 armchairs in the classroom.
This approach of building and working out the equations
will produce the right answer, but it takes a long time! What if
you strategically plugged in the answers instead? Since the numbers
ascend in value, let’s choose the one in the middle: C 16.
This is a smart strategic move because if we plug in 16 and discover
that it is too small a number to satisfy the equation, we can eliminate A and B along
with C. Alternatively, if 16 is too big, we can eliminate D and E along
So our strategy is in place. Now let’s work it out. If
we have 16 armchairs, then we would have 11 normal chairs and the
room would contain 27 total chairs. We needed the total number of
chairs to equal 31, so clearly C is not the right answer.
But because the total number of chairs is too few, we can also eliminate A and B,
the answer choices with smaller numbers of armchairs. If we then
plug in D, 18, we have 13 normal chairs and 31 total chairs.
There’s our answer. In this instance, plugging in the answers takes
less time, and just seems easier in general.
Now, working backward and plugging in is not always the
best method. For some questions it won’t be possible to work backward
at all. For the test, you will need to build up a sense of when
working backward can most help you. Here’s a good rule of thumb:
Work backward when the question describes
an equation of some sort and the answer choices are all simple numbers.
If the answer choices contain variables, working backward
will often be more difficult than actually working out the problem.
If the answer choices are complicated, with hard fractions or radicals,
plugging in might prove so complex that it’s a waste of time.
Substituting numbers is a lot like working backward, except
the numbers you plug into the equation aren’t in
the answer choices. Instead, you have to strategically decide on
numbers to substitute into the question to take the place of variables.
For example, take the question:
||If p and q are
odd integers, then which of the following must be odd?
||p + q
||p – q
||p2 + q2
||p + q2
It might be hard to conceptualize how the two variables
in this problem interact. But what if you chose two odd numbers,
let’s say 5 and 3, to represent the two variables? You get:
||p + q =
5 + 3 = 8
||p – q = 5 – 3 =
||p2 + q2 =
25 + 9 = 34
||p2 q2 =
25 9 = 225
||p + q2 =
5 + 9 = 14
The answer has to be D, p2 q2
it multiplies to 225. (Of course, you could have answered this question
without any work at all, as two odd numbers, when multiplied, always
in an odd number.)
Substituting numbers can help you transform problems from
the abstract to the concrete. However, you have to remember to keep
the substitution consistent. If you’re using a 5 to represent p,
don’t suddenly start using 3. Choose numbers that are easy to work
with and that fit the definitions provided by the question.