Description:
Making Up Numbers questions have variables in the questions and answers, which can
be replaced with numbers. Replacing variables with numbers removes much of the difficult
algebra on the SAT, and allows you to solve algebraic problems with only arithmetic skills.
Approach:
Follow the three steps below to master "Making Up Numbers" problems.
-
If you see variables or undefined quantities, make up a numbers for each
variable.
-
Use your numbers to find a numerical solution for the answer and circle it.
-
Plug your numbers into the answer choices, and find the number you just circled.
1) Practice:
If a
= 3b, b
= 2c, and d
= 5c, what is d
in terms of a?
-
3a / 5
-
5a / 3
-
5a / 6
-
6a / 5
-
3a
1.1) Explanation:
-
First:
Plug in 12 (a multiple of 2 and 3) for a.
-
Second:
Follow the constraints; when
a
= 12, b
= 4, c
= 2
and
d
= 10. Once you have solved for
d
circle your answer.
-
Third:
Plug in 12 (the value chosen for
a)
into all of the answers and
choose the answer that equals 10 (the value you circled). You should determine that the
correct answer is
c.
2) Make Up Good Numbers
Use numbers that will give you whole number results for the physical quantities in the
problem! If you are making up numbers on a problem dealing with percentages, give the
original variable a value of 100. If you are making up two different numbers, make them
multiples of each other unless the problem's constraints require a different relationship.
3) Numbers to Avoid:
-
Never assign any variable a value of zero or one.
-
Don't assign the same value to two different variables.
-
Try not to use numbers that are already in the problem.
4) Other Rules for Making Up Numbers
-
Always test all of the answer choices. If more than one answer seems to work, make up
another set of numbers and try again.
-
You must write down the numbers you make up and circle the target value! If you can't
keep track of your values, making up numbers won't help a bit.
5) Practice:
Billy has 7 dollars more than Freddy, but 3 dollars less than Sally. If Billy has x
dollars, how many dollars do Freddy and Sally have together?
-
2x - 10
-
2x - 7
-
2x - 4
-
2x - 3
-
2x + 10
