


Tackling Numbers Game Items
As you’ll see, our step method is almost identical to
Math and Supermath Heads. Follow these steps every time you see
a Numbers Game item:
Step 1: Determine what the item is really asking you
to solve.
Step 2: Determine which formulas and concepts to use.
Step 3: Do the math by writing out every step.
Step 4: Plug in numbers for variables to check your
math.
Numbers Game Items in Slow Motion
We’ll look at this first Numbers Game item together:

Step 1: Determine what the item is really asking you to
solve.
The stem here wants you to apply your knowledge of odd/even
number operations. What it really wants you to do is to discover
which n and r combination makes
the product odd, not even.
Step 2: Determine which formulas and concepts to use.
To solve this item, you should apply the formulas you
just learned in the Essential Concepts section.
Remember the multiplication table for odd/even numbers?
Here it is:
eveneven = even
evenodd = even
oddodd = odd
How about the addition table:
even + even = even
odd + odd = even
even + odd = odd
You definitely need to use these tables, so it is worth
writing them down before you move ahead.
Step 3: Do the math by writing out every step.
From the multiplication table, you know that oddodd
= odd. So both n and (n + r)
should be odd.
To make the sum of n + r odd,
either n or r must be odd. From
our multiplication chart, we know that if n + r is
odd, n must also be odd if we want the product
of the two to be odd. Therefore, r should be even. Now
go back to the answer choices. Answer B says that n is
odd and r is even. This combination turns the answer
into an odd number. Pick this answer choice.
Step 4: Plug in numbers for variables to check your math.
Now check your result with real numbers. If you don’t
know the formulas or don’t trust your memory, you can always use
real numbers to try out every answer offered or check the operations
you performed.
Try out answer choice A: substitute n and r for
odd numbers:
(3 + 5) 3 = 24
The answer is even and therefore should be eliminated.
Choice B: (3 + 2)3
= 15
The answer is odd, which contradicts the original condition.
Choice B gets to hang around.
Choice C: (2 + 2)2
= 8
The answer is even and should be eliminated.
Plug in numbers for choices D and E, and
you find out that answer B is the only combination
that results in an odd number.
Guided Practice
Try this one on your own.

Step 1: Determine what the item is really asking you to
solve.
What do you need to solve for to determine which of the
answer choices is true?
Step 2: Determine which formulas and concepts to use.
You’ve got a zero here: what concepts can you use to figure
this item out?
Step 3: Do the math by writing out every step.
Make sure you are using the concepts and formulas appropriately.
Be careful not to mix different concepts together.
Step 4: Plug in numbers for variables to check your math.
Substitute real numbers into the answer choices to ensure
you did everything right.
Guided Practice: Explanation
Step 1: Determine what the item is really asking you to
solve.
In this item, we are dealing with a multiplication expression
in which one of the numbers equals zero.
Step 2: Determine which formulas and concepts to use.
To verify/eliminate answer choices, you have to apply
the rules of multiplication by zero. Specifically, the product of
zero and a number is zero:
0n = 0
Step 3: Do the math by writing out every step.
Because a is zero, no matter what b and c are,
the product d is always zero:
(0)bc = d
(0)bc = 0
Answer choice B is correct.
Step 4: Plug in numbers for variables to check your math.
Just to make sure there is only one possible answer to
this item, check the equation with real numbers. Remember, the item
asks you to choose the answer that must be true.
Check answer A: if abc = d and a is
zero, b can equal zero. But because a =
0, b can be any number, because the product of a and b is zero
anyway. Therefore, this answer is not necessarily true.
We already know answer choice B works.
Check answer C: if abc = d and a is
zero, cb can equal 1. But because
a = 0, the product of c and b can
be any number, because the product of a, b, c is
zero anyway. Therefore, this answer is not necessarily true.
You can work through answer choices D and E and
find out that B is the only answer that must be
true.
Independent Practice
Flip the page once you solve this item on your own.

Independent Practice: Explanation
Step 1: Determine what the item is really asking you to
solve.
You need to determine a value for c,
given that a is a multiple of 5 and b is a
multiple of 7.
Step 2: Determine which formulas and concepts to use.
This item is about multiples and factors. If 5 and 7 are
factors of a and b, they both
have to be factors of c.
Step 3: Do the math by writing out every step.
The simplest way to approach this item is to find the
LCM shared by 5 and 7. Multiply the two numbers:
57 = 35
Can you reduce 35 to a smaller number that is divisible
by both 5 and 7? Nope, so the correct answer must be divisible by
35.
Step 4: Plug in numbers for variables to check your math.
Try dividing each answer choice by 35. If you do your
math carefully, you find that 175, choice D, is the
correct answer.
