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:

We’ll look at this first Numbers Game item together:

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.

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:

How about the addition table:

You definitely need to use these tables, so it is worth writing them down before you move ahead.

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.

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:

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.

Try this one on your own.

What do you need to solve for to determine which of the answer choices is true?

You’ve got a zero here: what concepts can you use to figure this item out?

Make sure you are using the concepts and formulas appropriately. Be careful not to mix different concepts together.

Substitute real numbers into the answer choices to ensure you did everything right.

In this item, we are dealing with a multiplication expression in which one of the numbers equals zero.

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:

Because a is zero, no matter what b and c are, the product d is always zero:

Answer choice B is correct.

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.

Flip the page once you solve this item on your own.

You need to determine a value for c, given that a is a multiple of 5 and b is a multiple of 7.

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.

The simplest way to approach this item is to find the LCM shared by 5 and 7. Multiply the two numbers:

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.

Try dividing each answer choice by 35. If you do your math carefully, you find that 175, choice D, is the correct answer.