# SSAT Upper Level Math : Number Concepts and Operations

## Example Questions

### Example Question #41 : Number Concepts And Operations

You are asked to fill in both circles in the statement

with the same number from the set

to make a true statement.

How many ways can you do this?

Four

None of the other responses is correct.

Six

Two

None

Four

Explanation:

The problem is asking for a number whose square is a number congruent to 1 in modulo 12 arithmetic - that is, a number whose square, when divided by 12, yields remainder 1. This square must be odd, so the number squared must also be odd. Therefore, we need only test the odd integers. We see that:

Four of the integers have squares congruent to 1 in modulo 12 arithmetic.

### Example Question #1 : How To Multiply

Multiply:

None of the other responses is correct.

Explanation:

We can write 2 pounds, 5 ounces as just ounces as follows:

Multiply:

Divide by 16, noting quotient and remainder, to get pounds and ounces:

Therefore, the correct response is 13 pounds, 14 ounces.

### Example Question #43 : Number Concepts And Operations

Fill in the circle to yield a true statement:

The other answer choices are incorrect.

The other answer choices are incorrect.

Explanation:

The problem is asking for a number whose product with 6 yields a number congruent to 5 in modulo 12 arithmetic - that is, a number which, when divided by 12, yields remainder 6.

However, 6 multiplied by any odd number yields a number which, when divided by 12, yields remainder 6, as is demonstrated using our choices:

Each of the choices yields a product congruent to 6 modulo 12, so none of them is a correct choice.

### Example Question #11 : Perform Operations With Numbers Expressed In Scientific Notation: Ccss.Math.Content.8.Ee.A.4

Write  in scientific notation.

Explanation:

Scientific notation is used to simplify exceptionally complex numbers and to quickly present the number of significant figures in a given value. The value is converted to an exponent form using base ten, such that only a single-digit term with any given number of decimal places is used to represent the significant figures of the given value. Non-significant zeroes can be omitted from the leading term, and represented only in the base ten exponent.

The given number has three significant figure () so we write out number as

You must move the decimal place two places to the right, or in other words multiply by . When you move the decimal place to the right, you multiply the number by , so it is .

### Example Question #1 : How To Divide Square Roots

Divide:

Explanation:

We can write 18 pounds, 2 ounces as just ounces as follows:

Divide:

Convert 58 ounces to pounds and ounces as follows:

That is, 3 pounds 10 ounces.

### Example Question #45 : Number Concepts And Operations

Simplify by rationalizing the denominator:

Explanation:

Multiply both numerator and denominator by the conjugate of the denominator, which is :

### Example Question #2 : How To Divide Square Roots

Simplify by rationalizing the denominator:

Explanation:

Multiply both numerator and denominator by the conjugate of the denominator, which is :

### Example Question #41 : Number Concepts And Operations

Simplify by rationalizing the denominator:

None of the other responses is correct.

Explanation:

Multiply both numerator and denominator by the conjugate of the denominator, which is :

### Example Question #41 : Number Concepts And Operations

Simplify by rationalizing the denominator:

The correct answer is not among the other responses.

The correct answer is not among the other responses.

Explanation:

Multiply both numerator and denominator by the conjugate of the denominator, which is :

This is not among the given choices.

### Example Question #2 : How To Divide Square Roots

Simplify by rationalizing the denominator: