### All SSAT Upper Level Math Resources

## Example Questions

### Example Question #1 : How To Multiply

**Possible Answers:**

**Correct answer:**

First multiply the fraction in the numerator.

Now we have

Never divide fractions. We multiply the numerator by the reciprocal of the denominator.

### Example Question #2 : How To Multiply

Which of these expressions is the greatest?

**Possible Answers:**

Twenty percent of one fourth

All of these expressions are equivalent

One fifth of

Twenty-five percent of one fifth

One fourth of

**Correct answer:**

All of these expressions are equivalent

The easiest way to see that all four are equivalent is to convert each to a decimal product, noting that twenty percent and one-fifth are equal to , and twenty-five percent and one fourth are equal to .

One fourth of 0.2:

One fifth of 0.25:

Twenty-five percent of one fifth:

Twenty percent of one fourth:

### Example Question #3 : How To Multiply

Write .007341 in scientific notation.

**Possible Answers:**

**Correct answer:**

The answer is .

### Example Question #4 : How To Multiply

If are consecutive negative numbers, which of the following is false?

**Possible Answers:**

**Correct answer:**

When three negative numbers are multiplied together, the product will be negative as well. All the other expressions are true.

### Example Question #5 : How To Multiply

Fill in the circle to yield a true statement:

**Possible Answers:**

**Correct answer:**

The problem is asking for a number whose product with 5 yields a number congruent to 3 in modulo 6 arithmetic - that is, a number which, when divided by 6, yields remainder 3. We multiply 5 by each choice and look for a product with this characteristic.

;

;

;

;

;

The only choice whose product with 5 yields a number congruent to 3 modulo 6 is 3, so this is the correct choice.

### Example Question #6 : How To Multiply

You are asked to fill in all three circles in the statement

with the *same* number from the set

to make a true statement.

How many ways can you do this?

**Possible Answers:**

Five

One

Three

Four

Two

**Correct answer:**

One

The problem is asking for a number whose cube is a number congruent to 9 in modulo 10 arithmetic - that is, a number whose cube, when divided by 10, yields remainder 9. If the quotient of a number and 10 has remainder 9, then it is an integer that *ends* with the digit "9". Since this makes the cube odd, the number that is cubed must also be odd, so we need only test the five odd integers:

Only 9 fits the criterion, so "one" is the correct response.

### Example Question #7 : How To Multiply

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?

**Possible Answers:**

None of the other responses is correct.

None

Two

Four

Six

**Correct answer:**

Four

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 #8 : How To Multiply

Multiply:

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

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 #9 : How To Multiply

Fill in the circle to yield a true statement:

**Possible Answers:**

The other answer choices are incorrect.

**Correct answer:**

The other answer choices are incorrect.

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 #10 : How To Multiply

Write in scientific notation.

**Possible Answers:**

**Correct answer:**

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 .

### All SSAT Upper Level Math Resources

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