### All GED Math Resources

## Example Questions

### Example Question #31 : Types Of Numbers And Number Theory

Is the following number:

divisible by three or by four?

**Possible Answers:**

Three but not four

Both three and four

Neither three nor four

Four but not three

**Correct answer:**

Four but not three

While this problem can be answered by straight division, an easier method of doing so would be to apply the division tests for 3 and 4.

An integer is divisible by 3 if and only if the sum of its digits is divisible by 3. The digit sum of the number is

The digit sum is not divisible by 3. It follows that 176,176,176,176 is not divisible by 3.

An integer is divisible by 4 if and only if the integer formed by its final two digits is divisible by 4. This integer is 76, and

.

The two-digit integer is divisible by 4. It follows that 176,176,176,176 is not divisible by 4.

### Example Question #31 : Numbers

Give the Arabic number equivalent for the Roman numeral:

**Possible Answers:**

**Correct answer:**

The Roman numeral can be broken down as follows:

:

:

; since the smaller-valued symbol precedes the greater-valued symbol, this is a subtraction, so .

:

Add these: , the correct response.

### Example Question #31 : Ged Math

Which of the following numbers is an integer?

**Possible Answers:**

**Correct answer:**

Which of the following numbers is an integer?

An integer is any positive or negative whole number, including 0.

is the ratio of circumference to diameter, and is a never ending decimal

and is known as an imaginary number.

-46.4 is a decimal, and thus not an integer.

Therefore our only integer here is 0

### Example Question #31 : Numbers

What sort of solutions are found when is solved?

**Possible Answers:**

real, rational solutions

No real solutions

real, irrational solutions

real, irrational solution

**Correct answer:**

real, irrational solutions

Look at the discriminant to figure out the number of solutions.

For this equation,

Since the discriminant is positive, this means that there will be real solutions. Since the discriminant is not a square of another number, this means that those two solutions will be irrational.

### Example Question #31 : Numbers

Sarah says 3 is a rational number. Tom disagrees and says 3 is an integer. Who is right?

**Possible Answers:**

Sarah

Both

42

Tom

Neither

**Correct answer:**

Both

They are both correct.

3 is most certainly an integer as integers are our positive and negative whole numbers.

Sarah is right too. Rational numbers are any number that can be written as a fraction of integers. 3 can be written as a fraction , so it is a rational number too.

In fact, all integers are rational (but not all rational numbers are integers)

### Example Question #32 : Ged Math

is the midpoint of ; is the midpoint of ; is the midpoint of .

What fraction of is ?

**Possible Answers:**

**Correct answer:**

Try thinking of as a number line with endpoint at 0, and endpoint at 8. , the midpoint of , would be at 4. , the midpoint of , would be at 2; , the midpoint of - whose endpoints are at 2 and 8 - would be at 5.

;

is of .

### Example Question #31 : Ged Math

is the midpoint of ; is the midpoint of ; is the midpoint of .

What percent of is ?

**Possible Answers:**

**Correct answer:**

Try thinking of as a number line with endpoint at 0, and endpoint at 8. , the midpoint of , would be at 4. , the midpoint of , would be at 2; , the midpoint of - whose endpoints are at 2 and 8 - would be at 5.

;

Therefore,

is of

### Example Question #1 : Number Lines

Refer to the above number line. Which of the points is most likely the location of ?

**Possible Answers:**

**Correct answer:**

Convert to a decimal by dividing 5 by 9.

, so it falls between 0.55 and 0.56 on the number line. Point is the correct response.

### Example Question #1 : Number Lines

Refer to the above number line. Which of the points is most likely the location of the number ?

Do not use a calculator.

**Possible Answers:**

**Correct answer:**

, so

Point is in this range, so this is the correct response.

### Example Question #1 : Number Lines

Refer to the above number line. Which of the points is most likely the location of the product of 2 and ?

Do not use a calculator.

**Possible Answers:**

**Correct answer:**

, so

Point falls between 6.2 and 6.3 on the number line, so this is the correct choice.