### All ISEE Middle Level Quantitative Resources

## Example Questions

### Example Question #1 : How To Find The Distributive Property

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(a) and (b) are equal

(b) is greater

(a) is greater

It is impossible to tell from the information given

**Correct answer:**

(a) and (b) are equal

Apply the distributive and commutative properties to the expression in (a):

The two expressions are equivalent.

### Example Question #2 : How To Find The Distributive Property

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(a) is greater

(b) is greater

(a) and (b) are equal

**Correct answer:**

(b) is greater

Apply the distributive property to the expression in (a):

, so regardless of .

Therefore,

### Example Question #3 : How To Find The Distributive Property

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

It is impossible to tell from the information given

(b) is greater

(a) is greater

(a) and (b) are equal

**Correct answer:**

(b) is greater

Apply the distributive property to the expression in (a):

Since , , and therefore, regardless of ,

### Example Question #4 : How To Find The Distributive Property

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(a) and (b) are equal

(b) is greater

(a) is greater

It is impossible to tell from the information given

**Correct answer:**

It is impossible to tell from the information given

We show that there is at least one value of that makes the (a) greater and at least one that makes (b) greater:

Case 1:

(a)

(b)

(b) is greater here

Case 2:

(a)

(b)

(a) is greater here

### Example Question #5 : How To Find The Distributive Property

Which of the following is equivalent to ?

**Possible Answers:**

**Correct answer:**

We can best solve this by factoring 4 from both terms, and distributing it out:

### Example Question #6 : How To Find The Distributive Property

and are positive integers.

Which of the following is greater?

(A)

(b)

**Possible Answers:**

(A) and (B) are equal

(B) is greater

It is impossible to determine which is greater from the information given

(A) is greater

**Correct answer:**

(A) and (B) are equal

(A) and (B) are equivalent variable expressions and are therefore equal regardless of the values of and .

### Example Question #7 : How To Find The Distributive Property

Simplify the below:

**Possible Answers:**

**Correct answer:**

In order to simiplify we must first distribute the -2 only to what is inside the ( ):

Now, we must combine like terms:

This gives us the final answer:

### Example Question #8 : How To Find The Distributive Property

Simplify the below:

**Possible Answers:**

This does not simplify

**Correct answer:**

We must use the distributive property in this case to multiply the 4 by both the 3x and 5.

### Example Question #9 : How To Find The Distributive Property

and are positive numbers. Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(a) is the greater quantity

(a) and (b) are equal

It is impossible to determine which quantity is the greater from the information given

(b) is the greater quantity

**Correct answer:**

(b) is the greater quantity

Since is positive, and , then, by the properties of inequality,

and

.

### Example Question #10 : How To Find The Distributive Property

is the additive inverse of . Which is the greater quantity?

(a)

(b)

**Possible Answers:**

It is impossible to determine which is greater from the information given

(b) is the greater quantity

(a) is the greater quantity

(a) and (b) are equal

**Correct answer:**

(b) is the greater quantity

is the additive inverse of , so, by definition, .

.