### All ISEE Upper Level Quantitative Resources

## Example Questions

### Example Question #41 : Operations

Which of the following is the greater quantity?

(A)

(B)

**Possible Answers:**

(A) is greater

(B) is greater

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

(A) and (B) are equal

**Correct answer:**

(B) is greater

(A) Substitute and evaluate, remembering that by order of operations, squaring precedes addition:

(B) Substitute and evaluate

(B) is greater

### Example Question #42 : Operations

is negative. Which of these quantities is the greater?

(A)

(B)

**Possible Answers:**

(A) is greater

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

(A) and (B) are equal

(B) is greater

**Correct answer:**

(B) is greater

Since and is negative, then by the multiplication property of inequality,

Also, , so by the addition property of inequality,

making (B) greater.

### Example Question #41 : Variables

is positive. Which of these quantities is greater?

(A)

(B)

**Possible Answers:**

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

(B) is greater

(A) is greater

(A) and (B) are equal

**Correct answer:**

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

The values of both terms depend on the value of .

Case 1:

, making (B) greater.

Case 2:

, making (A) greater.

Therefore, the information given is insufficient.

### Example Question #44 : Operations

When evaluating the expression

,

assuming you know the values of all five variables, what is the *third *operation that must be performed?

**Possible Answers:**

Multiplication

Squaring

Division

Addition

Subtraction

**Correct answer:**

Multiplication

The operation that must be performed first is the operation in parentheses, which is the division.

After this, the order of operations is:

Exponents

Multiplication and division (left to right)

Addition and subtraction (left to right)

The second thing that must be done is the exponentiation - the squaring. Of the three remaining operations, the multiplication takes precedence. The correct response is multiplication.

### Example Question #42 : Variables

The Fibonacci sequence is defined as follows:

For integers , .

Which is the greater quantity?

(a) The sum of and

(b)

**Possible Answers:**

(a) and (b) are equal

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

(a) is greater

(b) is greater

**Correct answer:**

(a) and (b) are equal

Using the definition of the sequence for all terms beginning with the third, substitute 778 for :

The two quantities are equal.

### Example Question #11 : How To Add Variables

is a negative integer. Which is the greater quantity?

(A)

(B)

**Possible Answers:**

(a) and (b) are equal

It cannot be determined which of (a) and (b) is greater

(b) is the greater quantity

(a) is the greater quantity

**Correct answer:**

(b) is the greater quantity

, so

and

is the greater quantity, regardless of .

### Example Question #12 : How To Add Variables

is a positive number.

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(a) is the greater quantity

(a) and (b) are equal

(b) is the greater quantity

It cannot be determined which of (a) and (b) is greater

**Correct answer:**

It cannot be determined which of (a) and (b) is greater

By examining two scenarios, we see that we cannot determine which is the greater quantity.

Case 1:

Then

and

This makes (a) the greater quantity.

Case 2:

Then

and

This makes (b) the greater quantity.

### Example Question #48 : Operations

is a negative number.

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

It cannot be determined which of (a) and (b) is greater

(b) is the greater quantity

(a) and (b) are equal

(a) is the greater quantity

**Correct answer:**

(a) and (b) are equal

The expressions and are each other's opposite, so they have the same absolute value. Therefore, regardless of the value of ,

.

### Example Question #13 : How To Add Variables

is a negative integer. Which is the greater quantity?

(A)

(B)

**Possible Answers:**

It cannot be determined which of (a) and (b) is greater

(a) and (b) are equal

(b) is the greater quantity

(a) is the greater quantity

**Correct answer:**

(a) is the greater quantity

,

so

and

regardless of the value of .

### Example Question #50 : Operations

is a negative integer. Which is the greater quantity?

(a)

(b)

**Possible Answers:**

It cannot be determined which of (a) and (b) is greater

(a) and (b) are equal

(b) is the greater quantity

(a) is the greater quantity

**Correct answer:**

(b) is the greater quantity

Since

,

it follows that

and

regardless of the value of .

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