ISEE Upper Level Quantitative : Variables

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

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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

Explanation:

(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

Explanation:

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

Explanation:

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

Explanation:

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

Explanation:

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

Explanation:

 

 

, 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

Explanation:

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

Explanation:

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

Explanation:

,

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

Explanation:

Since

,

it follows that

and

regardless of the value of .

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