ISEE Upper Level Quantitative : How to add variables

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

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Example Questions

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Example Question #1 : How To Add Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

Group and collect like terms:

Example Question #2 : How To Add Variables

Simplify the expression:

Possible Answers:

The expression cannot be simplified further.

Correct answer:

The expression cannot be simplified further.

Explanation:

There are no like terms among these three; one has only  as a variable, one has only , one has both. Therefore, no terms can be collected, and the expression cannot be simplified further.

Example Question #3 : How To Add Variables

Which is the greater quantity?

(a) The sum of the integers from 1 to 1,000

(b) The sum of the integers from 1,001 to 1,500

Possible Answers:

(a) is greater

It is impossible to tell from the information given

(a) and (b) are equal

(b) is greater

Correct answer:

(b) is greater

Explanation:

(a) The sum of the integers from 1 to 1,000 is 

(b) The sum of the integers from 1,001 to 1,500 is 

(b) is greater

Example Question #1 : How To Add Variables

Which is the greater quantity?

(A) 

(B) 

Possible Answers:

(B) is greater

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

(A) is greater

(A) and (B) are equal

Correct answer:

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

Explanation:

Which quantity is the greater depends on the value of 

Case 1: 

Then

and 

Subsequently, (A) is greater

Case 2: 

Then

and 

Subsequently, (B) is greater

Example Question #5 : How To Add Variables

Evaluate for :

Possible Answers:

Correct answer:

Explanation:

Substitute and evaluate, remembering that in order of operations, squaring comes before adding:

Example Question #2 : How To Add Variables

Which of the following is the greater quantity?

(A) 

(B) 

Possible Answers:

(A) and (B) are equal

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

(B) is greater

(A) is greater

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 #7 : How To Add Variables

 is negative. Which of these quantities is the greater?

(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:

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

Also, , so by the addition property of inequality,

making (B) greater.

Example Question #8 : How To Add Variables

 is positive. Which of these quantities is greater?

(A) 

(B) 

Possible Answers:

(B) is greater

(A) is greater

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

(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 #9 : How To Add Variables

When evaluating the expression

,

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

Possible Answers:

Addition

Multiplication

Division

Squaring

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 #10 : How To Add Variables

The Fibonacci sequence is defined as follows:

For integers .

Which is the greater quantity?

(a) The sum of  and 

(b) 

Possible Answers:

(b) is greater

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

(a) and (b) are equal

(a) 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.

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