ISEE Middle Level Quantitative : How to add variables

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

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Example Questions

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Example Question #11 : Algebraic Concepts

Define an operation on the real numbers as follows:

For all real values of  and ,

 is a positive number. Which is the greater quantity?

(a) 

(b) 

Possible Answers:

(b) is the greater quantity

(a) and (b) are equal

(a) is the greater quantity

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

Correct answer:

(a) and (b) are equal

Explanation:

so

and 

 

The two are equal regardless of the value of .

Example Question #12 : Algebraic Concepts

 and  are both negative numbers. Which is the greater quantity?

(a) 

(b) 

Possible Answers:

(b) is the greater quantity

(a) and (b) are equal

(a) is the greater quantity

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

Correct answer:

(a) and (b) are equal

Explanation:

The two quantities are equal regardless of the values of  and . To see this, we note that

and

Therefore, by the addition property of equality,

Example Question #13 : Algebraic Concepts

Which is the greater quantity?

(a) 

(b) 18

Possible Answers:

(a) is the greater quantity

(a) and (b) are equal

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

(b) is the greater quantity

Correct answer:

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

Explanation:

The information is insufficient, as we see by exploring two cases:

Case 1: 

 

Case 2: 

Remember, the three variables need not stand for whole numbers.

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