ISEE Middle Level Quantitative : How to add variables
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Example Questions
Example Question #11 : How To Add Variables
Define an operation on the real numbers as follows:
For all real values of 
(a)
(b)
(b) is the greater quantity
It is impossible to determine which is greater from the information given
(a) is the greater quantity
(a) and (b) are equal
(a) and (b) are equal
so
and
The two are equal regardless of the value of 
Example Question #11 : Algebraic Concepts
(a)
(b)
(a) is the greater quantity
It is impossible to determine which is greater from the information given
(b) is the greater quantity
(a) and (b) are equal
(a) and (b) are equal
The two quantities are equal regardless of the values of 
and
Therefore, by the addition property of equality,
Example Question #13 : How To Add Variables
Which is the greater quantity?
(a)
(b) 18
(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
It is impossible to determine which is greater from the information given
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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