ISEE Upper Level Quantitative : Algebraic Concepts
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All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #3 : Operations
N is a positive integer; 
(a)
(b)
(a) is greater.
(b) is greater.
(a) and (b) are equal.
It is impossible to tell from the information given.
It is impossible to tell from the information given.
If 
If 
Therefore, at least two possibilities can be demonstrated.
Example Question #4 : How To Multiply Variables
Which is the greater quantity?
(a)
(b)
(a) is greater.
(a) and (b) are equal.
It is impossible to tell from the information given.
(b) is greater.
(a) is greater.
Since 
Example Question #5 : Operations
Assume 
All four expressions given in the other choices are equivalent to 
Each expression can be simplified using the properties of exponents, among others:
The correct choice is 
Example Question #5 : How To Multiply Variables
Let 
(A)
(B)
(A) and (B) are equal
(A) is greater
It is impossible to determine which is greater from the information given
(B) is greater
(B) is greater
So by the multiplication property of inequality, when each is multiplied by the negative number 
and (B) is greater.
Example Question #1 : How To Multiply Variables
(A) One ninth of 117% of
(B) One eleventh of 143% of
(A) and (B) are equal
(A) is greater
(B) is greater
It is impossible to determine which is greater from the information given
(A) and (B) are equal
117% of 
One-ninth of this is
143% of 
One-eleventh of this is
Regardless of the value of 
Example Question #5 : Variables
Which of the following expressions is equivalent to
Use the difference of squares pattern as follows:
Example Question #171 : Algebraic Concepts
A hat sells for the same pre-tax price in Store A and Store B. Store A then discounts the hat 30%, and Store B discounts it 25%. After the discount, the hat is taxed at a 10% rate in Store A. The hat is taxed at a 5% rate in store B.
Which is greater?
(A) The amount that will be paid for the hat in Store A after discount and tax
(B) The amount that will be paid for the hat in Store B after discount and tax
It is impossible to determine which is greater from the information given
(A) is greater
(A) and (B) are equal
(B) is greater
(B) is greater
Let 
Store A discounts the hat by 30%, meaning that its discounted price before sales tax is
The amount paid after sales tax is this price plus 10% of it, or
Store B discounts the hat by 25%, meaning that its discounted price before sales tax is
The amount paid after sales tax is this price plus 5% of it, or
(B) must be greater regardess of 
Example Question #12 : How To Multiply Variables
A hat sells for the same price in Store A, where the sales tax is 8%, and Store B, where there is no sales tax. Store A then discounts the hat by 8%; Store B does not discount it.
Which is greater?
(A) The amount that will be paid for the hat in Store A after discount and tax
(B) The amount that will be paid for the hat in Store B
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(B) is greater
(A) is greater
(B) is greater
Let
Store A discounts the hat by 8%, meaning that its discounted price before sales tax is
The amount paid after sales tax is this price plus 8% of it, or
Since Store B neither discounts the price nor charges sales tax, the amount paid will be the original 
The hat will cost more in Store B, so (B) is greater.
Example Question #13 : How To Multiply Variables
Assume 
Using the associative property of multiplication,
Using the distributive property,
Using the commutative and associative properties of multiplication,
and
The expression 
The only expression that can be restated as 
Example Question #852 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
(A)
(B)
(A) and (B) are equal
It is impossible to tell which is greater from the information given
(B) is greater
(A) is greater
(A) is greater
We can compare these positive numbers by comparing their squares; the greater number will have the greater square.
Since 
Therefore,
and
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