ISEE Upper Level Quantitative : Variables
Study concepts, example questions & explanations for ISEE Upper Level Quantitative
All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #1 : How To Add Variables
Which of the following is the greater quantity?
(A)
(B)
(B) is greater
(A) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
(B) is greater
(A) Substitute and evaluate, remembering that by order of operations, squaring precedes addition:
(B) Substitute and evaluate
(B) is greater
Example Question #2 : How To Add Variables
(A)
(B)
It is impossible to determine which is greater from the information given
(A) and (B) are equal
(A) is greater
(B) is greater
(B) is greater
Since 
Also, 
making (B) greater.
Example Question #206 : Algebraic Concepts
(A)
(B)
It is impossible to determine which is greater from the information given
(A) is greater
(B) is greater
(A) and (B) are equal
It is impossible to determine which is greater from the information given
The values of both terms depend on the value of 
Case 1:
Case 2:
Therefore, the information given is insufficient.
Example Question #3 : 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?
Multiplication
Division
Subtraction
Squaring
Addition
Multiplication
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 #5 : How To Add Variables
The Fibonacci sequence is defined as follows:
For integers 
Which is the greater quantity?
(a) The sum of 
(b)
(b) is greater
It is impossible to determine which is greater from the information given
(a) and (b) are equal
(a) is greater
(a) and (b) are equal
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
(A)
(B)
(a) is the greater quantity
(b) is the greater quantity
(a) and (b) are equal
It cannot be determined which of (a) and (b) is greater
(b) is the greater quantity
and
Example Question #45 : Operations
Which is the greater quantity?
(a)
(b)
(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
It cannot be determined which of (a) and (b) is greater
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 #41 : Variables
Which is the greater quantity?
(a)
(b)
(a) and (b) are equal
(a) is the greater quantity
(b) is the greater quantity
It cannot be determined which of (a) and (b) is greater
(a) and (b) are equal
The expressions 
Example Question #891 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
(A)
(B)
(b) is the greater quantity
It cannot be determined which of (a) and (b) is greater
(a) is the greater quantity
(a) and (b) are equal
(a) is the greater quantity
so
and
Example Question #42 : Variables
(a)
(b)
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
(b) is the greater quantity
Since
it follows that
and
regardless of the value of 
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All ISEE Upper Level Quantitative Resources
