All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #41 : Operations
Which of the following is the greater quantity?
(A)
(B)
(B) is greater
It is impossible to determine which is greater from the information given
(A) is greater
(A) and (B) are equal
(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 #42 : Operations
is negative. Which of these quantities is the greater?
(A)
(B)
(B) is greater
(A) and (B) are equal
(A) is greater
It is impossible to determine which is greater from the information given
(B) is greater
Since and is negative, then by the multiplication property of inequality,
Also, , so by the addition property of inequality,
making (B) greater.
Example Question #3 : How To Add Variables
is positive. Which of these quantities is greater?
(A)
(B)
(A) is greater
It is impossible to determine which is greater from the information given
(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:
, making (B) greater.
Case 2:
, making (A) greater.
Therefore, the information given is insufficient.
Example Question #43 : Operations
When evaluating the expression
,
assuming you know the values of all five variables, what is the third operation that must be performed?
Multiplication
Subtraction
Squaring
Addition
Division
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 and
(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 #44 : Operations
is a negative integer. 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
(b) is the greater quantity
, so
and
is the greater quantity, regardless of .
Example Question #45 : Operations
is a positive number.
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 #45 : Operations
is a negative number.
Which is the greater quantity?
(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
(a) and (b) are equal
The expressions and are each other's opposite, so they have the same absolute value. Therefore, regardless of the value of ,
.
Example Question #891 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
is a negative integer. Which is the greater quantity?
(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
regardless of the value of .
Example Question #46 : Operations
is a negative integer. Which is the greater quantity?
(a)
(b)
(b) is the greater quantity
It cannot be determined which of (a) and (b) is greater
(a) and (b) are equal
(a) is the greater quantity
(b) is the greater quantity
Since
,
it follows that
and
regardless of the value of .