ISEE Upper Level Quantitative : ISEE Upper Level (grades 9-12) Quantitative Reasoning
Study concepts, example questions & explanations for ISEE Upper Level Quantitative
All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #135 : How To Find The Solution To An Equation
How many solutions does this equation have?
Four solutions
Infinitely many solutions
Two solutions
No solutions
One solution
One solution
Two numbers have the same absolute value if and only if the numbers are either equal or each other's opposite. We examine both possibilities.
Case 1:
Case 2:
a false statement. No additional solution is yielded.
The statement has one solution.
Example Question #136 : How To Find The Solution To An Equation
Let 
The graph of 
The 
As can be seen in the diagram below, 
The 
Example Question #137 : How To Find The Solution To An Equation
Which of the following is a true statement?
The equation has two solutions, both positive.
The equation has one solution, which is negative.
The equation has one solution, which is positive.
The equation has two solutions, both negative.
The equation has two solutions, one positive and one negative.
The equation has two solutions, one positive and one negative.
Two numbers have the same absolute value if and only if the numbers are either equal or each other's opposite. We examine both possibilities.
Case 1:
Case 2:
The equation therefore has two solutions, one positive, one negative.
Example Question #138 : How To Find The Solution To An Equation
Which is the greater quantity?
(a)
(b)
(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
It cannot be determined which of (a) and (b) is greater
so either
in which case
or
in which case
can be solved by factoring the trinomial. Since 
Either 
or
Each of 
Example Question #139 : How To Find The Solution To An Equation
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
It cannot be determined which of (a) and (b) is greater
or
Since 
or
Example Question #140 : How To Find The Solution To An Equation
Which is the greater quantity?
(a)
(b)
(a) is the greater quantity
It cannot be determined which of (a) and (b) is greater
(b) is the greater quantity
(a) and (b) are equal
(a) is the greater quantity
Both equations are quadratic, so solve as follows:
Since 
Either 
or 
Similarly,
1 and 3 have product 3 and sum 4, so the above becomes
Either 
or 
While the values of the variables cannot be determined with certainty, it can be determined that 
Example Question #141 : How To Find The Solution To An Equation
Which is the greater quantity?
(a)
(b)
(a) and (b) are equal
It cannot be determined which of (a) and (b) is greater
(a) is the greater quantity
(b) is the greater quantity
It cannot be determined which of (a) and (b) is greater
From these two scenarios, it can be seen that either (a) or (b) can be the greater.
Case 1: 
Case 2: 
Therefore, it cannot be determined which is greater.
Example Question #142 : How To Find The Solution To An Equation
Define 
Which is the greater quantity?
(a)
(b)
(a) and (b) are equal
(b) is the greater quantity
(a) is the greater quantity
It cannot be determined which of (a) and (b) is greater
(a) and (b) are equal
Also,
Therefore, 
Example Question #143 : How To Find The Solution To An Equation
Define 
Which is the greater quantity?
(a)
(b)
(b) is the greater quantity
(a) and (b) are equal
(a) is the greater quantity
It cannot be determined which of (a) and (b) is greater
It cannot be determined which of (a) and (b) is greater
Either
or
Since
it is not clear whether 
Example Question #144 : How To Find The Solution To An Equation
Above is the graph of a function 
(a)
(b)
It cannot be determined which of (a) and (b) is greater
(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
Examine this diagram:
As indicated by the blue circle in the diagram, the only point on the graph of the function with domain element 4 is 
As indicated by the red circles in the diagram, there are three points on the graph of the function with range element 4 - namely, 
All ISEE Upper Level Quantitative Resources
