All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #111 : How To Find The Solution To An Equation
For all real numbers and
, define an operation
as follows:
is a positive integer. Which is the greater quantity?
(A)
(B)
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
Substitute for both in the expression:
Since is positive, so is common denominator
, so we need only compare numerators. Since
must be positive,
and
making (B) greater.
Example Question #791 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
and
are both positive.
20 subtracted from five-sevenths of is equal to
. Which is the greater quantity?
(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
(A) is greater
The statement is equivalent to
or, alternatively,
Since is positive and
, we can derive:
making greater than
. This makes (A) greater.
Example Question #114 : Algebraic Concepts
Define and
What is the domain of the function ?
None of the other responses gives a correct answer.
None of the other responses gives a correct answer.
has as its domain the set of values of
for which its radicand is nonnegative; that is,
or
Similarly, has as its domain the set of values of
for which its radicand is nonnegative; that is,
or
The domain of the sum of two functions is the intersection of the domains of the two individual functions. This intersection is
The domain of is the single
value
, which is not among the choices.
Example Question #791 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
Three consecutive integers add up to 36. What is the greatest integer of the three?
To solve this problem, you can translate the question into an equation. It should look like: . Since we don't know the first number, we name it as x. Then, we add one to each following integer, which gives us x+1 and x+2. Then, combine like terms to get
. Solve for x and you get 11. However, the question is asking for the greatest integer of the set, so the answer is actually 13 (because it is the x+2 term).
Example Question #111 : Algebraic Concepts
Column A Column B
The value of x in The value of x in
The quantities in both columns are equal.
The quantity in Column A is greater.
The relationship between the columns cannot be determined.
The quantity in Column B is greater.
The quantity in Column A is greater.
First, solve for x in Column A. Subtract 2 from both sides so that . Multiply by 5 on both sides so that X equals 80. Then, solve for x in Column B. Add 3 to both sides so that
. X equals 4 in this equation. Therefore, Column A is greater.
Example Question #114 : How To Find The Solution To An Equation
On a 70-question exam, Lisa answered 60 percent correctly. How many answers did she get right?
If Lisa answered 60 percent of the questions on a 70-question exam correctly, the following equation can be used to determine how many quesitons she got right. is equal to the number of questions she answered correctly.
Given that , it follows that
Next, we cross multiply, which gives us:
Now, we divide each side by 5, resulting in:
Example Question #121 : How To Find The Solution To An Equation
If is negative and
, then what is
?
The equation has no negative solution.
, so either
or
We solve both equations separately:
Since the negative solution is being requested, we choose .
Example Question #122 : How To Find The Solution To An Equation
Give the solution set of the equation:
Either
or
,
so we solve the equations separately:
or
The solution set is
Example Question #121 : Equations
Which of the folllowing is a true statement?
The equation has one solution.
The equation has two solutions.
The equation has three solutions.
The equation has no solution.
The equation has infinitely many solutions.
The equation has infinitely many solutions.
Since the absolute value of a nonnegative number is the number itself, and the absolute value of a negative number is its (positive) opposite, we have to examine up to three cases: ,
, and
.
However, let us examine that third case.
This makes and
negative, so the equation can be rewritten:
This statement is identically true. Therefore, all values of less than
work, and we have already proved that there are infinitely many solutions. We do not need to go further.
Example Question #124 : How To Find The Solution To An Equation
Which of the following is a true statement?
,
so
Using two substitutions:
The correct choice is .
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All ISEE Upper Level Quantitative Resources
