All ISEE Middle Level Quantitative Resources
Example Questions
Example Question #22 : Equations
How many elements of the set can be substituted for
to make the inequality
a true statement?
None
Five
Two
Four
One
One
(Note that the inequality symbol switches here)
Of the elements of , only
fits this criterion.
Example Question #23 : Equations
If , then how many integers can be substituted for
to make the equation
a true statement?
It cannot be determined from the information given
Two
Infinitely many
One
Zero
One
If , the equation can be rewritten and solved as follows:
This is the only number that makes this statement true, so the correct choice is "one".
Example Question #24 : Equations
If , then how many integers can be substituted for
to make the equation
a true statement?
Three
Two
Zero
Six
One
One
If , then the equation can be rewritten and solved as follows:
The only integer that can be cubed to yield the result is
, so the correct response is "one".
Example Question #25 : Equations
If , then how many integers can be substituted for
to make the equation
a true statement?
One
Zero
Two
Infinitely many
It cannot be determined from the information given
Two
If , the equation can be restated and solved as follows:
Both and
make this true, so both make the original statement true. "Two" is the correct choice.
Example Question #26 : Equations
How many elements of the set can be substituted for
to make the inequality
a true statement?
Four
Five
One
Two
Three
One
Of the elements of the set , only
fits this criterion, making "one" the correct choice.
Example Question #27 : Equations
Which is the greater quantity?
(A)
(B)
(A) and (B) are equal
(B) is greater
(A) is greater
It is impossible to determine which is greater from the information given
(A) is greater
Since ,
.
, so (A) is greater.
Example Question #28 : Equations
If , then how many integers can be substituted for
to make the equation
a true statement?
Infinitely many
Four
Zero
One
Two
Infinitely many
If , this can be rewritten as
However, since zero multiplied by any number yields a product of zero, this is a true statement for all values of . This makes "infinitely msny" correct.
Example Question #31 : Equations
Evaluate .
It is impossible to evaluate from the information given
We will not be able to solve for the values of and
; instead, we need to group them together by reorganizing the equation.
Start by adding and subtracting
on each side. This will allow both variables to be on the left and both whole numbers to be on the right.
can be factored out of the left side.
Divide both sides by .
Example Question #151 : Isee Middle Level (Grades 7 8) Quantitative Reasoning
Divide 1,000 by 30. The quotient is ; the remainder is
. Which is the greater quantity?
(A)
(B)
(A) is greater
(B) is greater
It is impossible to tell which is greater from the information given
(A) and (B) are equal
(A) is greater
First, divide:
and
, so
.
(A) is greater.
Example Question #154 : Isee Middle Level (Grades 7 8) Quantitative Reasoning
Evaluate .
It is impossible to evaluate from the information given
It is impossible to evaluate from the information given
We cannot solve for and
on their own. Instead, we need to reorganize the equation to find
.
It quickly becomes clear that we cannot solve for with certainty.
If and
, then
, since
This makes
If and
, then
, since
This makes
Therefore, cannot be evaluated with certainty.
All ISEE Middle Level Quantitative Resources
