All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #933 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
 andÂ
 are positive integers. Which is the greater quantity?
(A)Â
(B)Â
It is impossible to tell which is greater from the information given
(A) is greater
(B) is greater
(A) and (B) are equal
(B) is greater
Since  andÂ
 are positive,Â
 for all positiveÂ
 andÂ
, making (B) greater.
Example Question #251 : Algebraic Concepts
 andÂ
 are negative integers. Which is the greater quantity?
(A)Â
(B)Â
(A) is greater
(A) and (B) are equal
(B) is greater
It is impossible to tell which is greater from the information given
(B) is greater
Since  andÂ
 are both negative,Â
.
 for all negativeÂ
 andÂ
, making (B) greater.
Example Question #935 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
 andÂ
 are positive integers. Which is the greater quantity?
(A)Â
(B)Â
(B) is greater
(A) is greater
(A) and (B) are equal
It is impossible to tell which is greater from the information given
It is impossible to tell which is greater from the information given
It is impossible to tell which is greater.Â
Case 1:Â
Then
andÂ
.
This makes (A) and (B) equal.
Case 2:Â
Then
andÂ
.
This makes (A) the greater quantity.
Example Question #41 : Variables And Exponents
 andÂ
 are positive integers greater than 1.
Which is the greater quantity?
(A)Â
(B)Â
It is impossible to determine which is greater from the information given
(A) and (B) are equal
(B) is greater
(A) is greater
(A) is greater
One way to look at this problem is to substitute . SinceÂ
,Â
 must be positive, and this problem is to compare
 and Â
.Â
andÂ
Since 2, , andÂ
 are positive, by closure,Â
, and by the addition property of inequality,
Substituting back:
(A) is the greater quantity.
Example Question #41 : Variables And Exponents
 andÂ
 are positive integers greater than 1.
Which is the greater quantity?
(A)Â
(B) Â
(A) and (B) are equal
(A) is greater
(B) is greater
It is impossible to determine which is greater from the information given
It is impossible to determine which is greater from the information given
Case 1:Â
Then
and Â
This makes the quantities equal.
Â
Case 2:
Then
and Â
This makes (B) greater.
Â
Therefore, it is not clear which quantity, if either, is greater.
Example Question #931 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
 andÂ
 are positive integers greater than 1.
Which is the greater quantity?
(A)Â
(B)Â
(B) is greater
(A) is greater
It is impossible to determine which is greater from the information given
(A) and (B) are equal
(A) is greater
One way to look at this problem is to substitute . The expressions to be compared areÂ
andÂ
Since  is positive, so isÂ
, and
Substituting back,
,
making (A) greater.
Example Question #261 : Algebraic Concepts
Factor:
The expression is a prime polynomial.
We can rewrite as follows:
Each group can be factored - the first as the difference of squares, the second as a pair with a greatest common factor. This becomes
,
which, by distribution, becomes
Example Question #45 : Variables And Exponents
 is a positive number;Â
 is the additive inverse ofÂ
.
Which is the greater quantity?
(a)Â
(b)Â
(a) and (b) are equal
(b) is the greater quantity
It is impossible to determine which is greater from the information given
(a) is the greater quantity
(b) is the greater quantity
If   is the additive inverse ofÂ
, then, by definition,Â
.
, as the difference of the squares of two expressions, can be factored as follows:
Since , it follows thatÂ
Another consequence of  being the additive inverse ofÂ
 is that
, so
 is positive, soÂ
 is as well.
It follows that .
Example Question #1 : How To Divide Exponential Variables
Half of one hundred divided by five and multiplied by one-tenth is __________.
2
5
1
10
1
Let's take this step by step. "Half of one hundred" is 100/2 = 50. Then "half of one hundred divided by five" is 50/5 = 10. "Multiplied by one-tenth" really is the same as dividing by ten, so the last step gives us 10/10 = 1.
Example Question #941 : Isee Upper Level (Grades 9 12) Quantitative Reasoning
Simplify: Â
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All ISEE Upper Level Quantitative Resources
