ISEE Middle Level Quantitative : How to add variables

Study concepts, example questions & explanations for ISEE Middle Level Quantitative

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Example Questions

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Example Question #1 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which quantity is greater if ?

Possible Answers:

It is not possible to tell from the information given

is greater

and are equal

is greater

Correct answer:

is greater

Explanation:

We know that is always positive for all values of . Therefore  would be negative for all values of . From this conclusion, we know:

So we have:

is the greater quantity.

Example Question #1 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which quantity is greater if ?

Possible Answers:

is greater

is greater

It is not possible to tell from the information given

and are equal

Correct answer:

It is not possible to tell from the information given

Explanation:

A positive number raised to the third power will be positive, while a negative number raised to the third power will remain negative.

If , then and .

If , then and .

Since we do not know if is positive or negative, we cannot draw a conclusion about which option is greater.

If , then is greater.

If , then is greater.

Example Question #2 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which quantity is greater if ?

Possible Answers:

It is not possible to tell from the information given

and are equal

is greater

is greater

Correct answer:

is greater

Explanation:

When we can write:

We know that and . Based on this, we can compare the two given quantities.

is the greater quantity.

 

Example Question #3 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which quantity is greater if ?

Possible Answers:

is greater

It is not possible to tell from the information given

is greater

and are equal

Correct answer:

is greater

Explanation:

We know that is greater than . We can easily test a few values for to determine if the values are increasing or decreasing.

If :

If :

If :

The value of is increasing, with the smallest possible value being . From this, we know that , so .

Example Question #1 : How To Add Variables

Which of the following is equivalent to  ?

Possible Answers:

Correct answer:

Explanation:

Using the distributive property:

and

Using the associative property of multiplication:

We can rewrite  as ; using the commutative and associative properties of multiplication:

 is the sum of unlike terms and cannot be simplified.

 is the correct choice.

 

Example Question #2 : How To Add Variables

 is a positive integer.

Which is the greater quantity?

(A) 

(B) 

Possible Answers:

It is impossible to determine which is greater from the information given

(B) is greater

(A) and (B) are equal

(A) is greater

Correct answer:

It is impossible to determine which is greater from the information given

Explanation:

Depending on the value of , it is possible for either expression to be greater or for both to be equal.

Case 1: 

and 

So the two are equal.

 

Case 2: 

and 

So (B) is greater. 

 

The correct response is that it cannot be determined which is greater.

Example Question #3 : How To Add Variables

 is a positive integer.

Which is the greater quantity?

(A) 

(B) 

Possible Answers:

(A) and (B) are equal

(A) is greater

It is impossible to determine which is greater from the information given

(B) is greater

Correct answer:

(A) is greater

Explanation:

Since , and  is positive,

then by the multiplication property of inequality,

making (A) greater regardless of the value of .

Example Question #7 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

 is a positive integer.

Which is the greater quantity?

(A) 

(B) 

Possible Answers:

(A) and (B) are equal

It is impossible to determine which is greater from the information given

(A) is greater

(B) is greater

Correct answer:

(A) and (B) are equal

Explanation:

Regardless of the value of , the expressions are equal.

Example Question #9 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

Which of the following is equivalent to  ?

Possible Answers:

None of the other responses is correct.

Correct answer:

None of the other responses is correct.

Explanation:

The expression is the sum of two unlike terms, and therefore cannot be further simplified. None of these responses is correct.

Example Question #8 : Isee Middle Level (Grades 7 8) Quantitative Reasoning

 is a positive integer.

Which is the greater quantity?

(A) 

(B) 

Possible Answers:

(A) is greater

(B) is greater

It is impossible to determine which is greater from the information given

(A) and (B) are equal

Correct answer:

(A) is greater

Explanation:

Since , , so (A) is greater regardless of the value of .

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