ISEE Upper Level Quantitative : How to subtract exponential variables

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

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Example Questions

Example Question #1 : How To Subtract Exponential Variables

Simplify the expression:

Possible Answers:

The expression cannot be simplified further.

 

Correct answer:

 

Explanation:

Group, then collect like terms.

Example Question #2 : How To Subtract Exponential Variables

Assume neither  nor  is zero.

Which is the greater quantity?

(a)  

(b)

Possible Answers:

(a) is greater.

(a) and (b) are equal.

(b) is greater.

It is impossible to tell from the information given.

Correct answer:

(a) and (b) are equal.

Explanation:

Simplify the expression in (a):

 regardless of the values of the variables, and (a) and (b) are equal.

Example Question #3 : How To Subtract Exponential Variables

 is a positive number.  is a negative number.

Which is the greater quantity?

(a) 

(b) 

Possible Answers:

It is impossible to tell from the information given.

(a) is greater.

(b) is greater.

(a) and (b) are equal.

Correct answer:

(b) is greater.

Explanation:

 is a positive number and  is a negative number, so  and . Therefore,

.

(b) is always greater.

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