ISEE Upper Level Quantitative : How to multiply variables

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

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Example Questions

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Example Question #1 : How To Multiply Variables

Multiply:

Possible Answers:

Correct answer:

Explanation:

This can be solved using the pattern for the sum times difference of two terms:

Example Question #2 : How To Multiply Variables

Multiply:

Possible Answers:

Correct answer:

Explanation:

This can be solved using the pattern for the sum times difference of two terms:

Example Question #3 : How To Multiply Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

This can be solved using the pattern for the square of a binomial:

Example Question #4 : How To Multiply Variables

N is a positive integer; . Which is greater?

(a) 

(b) 0

Possible Answers:

(a) is greater

(b) is greater

It is impossible to tell from the information given

(a) and (b) are equal

Correct answer:

(a) is greater

Explanation:

. Since , , and  . This makes (a) greater.

Example Question #5 : How To Multiply Variables

N is a positive integer; . Which is greater?

(a) 

(b)

Possible Answers:

(a) and (b) are equal.

(b) is greater.

It is impossible to tell from the information given.

(a) is greater.

Correct answer:

It is impossible to tell from the information given.

Explanation:

If , then .

If , then .

Therefore, at least two possibilities can be demonstrated. 

Example Question #6 : How To Multiply Variables

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:

(a) is greater.

Explanation:

Since ,

.

Example Question #7 : How To Multiply Variables

Assume  is nonzero. Which expression is not equivalent to ?

Possible Answers:

All four expressions given in the other choices are equivalent to .

Correct answer:

Explanation:

Each expression can be simplified using the properties of exponents, among others:

The correct choice is , as it is the only choice not equivalent to .

Example Question #8 : How To Multiply Variables

Let  be negative. Which of the following is the greater quantity?

(A) 

(B) 

Possible Answers:

(B) is greater

(A) is greater

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

(A) and (B) are equal

Correct answer:

(B) is greater

Explanation:

,

So by the multiplication property of inequality, when each is multiplied by the negative number ,

and (B) is greater.

Example Question #9 : How To Multiply Variables

 is a positive number. Which is greater?

(A) One ninth of 117% of 

(B) One eleventh of 143% of 

Possible Answers:

(B) is greater

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

(A) is greater

(A) and (B) are equal

Correct answer:

(A) and (B) are equal

Explanation:

117% of  is equal to .

One-ninth of this is 

 

143% of  is equal to 

One-eleventh of this is 

Regardless of the value of , the quanitites are equal.

Example Question #10 : How To Multiply Variables

Which of the following expressions is equivalent to 

 ?

Possible Answers:

Correct answer:

Explanation:

Use the difference of squares pattern as follows:

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