ISEE Upper Level Quantitative : How to divide variables

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

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Example Questions

Example Question #1 : How To Divide Variables

The ratio of 10 to 14 is closest to what value?

Possible Answers:

0.24

0.04

0.57

0.71

Correct answer:

0.71

Explanation:

Another way to express ratios is through division. 10 divided by 14 is approximate 0.71.

Example Question #2 : How To Divide Variables

If  is the quotient of  and , which statement could be true?

Possible Answers:

Correct answer:

Explanation:

A quotient is the result of division. If  is the quotient of  and , that means that  could be true.

Example Question #3 : How To Divide Variables

 is a negative integer. 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 which is greater from the information given

Correct answer:

(B) is greater

Explanation:

Since the quotient of negative numbers is positive, both results will be positive.

We can rewrite both of these as products of positive numbers, as follows:

, so

, and 

making (B) greater.

Example Question #4 : How To Divide Variables

 is a negative integer. Which is the greater quantity?

(A) 

(B) 

Possible Answers:

(A) is greater

(A) and (B) are equal

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

(B) is greater

Correct answer:

(A) is greater

Explanation:

Since the quotient of negative numbers is positive, both results will be positive.

We can rewrite both of these as quotients of positive numbers, as follows:

Since the expressions have the same dividend and the second has the greater divisor, the first has the greater quotient.

Therefore, (A) is greater.

Example Question #5 : How To Divide Variables

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

(A) 

(B) 

Possible Answers:

(B) is greater

(A) is greater

(A) and (B) are equal

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

Correct answer:

(B) is greater

Explanation:

The quotient of two negative numbers is positive. The expressions can be rewritten as follows:

Both expressions have the same dividend; the second has the lesser divisor so it has the greater quotient. This makes (B) greater.

Example Question #6 : How To Divide Variables

When evaluating the expression

,

assuming you know the values of all five variables, what is the second operation that must be performed?

Possible Answers:

Division

Addition

Multiplication

Subtraction

Squaring

Correct answer:

Subtraction

Explanation:

In the order of operations, any expression within parentheses must be performed first. Between the parentheses, there are two operations, an exponentiation (squaring), and a subtraction. By the order of operations, the exponentiation is performed first; the subtraction is performed second, making this the correct response.

Example Question #7 : How To Divide Variables

 is a negative number.

Which is the greater quantity?

(a) The reciprocal of 

(b) The reciprocal of 

Possible Answers:

(a) is the greater quantity

(a) and (b) are equal

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

(b) is the greater quantity

Correct answer:

(b) is the greater quantity

Explanation:

Since  is negative, its reciprocal  is also negative. Since 

,

by the Multiplication Property of Inequality,

That is, the reciprocal of  is greater than that of .

Example Question #8 : How To Divide Variables

.

Which is the greater quantity?

(a) The reciprocal of 

(b) The reciprocal of 

Possible Answers:

(b) is the greater quantity

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

(a) is the greater quantity

(a) and (b) are equal

Correct answer:

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

Explanation:

We show that the given information is insufficient by examining two cases.

Case 1: 

The reciprocal of  is , or .

Also, , the reciprocal of which is .

, so (b) is the greater quantity.

 

Case 2: .

The reciprocal of  is , or 2.

Also, , the reciprocal of which is .

, so (a) is the greater quantity.

 

 in both cases, but in one case, (a) is greater and in the other, (b) is greater.

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