GRE Math : Linear / Rational / Variable Equations

Study concepts, example questions & explanations for GRE Math

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Example Questions

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Example Question #1 :Linear / Rational / Variable Equations

Quantity A:

Quantity B:

Possible Answers:

The two quantities are equal.

Quantity A is greater.

The relationship cannot be determined from the information given.

Quantity B is greater.

Correct answer:

The relationship cannot be determined from the information given.

Explanation:

We are given that y = 32. Plug this value of y into the second equation.

32 = x2– 4

36 = x2

x = +/– 6.

Next find a value for Quantity A:

y/7 = 32/7

This number is less than +6, but more than –6. Thus, the relationship cannot be determined from the information given.

Example Question #1 :Linear / Rational / Variable Equations

Column A:

Column B:

Possible Answers:

Column B is greater.

Column A is greater.

The relationship cannot be determined.

The values are equal.

Correct answer:

The relationship cannot be determined.

Explanation:

Column B is greater for positive numbers.

The columns are equal for 0.

Column A is greater for negative numbers.

Because our answer changes depending on the value inserted, we cannot determine the relationship.

Example Question #1 :Linear / Rational / Variable Equations

Find the solution to the following equation if x = 3:

y = (4x2- 2)/(9 - x2)

Possible Answers:

6

3

0

no possible solution

Correct answer:

no possible solution

Explanation:

Substituting 3 in for x, you will get 0 in the denominator of the fraction. It is not possible to have 0 be the denominator for a fraction so there is no possible solution to this equation.

Example Question #2 :Linear / Rational / Variable Equations

Undefined_denom3

I.x= 0

II.x= –1

III.x= 1

Possible Answers:

II and III only

III only

II only

I only

I, II, and III

Correct answer:

I only

Explanation:

Undefined_denom2

Example Question #112 :Equations / Inequalities

Nosol1

Possible Answers:

There is no solution

3

–3

1

–1/2

Correct answer:

There is no solution

Explanation:

Nosol2

Example Question #1 :How To Find Out When An Equation Has No Solution

Possible Answers:

None of the other answers

Correct answer:

Explanation:

A fraction is considered undefined when the denominator equals 0. Set the denominator equal to zero and solve for the variable.

# 47例问题:Algebra

Solve:

Possible Answers:

Correct answer:

Explanation:

First, distribute, making sure to watch for negatives.

Combine like terms.

Subtract 7x from both sides.

Add 18 on both sides and be careful adding integers.

Example Question #1 :How To Find Out When An Equation Has No Solution

Solve:

Possible Answers:

No Solution

Infinitely Many Solutions

Correct answer:

No Solution

Explanation:

First, distribute theto the terms inside the parentheses.

Add 6x to both sides.

This is false for any value of. Thus, there is no solution.

Example Question #1 :How To Find Out When An Equation Has No Solution

Solve.

Possible Answers:

No solutions

Correct answer:

No solutions

Explanation:

By definition, the absolute value of an expression can never be less than 0. Therefore, there are no solutions to the above expression.

Example Question #51 :Algebra

Quantity A:

Quantity B: 11

Possible Answers:

Quantity A is greater

Quantity B is greater

The relationship cannot be determined.

The two quantities are equal.

Correct answer:

Quantity B is greater

Explanation:

Expandout into.

Since, it can be seen that

so Quantity B is greater.

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