GRE Math : How to find out when an equation has no solution

Study concepts, example questions & explanations for GRE Math

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Example Questions

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Example Question #1 : Equations / Inequalities

Quantity A:

 

Quantity B:

Possible Answers:

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

The relationship cannot be determined from the information given.

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 #2 : Equations / Inequalities

Column A:                              

Column B: 

 

Possible Answers:

Column B is greater.

The relationship cannot be determined.

Column A is greater.

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 : How To Find Out When An Equation Has No Solution

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

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

Possible Answers:

3

0

6

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

Undefined_denom3

 

I.  x = 0

II. x = –1

III. x = 1

Possible Answers:

II only

I, II, and III

III only

I only

II and III only

Correct answer:

I only

Explanation:

 Undefined_denom2

Example Question #2 : How To Find Out When An Equation Has No Solution

Nosol1

Possible Answers:

–3

1

3

There is no solution

–1/2

Correct answer:

There is no solution

Explanation:

Nosol2

Example Question #3 : 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.

Example Question #112 : Equations / Inequalities

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 #3 : Linear / Rational / Variable Equations

Solve: 

Possible Answers:

Infinitely Many Solutions 

No Solution 

Correct answer:

No Solution 

Explanation:

First, distribute the  to the terms inside the parentheses.

Add 6x to both sides. 

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

Example Question #2 : 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 #1 : How To Find Out When An Equation Has No Solution

Quantity A: 

Quantity B: 11

Possible Answers:

The two quantities are equal.

Quantity B is greater

The relationship cannot be determined.

Quantity A is greater

Correct answer:

Quantity B is greater

Explanation:

Expand  out into .

Since , it can be seen that 

 so Quantity B is greater.

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