All GRE Math Resources
Example Questions
Example Question #1 : How To Find Out When An Equation Has No Solution
Quantity A:
Quantity B:
The relationship cannot be determined from the information given.
The two quantities are equal.
Quantity B is greater.
Quantity A is greater.
The relationship cannot be determined from the information given.
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 : How To Find Out When An Equation Has No Solution
Column A:
Column B:
Column B is greater.
The values are equal.
The relationship cannot be determined.
Column A is greater.
The relationship cannot be determined.
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 #3 : 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)
no possible solution
3
0
6
no possible solution
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 : Linear / Rational / Variable Equations
I. x = 0
II. x = –1
III. x = 1
II only
I only
III only
II and III only
I, II, and III
I only
Example Question #1 : How To Find Out When An Equation Has No Solution
–3
1
There is no solution
3
–1/2
There is no solution
Example Question #6 : How To Find Out When An Equation Has No Solution
None of the other answers
A fraction is considered undefined when the denominator equals 0. Set the denominator equal to zero and solve for the variable.
Example Question #1 : How To Find Out When An Equation Has No Solution
Solve:
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 #8 : How To Find Out When An Equation Has No Solution
Solve:
Infinitely Many Solutions
No Solution
No Solution
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 #1 : How To Find Out When An Equation Has No Solution
Solve .
No solutions
No solutions
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 #10 : How To Find Out When An Equation Has No Solution
Quantity A:
Quantity B: 11
The relationship cannot be determined.
Quantity B is greater
Quantity A is greater
The two quantities are equal.
Quantity B is greater
Expand out into
.
Since , it can be seen that
so Quantity B is greater.
All GRE Math Resources
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