GRE Math : Linear / Rational / Variable Equations
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Example Questions
Example Question #51 : Equations / Inequalities
Jon invested part of $16,000 at 3% and the rest at 5% for a total return of $680.
Quantity A: The amount Jon invested at 5% interest
Quantity B: The amount Jon invested at 3% interest
The two quantities are equal
Quantity B is greater
The relationship cannot be determined from the information given
Quantity A is greater
Quantity A is greater
First, let 
Solve for 
Example Question #81 : Equations / Inequalities
Audrey, Penelope and Clementine are all sisters. Penelope is 8 years older than Clementine and 2 years younger than Audrey. If the sum of Penelope and Clementine's age is Audrey's age, how old is Clementine's age?
Let 
Since 
Furthermore, 
Through substitution, 
Example Question #91 : Algebra
If 
We could use the substitution or elimination method to solve the system of equations. Here we will use the elimination method.
To solve for 
Multiplying the first equation times 2:
Adding this result to the second equation:
Isolate 
Example Question #51 : Equations / Inequalities
If 
Since the expression we want just involves z and x, but not y, we start by solving 
Then we can plug that expression in for y in the first equation.
Multiply everything by 12 to get rid of fractions.
Example Question #55 : Linear / Rational / Variable Equations
If 
Use inverse operations to isolate x. Working from the outermost part on the left side, we first divide both sides by 5.
To isolate the x term, subtract y from both sides.
Finally, isolating just x, divide both sides by 3.
Example Question #81 : Equations / Inequalities
If 
Cannot be determined
You can solve this problem by plugging in random values or by simply solving for k. To solve for k, put the s values on one side and the k values on the other side of the equation. First, subtract 4s from both sides. This gives 4s – 6k = –2k. Next, add 6k to both sides. This leaves you with 4s = 4k, which simplifies to s=k. The answer is therefore s.
Example Question #57 : Linear / Rational / Variable Equations
The sum of two consecutive odd integers is 32. What is the value of the next consecutive odd integer?
Cannot be determined
Let 
We have that 15 and 17 are the consecutive odd integers whose sum is 32, so the next odd integer is 19.
Example Question #81 : Equations / Inequalities
John has $50 for soda and he must buy both diet and regular sodas. His total order must have at exactly two times as many cans of diet soda as cans of regular soda. What is the greatest number of cans of diet soda John can buy if regular soda is $0.50 per can and diet soda is $0.75 per can?
75
50
None of the other answers
25
51
50
From our data, we can come up with the following two equations:
0.50R + 0.75D = 50
2R = D
Replace the D value in the second equation into the first one:
0.5R + 0.75 * 2R = 50
0.5R + 1.5R = 50; 2R = 50; R = 25
However, note that the question asks for the number of diet cans, so this will have to be doubled to 50.
Example Question #31 : How To Find The Solution To An Equation
Quantity A
Quantity B
The relationship cannot be determined from the information given.
Quantity A is greater.
Quantity B is greater.
The quantities are equal.
The quantities are equal.
In order to solve for y, place x in terms of y in the first equation and then substitute that for x in the second equation.
The first equation would yield: 
Substituting into the second equation, we get: 
Simplify:
Example Question #1 : Algebra
If 6x = 42 and xk = 2, what is the value of k?
1/7
1/6
5
7
2/7
2/7
Solve the first equation for x by dividing both sides of the equation by 6; the result is 7. Solve the second equation for k by dividing both sides of the equation by x, which we now know is 7. The result is 2/7.
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