# GRE Math : Equations / Inequalities

## Example Questions

### Example Question #61 : How To Find The Solution To An Equation

Abby works at a car dealership and receives a commission "c" which is a percent of the profit the dealership makes from the sale, which is the difference between the price "p" of the car and the value "v" of the car. How much, in dollars, does the dealership earn per transaction?

pv(0.01c)

(p – v)(1 – 0.01c)

(p – v)(1 – c)

p(v – 0.01c)

(p – v)(0.01c)

(p – v)(1 – 0.01c)

Explanation:

To show that c is of the profit of the transaction, we must represent the profit as the difference between the price and the value of the car, or "(p – v)"

To show that Abby's commission in dollars is a percentage of the profit, we use 0.01 * c to convert the commission she earns to a percent.

To shift the earnings from Abby to the dealership (which is what the question requires of us), we must take 1 – 0.01c since this will accommodate for the remaining percentage. For example, it shifts 75% (0.75) to 25% (1 – 0.75 or 0.25).

Putting this all together, we get a final expression of:

(p – v)(1 – 0.01c) = dealership earnings

Check answer with arbitrary values: letting p = 300, v = 200, and c = 20, we get a value of 80 which makes sense as the $100 profit must be distributed evenly between Abby ($20) and the dealership ($80). ### Example Question #41 : Equations / Inequalities Sally is 2 years younger than Abby Daisy is 5 years older than Tracy Abby is 6 years older than Tracy A --- Sally's age B --- Daisy's age Possible Answers: The relationship cannot be determined Quantity A is greater Quantity B is greater The two quantities are equal Correct answer: Quantity B is greater Explanation: To simplify the word problem, express the ages in terms of variables in a system of equations. Note that we want to compare S with D: S = A – 2 D = T + 5 A = T + 6 By substituting A for T in the first equation, we can get S in terms of T, which will let us directly compare the values of S and D. S = (T + 6) – 2 = T + 4 If D = T + 5, and S = T + 4, D must be the greater value and Daisy is one year older than Sally. B is the correct answer. ### Example Question #81 : Algebra Quantitative Comparison 3x + 4y = 5 x – y = 6 Quantity A: x Quantity B: y Possible Answers: The relationship cannot be determined from the information given. Quantity B is greater. The two quantities are equal. Quantity A is greater. Correct answer: Quantity A is greater. Explanation: First let's solve for y using the second equation, x – y = 6. x = 6 + y. Then plug this in to the other equation. 3 (6 + y) + 4y = 5 18 + 3y + 4y = 5 18 + 7y = 5 7y = –13 y = –13/7. Now plug this value back into x = 6 + y. x = 6 – 13/7 = 29/7. x is positive and y is negative, so clearly x is larger, so Quantity A is bigger. ### Example Question #85 : Algebra x + y = 12 and 2xy = 6 Quantity A: x Quantity B: y Possible Answers: The two quantities are equal. The relationship cannot be determined from the information given. Quantity A is greater. Quantity B is greater. Correct answer: The two quantities are equal. Explanation: Because there are two different equations for the two variables (x and y), you are able to solve for the value of each. You can rearrange the first equation to show that y = 12 – x by subtracting x from both sides. Then you can substitute this equation into the second equation to give you 2x – (12 – x) = 6. This new equation can be simplified to 2x – 12 + x = 6 3x =18 x = 6 Filling this back into the first equation, we get 6 + y = 12 which means y must also equal 6. Because x and y are equal, we choose the option both quantities are equal. ### Example Question #71 : How To Find The Solution To An Equation A theme park charges$10 for adults and $5 for kids. How many kids tickets were sold if a total of 548 tickets were sold for a total of$3750?

346

269

431

157

248

346

Explanation:

Let c = number of kids tickets sold. Then (548 – c) adult tickets were sold. The revenue from kids tickets is $5c, and the total revenue from adult tickets is$10(548 – c). Then,

5c + 10(548 – c) = 3750

5c + 5480 – 10c = 3750

5c = 1730

c = 346.

We can check to make sure that this number is correct: