### All GRE Math Resources

## Example Questions

### Example Question #1 : How To Find Amount Of Profit

Mary buys a car from a mean salesman who charges her 12% over the original price of a $15,000 car. Luke buys the same car from a much nicer salesman who gives him an 8% discount off of the original price. How much more does Mary spend on the car than Luke does?

**Possible Answers:**

$2000

$1200

$3000

$2500

**Correct answer:**

$3000

12% of 15,000 is 0.12 * 15,000 = 1800.

8% of 15,000 is 0.08 * 15,000 = 1200; therefore in total, Mary spent 1800 + 1200 = $3000 more.

### Example Question #1 : Profit Margin

A grade school pays Mr. Day a salary of $24,585 per school year. Each school year contains 165 days. Suppose Mr. Day is sick for a week (5 work days) and the school doesn't have to pay him for those days. Instead, they must pay a substitute teacher to teach his classes. They pay the substitute $90 per day. Totally, how much does the school save for the week Mr. Day is sick?

**Possible Answers:**

The school must pay $59 extra for the substitute teacher.

$59

$295

$205

The answer cannot be determined from the given information.

**Correct answer:**

$295

Divide Mr. Day's salary by 165 to determine how much the school pays him per day: Mr. Day makes $149 per day. They only have to pay substitute $90 per day, saving them $59 per day. To figure out how my they save totally, multiply by 5 to get how much they save for the week Mr. Day is sick: $295.

### Example Question #1 : Profit Margin

What percentage of profit is made on a product sold for $20 if its overall production cost was $17.50?

**Possible Answers:**

46.67%

15.252%

25%

14.29%

87.5%

**Correct answer:**

14.29%

To find the profit percentage, you must first determine the amount of profit made on this transaction. If the sale price was $20 and the production cost $17.50, then the profit made was: 20 -17.5 = $2.50. The profit percentage is determined by dividing the amount of profit made by the original price, or 2.5 / 17.5 = (approx.) 0.14286 or 14.29%.

### Example Question #4 : How To Find Amount Of Profit

Manufacturer X has a base monthly operating cost of $30,000. It makes only one product, which costs $5 per piece in addition to the base operational costs for the plant. These products are each sold for $15 apiece. How many products must the company sell in order to break even in any given month?

**Possible Answers:**

10,000

2,500

3,000

2,000

1,500

**Correct answer:**

3,000

Begin by translating your problem into an equation. What we want to ascertain is the situation when the profit equals exactly 0. The profit and loss for a given month can be summarized by the following equation:

(Total product revenue) - (Base operating costs) - (Individual costs for products) = 0

Given our data, we can rewrite this:

15 * x - 30,000 - 5 * x = 0

Combine like terms:

10 * x - 30,000 = 0

Isolate x:

10 * x = 30,000; x = 3,000.

Therefore, the manufacturer must sell at least 3,000 items per month in order to "break even."

### Example Question #5 : How To Find Amount Of Profit

A new t-shirt has a total cost of 8 dollars for a given retailer. Its current price is $15. If the retailer discounts the cost of the shirt by 20%, how many must it sell in order to make the same amount of profit as when it sold 300 of the shirts at the original price?

**Possible Answers:**

None of the other answers

400

395

525

360

**Correct answer:**

525

First, we must ascertain the original profit. Per shirt, the retailer made 15 – 8, or $7. Selling 300 shirts, it made a profit of $2,100.

The new price, discounted by 20% is equal to 80% of the original price, or 15 * 0.8 = $12. This yields a profit of $4 per shirt.

To ascertain the number of sales needed to make $2,100 in profit, we must solve the following equation:

4x = 2100; x = 525 shirts

### Example Question #1 : How To Find Amount Of Profit

A laptop computer costs $235 to manufacture. If it is sold for $578, what is the percent of profit made on the item?

**Possible Answers:**

343%

145.96%

59.34%

245.96%

53.38%

**Correct answer:**

145.96%

The amount of profit made on the item is 578 – 235 = $343. This is 343/235 or (approximately) 1.4596, which is 145.96% of the original price.

### Example Question #2 : How To Find Amount Of Profit

Sally buys a dress that is a 20% discount from the original price. If she sells it at a 10% markup from her purchase price and profits $10 from the sale, what was the original price of the dress?

**Possible Answers:**

125

100

110

20

120

**Correct answer:**

125

Set Original = O

and Discount = D

then

D = (1 – 20%) x O = 0.80 x O

and Profit = $10 so:

10 = ((1 + 10%) x D) – D = 1.1 * D – D = 0.1D

D = 100

and O = D / 0.8 = 125

### Example Question #1 : Profit Margin

A shirt costs $12 to manufacture. If the marketing and sales costs are a 75% addition to this manufacturing cost. What is the minimum price necessary for making a 50% profit?

**Possible Answers:**

$31.5

$10.5

$21

$18

$16.5

**Correct answer:**

$31.5

Based on the prompt, we know that the additional marketing and sales costs are 12 * 0.75 = 9; therefore, the total cost for purchase and sale is 12 + 9 = $21. To make a 50% profit, we must make 21 * 0.5, or $10.5, on the sale; thus the shirt must be sold for 21 + 10.5, or $31.5.

### Example Question #1 : How To Find Amount Of Profit

A factory has fixed costs of $25,000 per month. It manufactures widgets at a total manufacturing cost of $45 per widget. They are sold at $60. How many widgets must be sold in any given month in order to break even?

**Possible Answers:**

555

1753

556

1666

1667

**Correct answer:**

1667

Let's first represent the total costs per month:

C = 25000 + 45n, where n is the number of widgets manufactured.

The profit can be represented as 60n – C or 60n – 25000 – 45n = 15n – 25000. Now, we merely have to solve this for 0 in order to find the "break even" line.

15n – 25000 = 0 → 15n = 25000 → n = 1666.67. We must sell a whole number of widgets, so it must be 1667.

### Example Question #51 : Percentage

A boy with a lemonade stand sells cups of lemonade for a quarter each. He has bought worth of supplies and is able to make of lemonade with the supplies. If he has to pay a business tax of for each cup he sells, how many cups will he have to sell in order to break even?

**Possible Answers:**

**Correct answer:**

To solve this problem we must first find out how cups he must sell without tax to break even. If each cup of lemonade costs a quarter and he has spent $20 on supplies, that means in order to make back the original $20 he spent, he must sell . Due to this 4% business tax, he must sell 4% more in order to break even. To find that amount, we simply multiply that 4% by the number of cups he must sell without tax to break even, . He must sell an additional 3.2 cups in order to break even, however it is impossible to sell 0.2 of a cup of lemonade, therefore he must sell a minimum of 84 cups of lemonade in order to break even.