Percentage - GRE Quantitative Reasoning

To do this problem, translate each expression into mathematical terms:

is percent of :

is percent of :

Quantity B is greater.

To solve this problem, consider writing the quantities in terms of only fractions:

Quantity A: 20% of

Quantity B: 30% of

Quantity B has the smaller denominator for an equal numerator. There is no need for calculation beyond this, and time on the GRE would be best spent elsewhere.

Quantity B is greater.

This problem is fairly simple. If we know he scored a , then we know that he got correct answers.

Both the numerator and denominator of the expression are divisible by two, so your final, simplified answer should be:

.

To solve this problem, first convert the percentage into a decimal by dividing the percentage by 100:

Then, you can convert the decimal into a fraction:

Both the numerator and the denomenator are divisible by , so now you may simplify:

To find your answer, first convert the percentage into a decimal:

Then, you can place the digits of the decimal over one, followed by a number of zeroes equal to the number of digits (in this case, 1,000):

Both the numerator and denomenator are divisible by , so you can simplify to:

To convert, simply first convert the percentage into a decimal:

Then, you can convert the decimal into a fraction, by putting the digits over one, followed by a number of zeroes equal to the number of digits:

Both are divisible by five, so you can simplify:

To convert, first express the percentage as a decimal:

Then, you can place the digits of the decimal over one followed by a number of zeroes equal to the number of digits:

Both of these numbers are divisible by , so you can simplify:

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.

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.

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%.

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."

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

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.

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

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.

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.

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.

The easiest way to convert between percent and decimal is to first convert the percentage into a fraction:

Then, from the fraction, you can convert quite easily to a decimal:

HOWEVER--in this problem, they are asking you for the portion that makes up the rest of the cereal--so you need to subtract your decimal above from , which yields the correct answer:

When converting percents into decimals, know that the tens and ones digit of the percent will occupy the tenths and hundredths places of the decimal. Any decimal following the whole percent will follow in sequence (i.e. the first decimal place in a percent corresponds to the thousandth place, and so on). Therefore, ninety-seven point five percent is equal to: