Percents & Ratios

Percent decrease in a value is..

"change" divided by original amount.

The GRE may try to trick you by asking you what is the value of .03 percent of a given value, but remember that .03 percent is really ...

.03 (1/100), which is .0003. so the GRE is really asking you to find (0.003) (Principle value). DO NOT let the decimal point trick you.

Be careful when dealing with percents and their representations, remember that ..

.50 percent is not the same as .05% ( a mistake you made). 6/12 = 1/2 = .50, But 6%/12 = 1/2% = .05%

When performing compound Interest problems, remember that the rate is a percent increase, which means your multiplier will be ...

1+ the rate or (1+R), which represents more than a 100% increase. So if a principle value experience a compounded interest annually for one year, then it would be A (1+R), for two years it would be A (1+R) (1 +R)

When trying to solve any problem on the GRE, here are the steps you should follow ....

1. Analyze the question 2. Identify the task, Approach strategically 3. Confirm your answer.

Other ways to express a product multiplier in words is to use the terms "less than" and "more than". For example if you say Tuk weights 60% more than Kim, we would use the product multiplier ...

1.6 because Tuk weighs 60% more than Kim. That means Tuk weighs 160% of Kim's weight; thus we use 1.6 instead of 0.6. The same goes for 1.25. Pat weighs 25% more than Lee, so Pat weighs 125% of Lee's weight, and we use 1.25.

When dealing with percents when we're not given specific numbers, ______ is a good number to use.

100

Practice: When dealing with Percents if you have to compare a percentage of a number over 100 to any other number, simply first figure out the percentage of ...

100, and then use that to inform your comparison. Ex if you are asked to figure out 35% of 203, well you already now that 35% of 100 is 35, so doubling this would let us know that our answer is a little higher than 70.

Product multipliers example...

20% decrease of $100 is .80

In terms of portioning... 3 boys and 5 girls is..

3 part boys, 5 part girls which is a total of 8 parts to create the whole.

36% means

36/100

In ratio form, 36% can be represented as ...

36/100

3.6% can also be written as ...

360/100

Example of product multipliers...

60 % increase of $100 is 1.6

Rate

A ratio that contains different units in the numerator and the denominator.

Ratio

A relationship between part to part, or whole to whole.

Compound Interest

A unique situation where the dollar amount added is never the same for each cycle of time, but the percent increase stays the same.

The equation for compound interest is ...

A= P(1+r/n)^nt, where A is the "amount", P is the "principle value",R is the "rate of interest", n is the amount of times per year the interest is compounded, and t is "time in years". Simply stated it is the amount [Principle value] (x) the percent increase per cycle [ 1 + r/n] (x) the amount of cycles required [nt].

When dealing with ratios...

Always think about the scale factor or each ratio. Within a ratio, you should always think of the denominator as being multiplied by a factor, and the numerator as being multiplied by that same factor.

Representation of ratios...

Are never the true representation of the full quantity.

A more specific and direct way of Picking Numbers is to ...

Back Solve. When Back solving you simply pick one of the 5 answer choices and plug it back into the question. Remember that the numerical answer choices are always in ascending or descending order. As a result always start testing with answer choice (B), and if (B) turns out to be too small then try answer choice (D). Back solving allows you to find the correct answer without ever needing to test more than two of the answers.

This form of cancellation within fractions in proportions can be done...

Between the numerator and the denominator within the same fractions. Between the two numerators on both sides of the equal sign. Between the two denominators on both sides of the equal sign.

With Proportions, you can

Cross Multiply. But with proportions, always cancel/simplfy before you cross multiply.

This form of cancellation within fractions in proportions cannot be done...

Cross cancellation across the equal sign

3:4, 3/4, or 3 to 4 means...

For every 3 portions, there is 4 portions. Which also means there are 3+4 or 7 total parts. Another example is, ratio of Apple trees : Peach trees : Cherry trees is, 2 : 3 : 6. So For every 3 peach trees, there are 2 apple trees and 6 cherry trees. If we sum these values, we get 3 + 2 + 6 = 11 trees That means that in every set of 11 trees, there will be 3 peach trees, 2 apple trees, and 6 cherry trees. We want to know how many peach trees there are in the orchard, which contains 33 trees total. That means that there are 3 sets of 11 trees in the orchard, and in each set there are 3 peach trees. 3*3 = 9 peach trees total.

Proportion has the form

Fraction equal fraction, ratio equals ratio

Ratios can also be expressed in fraction form, when changes our in the full quantity. Ex...

If the ratio between two items is A/B, but for some reason a loses a value of 15, then the ratio now becomes (A-15)/B, where you can compare it to the original ratio which is A/b. So it really should be [(A-15)] / (B) = (A)/(B), where you can now cross multiply.

What does the "Ratio Sum Rule" state?

If two positive integers (x, y) have the sum of "K", and the ratios of those same integers is x:y, then "k" must be divisible by x + y. In other words, The important thing to notice here is that if a group/number can be split up into a ratio of x:y, then that number must be divisible by x+y. Ex: When the whole is 24, a possible ratio could be 1:2, because 1 + 2 = 3 , and three is divisible by 24. The same is true for 3:5, 1:1 or 7:5

Whats the difference between "wholesale" and "retail" merchandise...

In simple terms, retail means that you, the product manufacturer or producer, sell your product directly to the consumer. Selling wholesale means you typically sell your product in bulk quantities to a "middle man" who in turn sells it to the consumer

How would you describe 2/7

Is 2 divided by 7 , 2 portions of 7 total pieces, or 2 out of 7

Scale factor

Is the power link that controls the flow between the ratio and information about full quantity

When problems solving, depending on the type of problem, you may need to use the straightforward math-the textbook approach- to calculate the answer. Or you may need to use an alternative method such as Picking ...

Numbers, Back Solving or Strategic Guessing.

Combining Ratios ( method 1)

One method is to find the equivalents, so that common terms are equal in both ratios, then combine ratios.

The algebraic representation of the "percentage of a given amount" is ..

Part/whole

When dealing with problems that are difficult to solve, problems where either the question or the answer choices have variables, problems that tests a number property you don't recall, or problems where the question and answer choices deal with percents or fractions without actual values, these situations would be perfect candidates for the ...

Picking Numbers Strategy.. Ex: Pick 100 for nice round numbers. Imagine if the prompt stated ... At a certain company, 30 percent of the male employees and 50 percent of the female employees have an MBA. If 40 percent of the employees are female, what percent of the employees do not have an MBA? 100 would be the easiest number to start from.

When dealing with rates, its always easiest to setup...

Ratios in relation to Proportions

Simple formula to remember, Profit = ...

Revenue - Cost, where revenue is how much money "earned or gained" and "cost" is how much money spent.

When dealing with Proportions, 1st you should...

Simplify through cancellation

Combining Ratios (method 2)

Solve for one individual value,meaning find the scale factor. Then use the ratios and scale factor to solve for each additional value. Ex: The ratio of two scores is 2:x:7, but after two years the ratio becomes 4:10:14, what is the value of x? You can divide 4 by 2 which produces 2. Then divide 10 by 2 which would produce 5, where 5 is the answer. Another alternative is to realize that 2/4 is 1/2, so you can setup a proportion where 1/2= x/10, through cross multiplication you would find that x=5.

If you can eliminate some of the answer choices by applying number property rules or by estimating because of gaps between answer choices are wide. then this is a great candidate for ...

Strategic Guessing

Simple Interest

Unique situation where the same dollar amount is added for each cycle of time. The equation is Simple Interest = (Principal Interest) (Rate) (Time)

When dealing with percent decrease and increase...

Use product multipliers

Portioning

When we think of ratios in terms of parts and wholes.

A "Product Multiplier" refers to ...

a decimal percent that aides in finding the percent change of a value.

When dealing with ratios, it sometimes may be easier to work with portioning when dealing with ratios which represents...

a division among groups. For instance, if the prompt states that between person "A" and person "B" there is a 6/5 ratio that represents how "x" amount of dollars is divided. In this scenario we understand that for every 6 that "A" receives, "B" receives 5 of total "x". We also understand that 6+5 is 11, which represents one whole, which means "A" receives the percentage equivalent of 6/11 of "x" and "B" receives the percentage equivalent of 5/11 of "x".

A rule states that if you have a/b=c/d, then ...

a(d)=b(c). Simply another way to represent cross multiplication.

In sequential percentage change, never ...

add and subtract percentages, instead use product multipliers.

When problems solving, before you answer the question, be sure you understand what is being asked. This will give you a better idea of what the correct ...

answer should look like. This is important because the GRE will intentionally provide wrong answers for those who get the right answer to the wrong question.

When dealing with compound interest problems, when you see the words "Approximately" within the prompt and the and answer choices are spread out, this is a good indication that ...

average the values provided within the prompt into nice round numbers, and plug in the answer choices to a simple interest formula, where the answer will indicate around what area the true answer will fall. Ex:If someone deposits 61,000 in an account that is compounded quarterly and in five years she has 76,000, Approximately what was the annual percent rate of interest. In this scenario, just make the numbers 76,000 and 61,000, where there is a difference of 15,000, so divide 15000 by the original to receive the percent increase of 25%. Divide this by 5 years and on-average it increased annually by 5%

To go from decimal to percent, multiply ..

by 100. To go from percent to decimal, divide by 100. Formula for converting to a percent, A/B= 100A/B = A/B%

You can quickly approximate the percentage value of a fraction by multiplying the denominator by ...

by a number that gets you closer to 100 ( multiply the numerator and denominator by the same value). Then compare that value to the actual fraction with the 100 value as the denominator. EX: 3/4 = 3 (25)/ 4(25) = 75/100 or .75

When Picking Numbers to substitute for variables, choose numbers that are manageable and fit the ...

description given in the problem. For example when dealing with percents, you can choose 100%. Or if the prompt states when a variable "x" is divided by 3 it has a remainder of two. In this case a good number for the variable would 5, 8 or 11

"Percent" or percentage symbol (%) means ...

divide by 100 or multiply by 1/100

When dealing with compounded interest...

divide the proposed annual compounded interest by the amount of times it occurs each year, to find the percent increase for each cycle. Apply that percent the full value, to give you an idea about how much the principal value will increase each cycle.

When dealing with word problems involving decimals. Remember that "is" means ...

equal, "of" means to multiply .

Product multipliers can also be represented in the form of ...

fractions. Ex: if someone spent 1/3 of their earnings today, and spent 2/5 of the remaining earnings the next day, then that person spent (2/3)(3/5) of there earnings or (2/3)(3/5)x.

Whenever you start any problem from any section or difficulty, you should first always ...

look for ways to reduce or simplify the problem.

When dealing with percents, fractions and whole numbers, you must understand and see the connections. By seeing the relationships, you will be able to ...

manipulate properties and facts to solve problems. Ex: when a prompt asks for 20% of 35, you should see 20% as 1/5, and see that 1 of 35/5 is 7. Or 10% of 35 is 3.5, so 201% is 7. Similarly 15% of 35, you should see 3/20 of 100, where 1 of 100/20 is 5, so 3 of 100/20 is 15.

When setting up proportions to solve rates, make sure the units on both side of the numerators and denominators...

match

When problem solving on the GRE, you need to unpack as much information as possible by first asking what area of ...

math is the question testing you on. Next what are the trends in the answer choices. For instance do the answer choices have only numbers, numbers & variables, non integers. Identifying the trend will help you better understand how to go about solving the answer..

The sum of the denominator and numerator represents how many ...

parts exist in the entire whole "portioning".

When dealing with percent increase and decrease, although you have a calculator available to you, it is important that you use your...

portioning abilities as well. Ex: if a calculator tell you that a jump form 40 to 170 is a 320% increase, through portioning you should clearly see that increasing by 40 to 160 is 300% because you 40 +40 +40 +40 , or 40 + 100% of 40 + 100% of 40 +100% of 40. So the answer should be a little over 300%

When dealing with compound interest problems and the exact equation, think of the "(1+r/n)" portion as the ...

product multiplier. Remember that a product multiplier is the 1+(interest rate), the interest rate is divided by how many times the cycle occurs per year. So really that section can be expanded to represent 1+ P/100 (1/n), where "n" is how many times the cycle repeats per year and "P" is the interest as a percent.

When dealing with percentage multipliers, if percent changes occur in a row, and you are looking for the overall percent change, simply multiply the ..

product multipliers of each percentage change, and the result is the product multiplier for the overall percent change. Ex: if a price is increased by 25% and then the new price is increased by 25% then the original price is increase by a product multiplier of (1.25) (1.25) = 1.5625, and where the actual percent increase is 56.25.

When dealing with word problems that set up scenarios involving changing values due to fractional changes, it may be easier to think of everything in terms of ...

proportions of the whole. Ex if you are told that there are $32 remaining after Ginet took 1/3rd of the original amount. You should quickly see that since 1/3rd was removed, this must mean that 2/3rds remains. So $32 represents 2/3rds of an unknown value. Divide 32 by 2/3rds and we find that the original value was $48.

When dealing with compounded interest problems, think of time as a ...

ratio. An amount compounded quarterly would be an interest multiplied by 1/4, or 1 year/ 4 times. Another example would be compounded every other month, where the interest is multiplied by 1/6.

Prices are always in the same ...

ratio: in other words, we can always use proportional thinking to figure out the new price of a new quantity of an item. Ex: if a problem states that you can buy 4 cans of milk for $2, how many cans can you purchase for $6, then you can easily set up a proportion 4 cans/$2 = X (cans)/$6, to solve this answer.

Percents can also be thought of as ...

ratios. Ex. when comparing 24% of a principle value , and 20% of a principle, you can think of it as 20%/24% since they are portions of the same principle value. From this we understand that 5/6(24%) (Principal value) = 20% (Principle Value)

If the situation arises that you need to estimate the value of a compound interest problem or the prompt uses the word "Approximately", just simply use ..

simple interest. The answer for compound interest will be somewhere in the vicinity of the answer for simple interest.

When you divide by 100 the number gets...

smaller, but when you multiply by 100, the number gets larger.

There may be situations where you can combine approaches when problem ...

solving. For instance you could use straight-forward math to simplify the question and then pick manageable numbers for the variables to solve that equation.

When the prompt states that a barrel or container is 1/3 full, this means that ..

the container is 33% filled or 2/3rds empty, or algebraically it means that (1/3)(x) is filled. Remember to always include the variable, because it is representative of the whole amount.

The GRE knows that people generally divide part by whole when trying to find a percent , and then mentally move the decimal point over to the left two places. So it will try too trick you by providing answer choices that have ...

the decimal form of the part divided by the whole,with a percent sign but without moving the decimal point. So you have to remember, to divide part by whole, and then move the decimal point to the right two places or multiply by 1/100 before adding the percent sign.

To go from fraction to percent, divide the numerator by ...

the denominator. and then multiply by 100.

The percent change between two values is simply ...

the difference between the new value and the original value ( or larger value minus smaller value), divided by the original value. Ex: an item was 20 dollars, but is now 10 dollars. 20-10/ 20 = 10/20= 1/2 or .50 (100) = 50% decrease

Compound interest always produces a larger value amount than simple interest, except during ...

the first cycle where the value increase is the same.

The smaller the compounding period is, the greater...

the number of times the interest will be compounded. As a result, the number of times we compound goes up, but the percentage by which we compound each time goes down. Therefore, we will get the most money with the smallest compound period; seconds being the smallest, than minutes, than hours, than daily and so on.

Its very important that you keep an eye out for the trap that is inherently apart of percent increase problems. Remember that a 100 percent increase means that the value has increased by double, a 200 percent increase means that the value increased by triple, and a 300 percent increase means that the value increased by quadruple. A simple way to avoid the mistake of thinking that a value that the numerical increase is the same as the percentage increase is to always apply...

the percent change formula which states that the percent increase or decrease is the final value minus the original value, divided by the original value. Or it is the percent change divided by the original. Ex: the price went up from 20 to 40? well the price doubled in price numerically, but relating to percentage, it was 40-20=20, 20/20=1, 1 x 100 =100% increase.

When you are trying to find the percentage value of one quantity by dividing it over the whole, you can estimate it by comparing ...

the values in the tens or hundreds place within both quantities. Ex: When trying to find what the percentage value of 123/749, you can say what is 1/7 which is 0.14 or what is 12/79 which is close to 12/72 which is 16%, so it makes sense that 123/749 is 16.4%

More often than not, the prompt will ask you to find a number when dealing with percents, but in the rare occasion that it asks you to find a percent, it may be easier..

to ignore the whole numbers provided by the prompt and just use simple numbers using the same percentage scenarios. Ex: If 355 birds are tagged which represents 20% of the total, what percent of the untagged birds should be tagged in order for half of all birds to be tagged? In this situation, simply use the 10 birds, were 20% or 2 are tagged and 3/8 ths or 37.5% of the remaining birds need to be tagged so that half of all are tagged.

On Average you have 1 min and 30 seconds to solve each question, but if you happen to finish the question quicker than the allotted amount of time, then you should ...

use the extra time to check your answer and your math.

A rule relating to percent states x% is ...

x/100 Ex: x percent of 3/2 is? x/100 (3/2)= 3x/200