Percentages (MK)

What are Percentages?

Percentages are all around us in the world. We are always hearing in stores, “25% of everything!” and “Buy 1 and get 50% of another one!”

But what does it all mean? Lets break down the word, PERCENT. It roughly means “Each Hundred”, but that isn’t going to help you solve the problems now is it? Lets get out of Latin lesson get on these percentage problems!

Ways you will see percentages used in the ASVAB:

1. The question will ask for you to solve a word problem directly or..

2. The question will be part of a word problem

Lets take a look at the more obvious questions you will encounter and then we can handle the more devious ones.

 

Parts of a Percentage Problem

A percentage problem will be made up of 3 parts: X, Y, and a percentage. X is the partial number usually the smaller number (but not always!) Y is the “of” number, this is easily figured out by how it is written in the question (ie What is 50% of 100? Here 100 follows the “of”) and the percentage. Since there are 3 variables, the questions can be asked THREE different ways:

 

QUESTION TYPE A

What is 10 percent of 100?

A. 20

B. 10

C. 15

D. 25
This problem is looking for number that is equal to 10 percent of 100. Here is how we find that out: Multiply the percentage by the target number (Y) and then divide my 100 or  (Percent * Y)/100

So here is what it looks like solved:

100 * 10 is 1000 then divide by 100 to find the answer. To put it all together: 10 percent (10%) of 100 is 10 (answer b)!

 

QUESTION TYPE B

10 is what percentage of 100?

A. 20

B. 10

C. 15

D. 25

This is a very similar question to TYPE A, but what is the problem asking for? The missing factor is the percentage. So lets see how to find the percentage in this problem:

When the percentage is the missing factor, you take the first number (X) and divide by the “of number“. This is easy to find since somewhere in the problem there should be an “of …”. So just divide X or 1o in this example and divide by 100. The equation looks like this: 10/100 = 0.10  This is the decimal equivalent of the answer, to convert the decimal to a “per 100″, you simply multiply it by 100!

10 / 100 = 0.10   to find the percent multiply by 100 or   0.10 * 100 = 10%. This means that the correct answer is B.

 

QUESTION TYPE C

10 is 25 percent of what number?

A. 200

B. 100

C. 150

D. 250

This is the third way you might see a percentage problem. You are given the percentage and the amount of the percentage. We are trying to find the “of number” that we had in the previous problems. The solution is very similar to how we found the answer in TYPE A, but in reverse:

To solve for the “of number”, you first divide the percentage (10%) by 100. This is convert it back into decimal format (10/100 = .10) and then divide the known number by the converted percentage. It looks like this:

25 / 100 = .25  then 10/.25 = 40

If you have problems dividing decimals you can always solve it another way by multiplying the known number by 100 and then dividing my the UN-converted percentage. This way you don’t need to worry about diving by decimals. This is how that would look solved:

10 * 100 = 1000   then 1000/25 = 40.

Which ever way you feel more comfortable with, go with that!

 

PERCENTAGES RECAP

Percentage problems have three parts: the partial number, the “of” number and the percentage.

Figure out which part is missing and which part the question is asking for

To find percentage:

• Divide the partial number by the “of” number then multiply by 100  -  (X/Y)*100 = percent
  

To find the “of” number:

• Multiply partial number by 100 then divide by the percentage   -  (X*100)/percent = Y

To find the partial number:

• Multiply the percentage by the “of” number and then divide by 100  – (Percent * Y) /100 = X

 

One last tidbit before heading down to the video examples:

I have heard that some of the percentage questions are being “disguised” recently. The question will not directly ask “what percent?”, but rather it will give you the decimal value and ask for the missing factor. Here is an example of that:

Bill sold 10 cars this week. The cars Bill sold only represent 0.25 of the total that Bill sold this month. How many total did Bill sell this month?

Here is the tricky part, this is asking for the “of” number, but it doesn’t set it up as a percentage question. They disguise the percentage as a decimal. So if you are stuck on what type of problem you are looking at, see if it looks something like the example. I’ll break down the example for you so you can see how it works out:

• Bill sold 10 cars (this isn’t the total, so it must be the partial number)
• Bill sold only .25 of the total (0.25 is the decimal of the percent, so multiply by 100)
• Bill sold how many total cars? (sound like you need to solve for the “of” number!)
• Solution:    (X*100)/percentage  or (10*100)/25 or 1000/25= 40
  
• Bill sold 10 cars this week, but that is only 25% of the total of 40 cars this month.

If you have any questions please comment and good luck on your studying for the ASVAB exam!

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