What's the Chance, Part Deux

A quick review...

The GED often features one or two probability questions.

You will PROBABLY get one. Or two. 

One way to look at these questions is to think...

The chances of one thing happening...

                           ...divided by all possible chances.

For example, what is the chance of spinning a "yellow" when you use the spinner below?

The chance of the "one" thing is 1. (There is one yellow section.)

The "all possible chances" is 4. (There are 4 sections.)

The chances of one thing happening...

                           ...divided by all possible chances is..

1/4. 

Or... 1 out of 4 or...

.25 or...

25%

(These are all equivalents.)

So... what if you have 2 spinners?

What are the chances of both spinners landing on a section with the word "yellow"?

The chance for the first spinner is ¼

The chance for the 2nd spinner is ⅕

You now need to multiply these fractions.

¼  x ⅕ = 1/20. 

(Remember, 1 x 1 = 1 and 4  x  5 = 20)

What are the chances of both spinners landing on a section with the word "yellow"? 

 1/20. 

What's the Chance? Part 1

The GED often features one or two probability questions.

You will PROBABLY get one. Or two. 

One way to look at these questions is to think...

The chances of one thing happening...

                           ...divided by all possible chances.

For example, what is the chance of spinning a "yellow" when you use the spinner below?

The chance of the "one" thing is 1. (There is one yellow section.)

The "all possible chances" is 4. (There are 4 sections.)

The chances of one thing happening...

                           ...divided by all possible chances is..

1/4. 

Or... 1 out of 4 or...

.25 or...

25%

(These are all equivalents.)

Another example might be...

What is the chance of landing on a colour that has more than 3 letters, when you use the spinner above?

3/4. 

Or... 3 out of 4 or...

.75 or...

75%

So... what if you have 2 spinners? 

See the next post.

"Than" is the Man

Word questions in Algebra. 4 words to...

...scare anyone. However, there is hope...

Remember, "than" is the man. "Than" is the key to solving these questions. For example...

3 numbers add up to 180. The smallest is 20 less than the largest. The third is 10 more than the smallest. Name the three numbers.

These numbers are referenced against the other numbers. The word "than" helps us here. I see the word "smallest" appear twice, so I am going to use that as my reference, or "x". The word that appears the most should become your reference.

So...

...       if...

...the smallest is 20 less than the largest, then the largest must be 20 more than the smallest, 
or x + 20. We now have...

1) The smallest = x
2) The largest = x + 20

We just need the third number.

The third is 10 more than the smallest. The smallest = x, so the third number must be x + 10.

We now have...

1) The smallest = x
2) The largest = x + 20
3) The third number = x + 10.

Still don't have an answer, though, do we?

We will have an answer, however, if we build an equation...

We know that the 3 numbers add up to 180, so...

x + x + 20 + x + 10 = 180

Group your " x's "...

3x + 20 + 10 = 180

Group the 20 and 10...

3x + 30 = 180

Drop 30 from each side..

3x = 150

x = 50

Still don't have an answer, though, do we?

Almost there - promise...

x = 50

Remember...

1) The smallest = x, so the smallest number is 50.

2) The largest = x + 20, so the largest is 70.

3) The third number = x + 10, so it is 60

50 + 60 + 70 = 180 

In the Dog House, Part Deux - Captain Zero to the Rescue (Yet Again)

A quick review...

Look familiar? 
Pat scored 54 out of 200 on a test. What percent is this?

The key to solving these types of questions comes in the words " out of ".

The " out of " number needs to be thrown " out of " the house.  200 is not allowed in the house.

54 is inside...

and 200 is out of the house, in the dog house...

So now we have...

200 divided into 54. 

This is a job for Captain Zero. (More powerful than a speeding doughnut, able to leap tall O's in a single bound...)

Put as many zeroes as you like. Captain Zero never runs out. Make sure you put a decimal point immediately to the right of the 54, and one directly above.

Now you have a standard long division question.

Looking at the roof line, you will see that 27 is to the right of the decimal. Whatever is to the right of your decimal becomes your %. So...

.27 = 27%

.03 = 3%, etc.

Pat scored 54 out of 200 on a test. What percent is this? 27%

In the dog house

Look familiar? 

1) Pat scored 54 out of 200 on a test. What percent is this?

or...

2) 36 out of 300 people ride bikes to work. What percent is this?

The key to solving these types of questions comes in the words " out of ".

The " out of " number needs to be thrown " out of " the house. 200 has forgotten the wedding anniversary (yet again!) and has to go and sleep in the dog house. 200 is not allowed in the house.

54 is inside...

and 200 is out of the house, in the dog house...

So now we have...

 200 divided into 54. 

This is a job for Captain Zero and will be covered in the next blog post. 

Note: Do not get into the habit of assuming you are dividing the "bigger number" into the smaller one. You might get a question such as...

Pat scored 154 out of 150 on a test. Bonus marks were scored! What percent is this? 

If Pat scored more than 150, then the answer has to be more than 100%. In this case, 150 is your " out of " number.

          

Inequalities < > (#@!^@@@$$$!!!!!)

Look familiar?

"Which inequality is represented by this picture?"



Well, you've always got 4 options. Something (usually represented as "x") is either...


1) Greater than a given number
2) Greater than, or equal to, a given number
3) Less than a given number
4) Less than, or equal to, a given number



Examples...

1) Greater than a given number

Answer      x > -1 (x is greater than minus 1)

2) Greater than, or equal to, a given number

Answer      x > -1 (x is greater than, or equal to, minus 1)

Notice a difference? If the circle above the number line is OPEN, your < or > sign has NO line under it. 

If it is a closed circle, your < or > sign has a line under it. 

This line signifies "or is equal to."

3) Less than a given number

Answer      x < -1 (x is less than minus 1)

4) Less than, or equal to, a given number

Answer      x < -1 (x is less than, or equal to minus 1)

Ah, yes, the good old Circular Lawn or Swimming Pool Question

You may get a question that not many people, outside of a math test, would worry about. Or think about.

The old circular lawn or swimming pool question.

As the incredibly professional-looking graphic above looks more like a pool than a lawn, let's go with this type of question...

A circular pool has a sunbathing deck in the middle. The distance from the centre to the inner edge of the water is 4m. The distance from the centre to the outer edge is 6m. What area does the water cover?

(Hint: It isn't 2 metres.) 

What is missing?

Imagine the pool deck is a like the centre of a pie that has been eaten.The water is the pie that hasn't been eaten. So, work out the area of the whole pie and subtract the area of the piece that was eaten. What is left is your answer.

The area of a circle is...

pi X radius squared

So...

pi x 6 squared         subtract        pi x 4 squared

62.83 square metres.

Note: You won't get the right answer by working out pi x 2 squared (2 being the difference between 6 and 4.)

Perhaps the easiest way to remember this is  

pi x big radius squared  

subtract 

pi x small radius squared