ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos


Algebra II Videos 54 videos

SAT Math 4.1 Algebra and Functions
1196 Views

SAT Math 4.1 Algebra and Functions

SAT Math 5.4 Algebra and Functions
291 Views

SAT Math 5.4 Algebra and Functions

SAT Math 8.5 Algebra and Functions
214 Views

SAT Math 8.5 Algebra and Functions

See All

SAT Math 2.5 Statistics and Probability 241 Views


Share It!


Description:

SAT Math 2.5 Statistics and Probability

Language:
English Language

Transcript

00:02

Here’s your shmoop du jour, brought to you by Patterns.

00:06

Because no self-respecting clown ever wore a solid color tie.

00:10

The first term in a sequence is x. Each following term is 2 less than half of the previous term.

00:18

If x is greater than 12, what percent of the first term is the third term?

00:23

And here are the potential answers…

00:28

We can solve this problem while keeping x as a variable.

00:31

The problem tells us that the following term is 2 less than half of the previous, so to find

00:38

the second term, we subtract 2 from half of x, which is our very first term.

00:43

Then, we repeat this process to find the next term.

00:46

We get N sub 3 equals x over 2 minus 2 all over 2 minus 2.

00:58

First, instead of dividing by 2, we can multiply by one-half.

01:03

The x over 2 minus 2 still bothers us though…so let’s multiply the fraction and negative 2 by 2…

01:08

and put them under a common denominator of 2.

01:11

x minus 2 times 2 is 4… all over 2.

01:15

Multiplying that by 1/2, we have x minus 4 all over 4.

01:19

Separating it out from a common denominator, we have x over 4 minus 1.

01:25

But…let’s not forget the minus 2 from before. Negative 1 minus 2 is negative 3.

01:30

So n sub 3 equals x over 4 minus 3.

01:36

Now that our equation looks much better, we can solve the problem with a little logic.

01:40

When we divide a number by 4, we get 25% of the original number.

01:44

A quarter is…25%.

01:50

Now…any x over 4 MINUS 3 will make the number even smaller than 25%.

01:56

And the only answer choice that has a percentage less than 25% is A, at 12.5%.

02:02

Another way to solve this is by plugging in a real number.

02:05

We can start with 24 as x, and divide by 2. We’ll get 12. Then, we subtract 2 to get 10.

02:11

This is our second number.

02:14

To find the third, we repeat. Divide by 2, that's 5, subtract 2, that's 3.

02:20

3 is 12.5% of 24 and our answer is still (A).

Related Videos

SAT Math 2.1 Geometry and Measurement
2779 Views

SAT Math 2.1 Geometry and Measurement. What is the measure of angle z in terms of x and y?

SAT Math 9.4 Algebra and Functions
1300 Views

SAT Math 9.4 Algebra and Functions

SAT Math 9.2 Algebra and Functions
377 Views

SAT Math 9.2 Algebra and Functions

SAT Math: Identifying an Equation for the Average of Two Percentages
23 Views

In 2014, the unemployment rate of one county in California was 7%. In another county, the unemployment rate was 11%. Which of the following express...

SAT Math: Which Equation Represents Profit?
13 Views

Angela is making cookies for a bake sale. She expects each batch of her cookies to sell for $40. It costs her $10 to make one batch of cookies, and...