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Statistics and Probability Videos 63 videos

SAT Math 1.1 Statistics and Probability
289 Views

SAT Math 1.1 Statistics and Probability. In which of the following data sets are the arithmetic mean and the median equal?

SAT Math 1.2 Statistics and Probability
1060 Views

SAT Math: Statistics and Probability Drill 1, Problem 2. If the four largest numbers in the set were doubled, what would happen to the median...

SAT Math 1.3 Statistics and Probability
276 Views

SAT Math 1.3 Statistics and Probability. Approximately what is the probability that they will be placed in alphabetical order?

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SAT Math 2.5 Statistics and Probability 241 Views


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SAT Math 2.5 Statistics and Probability

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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).

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