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SAT Math 2.5 Statistics and Probability 241 Views
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Description:
SAT Math 2.5 Statistics and Probability
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…
Full Transcript
- 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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