Never Miss A Percentage Question On The SAT: The Three Setups You MUST Know
Summary
TLDRThis educational video focuses on solving percent increase and decrease problems, a common and challenging question type on the SAT's calculator section. The instructor introduces a straightforward method using '1 plus or minus the percentage as a decimal' to simplify calculations. Examples include project duration adjustments due to weather, tomato yield comparisons, and sequential price changes of a painting. The video emphasizes the importance of understanding the framework of these problems to tackle them efficiently, offering a valuable strategy for students preparing for the SAT.
Takeaways
- 📚 The video focuses on solving percent increase and decrease questions, which are often among the most challenging on the SAT's calculator section.
- 🔢 Percent increase or decrease problems can be approached by using the formula of '1 plus or minus the percentage expressed as a decimal'.
- 🛠️ For an increase, multiply the original amount by '1 plus the percentage as a decimal', and for a decrease, divide by '1 minus the percentage as a decimal'.
- 🌨️ An example problem involves Jarvis Construction Company, which initially planned for a project to take 250 days but expected it to take 12% longer due to bad weather.
- 🚀 The video suggests a shorthand method for students to quickly grasp the concept of percent increase and decrease, making it easier to solve complex problems.
- 🔄 The concept of 'percent reversal' is introduced, where the task is to undo a percent change that has already occurred, using division to find the original amount.
- 🎨 Multiple percent changes in a sequence are also discussed, with the emphasis on applying the '1 plus or minus' framework to each change before multiplying the results.
- 📉 The video explains how to calculate the original price of an item after it has undergone a series of price changes, using multiplication of the adjusted values.
- 📈 The difference from 1 in the final calculated value represents the overall percent increase or decrease from the original value.
- 📝 The script provides a step-by-step method for solving SAT questions involving percent changes, including simplifying expressions to find the original quantity.
- 🔑 The importance of understanding the '1 plus or minus' framework is highlighted as a key to solving a variety of percent increase and decrease problems on the SAT.
Q & A
What is the main topic of the video?
-The main topic of the video is teaching how to solve percent increase and decrease problems, which often appear as difficult questions on the SAT calculator section.
Why are percent increase and decrease questions considered difficult on the SAT?
-Percent increase and decrease questions are considered difficult because they often appear as the last multiple-choice questions (29 and 30) on the SAT calculator section, and they require a specific approach to solve efficiently.
What is the basic formula used for percent increase and decrease problems?
-The basic formula used for percent increase and decrease problems is to multiply or divide by one plus or minus the percent change expressed as a decimal.
How does the video suggest simplifying the approach to percent increase problems?
-The video suggests simplifying the approach by using the shorthand method of 'one plus or minus the percent expressed as a decimal' to quickly calculate the changes.
What is an example of a percent increase problem presented in the video?
-An example given is Jarvis Construction Company's project initially estimated to take 250 days but expected to take 12 percent longer due to bad weather, which simplifies to 250 days multiplied by 1.12 to get 280 days.
How does the video handle percent decrease problems?
-For percent decrease problems, the video suggests dividing the final amount by one minus the percent decrease expressed as a decimal to find the original amount.
What is the concept of 'percent reversal' mentioned in the video?
-'Percent reversal' refers to problems where you are given the amount after a percent change has occurred, and you need to reverse the process to find the original amount.
Can you explain the strategy for solving problems with multiple percent changes in a row?
-The strategy involves multiplying the original amount by a series of 'one plus or minus the percent change' factors for each change, and then interpreting the final result as a percentage increase or decrease from the original.
What is the common mistake students make with percent increase and decrease problems according to the video?
-The common mistake students make is not correctly applying the 'one plus or minus' framework, which leads to incorrect calculations of the final percentage change.
How does the video suggest using the framework for recent SAT examples?
-The video suggests applying the 'one plus or minus' framework to recent SAT examples by setting up the equation based on the given information and solving for the original or final amount as required by the question.
What is the purpose of the video's suggestion to plug in numbers for testing understanding?
-The purpose of plugging in numbers is to test and reinforce understanding of the framework by using concrete values to verify the calculations and results.
Outlines
📚 Understanding Percent Increases and Decreases for the SAT
This paragraph introduces the topic of percent increases and decreases, a common and challenging question type on the SAT's calculator section. The speaker emphasizes the importance of mastering this concept as it frequently appears as one of the last multiple-choice questions. The paragraph outlines a strategy for solving such problems by using the shorthand method of 'one plus or minus the percent as a decimal,' which simplifies the process of finding the increased or decreased value. The example of Jarvis Construction Company is used to illustrate the application of a 12% increase in project duration due to weather forecasts.
📉 Applying Percent Changes with Multiple Scenarios
The second paragraph delves into various scenarios involving percent changes, including increases, decreases, and a series of consecutive percent changes. The speaker simplifies the process by using the 'one plus or minus' framework, which is applied to examples involving tomato production, painting prices, and cell phone sales. The paragraph clarifies the difference between applying a percent increase or decrease (multiplying or dividing by the adjusted value) and reversing a percent change (dividing or multiplying by the inverse of the percent change). The goal is to help students understand how to quickly identify and solve percent change problems on the SAT.
📈 SAT Consistency and Percent Change Problem-Solving
The final paragraph wraps up the discussion on percent increases and decreases, highlighting the SAT's consistency in testing these concepts. The speaker reviews specific SAT questions, demonstrating how to apply the 'one plus or minus' framework to find the original quantity or the percent change in various contexts. The paragraph reinforces the idea that understanding this framework can make solving these problems straightforward. The speaker also encourages students to practice with real SAT questions and offers to provide further clarification if needed, emphasizing the importance of mastering this skill for test success.
Mindmap
Keywords
💡Percent Increase
💡Percent Decrease
💡Calculator Section
💡Multiple Choice
💡Conceptual Framework
💡Decimal
💡SAT
💡Problem-Solving
💡Percent Reversal
💡Consistency
💡Test Preparation
Highlights
The video discusses how to solve percent increase and decrease questions on the SAT, often the hardest in the calculator section.
Percent increase and decrease questions frequently appear as questions 29 and 30 on recent SAT tests.
A simplified method for solving these problems is introduced, which involves using one plus or minus the percentage as a decimal.
For percent increase, multiply the original value by one plus the percentage in decimal form.
For percent decrease, divide the original value by one plus the percentage in decimal form.
An example is given where a construction project's duration is estimated to increase by 12% due to weather, calculated as 250 days times 1.12.
A 'percent reversal' example is shown where the amount of tomatoes grown in 2019 is 15% more than in 2018, using the formula 2018's amount times 1.15.
To find the original amount before the percent change, divide the post-change amount by one plus the percentage in decimal form.
Multiple percent changes in a sequence are handled by multiplying the one plus or minus percentage factors.
The final value from a series of percent changes indicates the overall increase or decrease from the original by how much it differs from 1.
An SAT question is solved involving a quantity decreased by 45%, using the framework of dividing by (1 - percentage/100).
For SAT question 29, the original quantity is found by dividing the resulting value by 0.55 after a 45% decrease.
Hongbild Hongbo's cell phone sales example illustrates a 128% increase from 2013 to 2014, calculated as the original sales times 2.28.
An SAT question about decreasing a positive quantity x by a certain percent is solved by finding the difference from 1 to the given result.
For a 30% increase in the number of books in a library, the expression representing 2014's quantity in terms of 2002's is x times 1.3.
The video emphasizes the SAT's consistency in the types of percent problems presented, suggesting a reliable framework for tackling them.
The presenter offers to make additional videos for further clarification if needed, showing a commitment to student understanding.
Transcripts
[Music]
all right in this video here we're going
to talk about one question type you need
to know how to solve if you're going to
be taking the sat
and it almost always shows up as one of
the hardest questions on the calculator
section which are going to be 29 and 30
for your multiple choice ones and what
you can see as i've grabbed some
examples from the last two years of the
test is it's a really similar question
time and time again so once you
understand how to approach this it's
going to be something that you can keep
in your back pocket and you're going to
be really comfortable handling when you
see it on test day this is percent
increases in decreases so as always if
you want to go ahead you can pause the
video take a shot at 29 here but we're
going to jump on over
run through a little lesson then we're
going to come back to these and
hopefully you guys are all going to
understand exactly how to approach these
now as always if this video helps you
out please like subscribe share with any
of your friends but let's jump right
into percent increase and decrease all
right so for percent increase decrease
shows up really all the time for those
late questions so
this is a basic way we can set this up
but we're going to talk about a little
bit more of a shorthand way that i
always teach my students because this
really helps it click a lot better for
those difficult question types so we're
going to kind of just go through this
first example here jarvis construction
company is building a new exit ramp for
the local highway the company initially
said the project would take 250 days but
a forecast for bad winter weather led
the company to estimate that the project
is going to take 12 percent longer to
finish so
this is the way you may have been taught
back in math class but the easy
conceptual way which makes some of these
problems click a lot better is if you're
ever doing an increase or a decrease
you're always doing one plus or minus
the percent expressed as a decimal now
if we're applying that percent increase
we're going to be multiplying if we're
undoing it we're going to be dividing
we'll get to that part in a second here
but since we are applying the percent
increase because we know it originally
was going to take us 250 days
and it's now going to take 12 percent
longer we simply can do 250 times 1 plus
our percent expressed as a decimal so
this is going to be the same as 250
times 1.12
and that's going to give us our answer
of 280 without having to do all of the
big setup here
now
that's exactly what's kind of talked
through here so we're going to skip over
that part but for our second example
we're going to see one of what we can
always think of as a percent reversal
where we are undoing the percent change
that already happened
so here we see tim grew 15 more tons of
tomatoes in 2019 than in 2018. so really
conceptually all we're thinking about is
well
2018's amount times 1.15 right that's
going to be our 1
plus or minus is the percent and since
it's 15 more we're doing 1.15 is going
to equal the amount he grew in 2019
but now for all these reversal problems
you're going to be given the amount
after the percent has already been
applied
so only thing we know here is the amount
we grew in 2019 so what we really can
think about is now 1.15
times the amount in 2018 is going to
equal 23 so now we're simply dividing
out the 1.15
the other way we could write this out is
because since we knew he grew 15 percent
more in 2019 than in 2018 is what we
could say is x is going to equal 2018 we
could simply say 1.15
times x
is going to equal 23.
and so here same exact thing we did in
the kind of more talk through example
we're simply going to be dividing by
1.15 and we can find our original amount
now the third really common variety we
see is when we have kind of multiple
percent increases or decreases in a row
but the same thing we always have to
understand for all of these is simply
our one plus or minus and this example
is usually where it really clicks for a
lot of students if they felt a little
iffy
so here the price of a painting
decreased by 8
in 2017.
so that can be expressed because we
always do 1 plus or minus the percent
expressed as a decimal
eight percent is the same as point zero
eight so to start with we can do one
minus point zero eight
it increased by twenty five percent in
2018 so that part we can express is one
plus 0.25
and it increased by 40 in 2019
that can be expressed as one plus 0.40
so what percent greater is the price of
the painting in 2019 than the original
piece at the beginning of 2017 well we
could say p is our original price you
could also put x in here but we could
simply say p times
that one minus .08
is 0.92
that 1 plus 0.25 is 1.25 and that 1 plus
0.4 is 1.4
so we're simply going to multiply all of
those values together and then we're
going to get 1.61 p
but this is what you always have to
remember with these percent increase
decrease which is where the number one
mistake for students comes
it's always your one plus or minus is
going to tell you how much when you're
applying it how much you've increased or
decreased but here if we get our final
value
it's the difference away from 1 which is
going to tell us the amount we increased
or decreased
so since we see 1.61
the 0.61
is going to show us how much we increase
by
so therefore that's going to be 61
percent higher than the price back at
the start of 2017. the big framework
you're always looking out for is 1 plus
or minus that is what all of these
questions kind of come back to so now
we're going to jump back to those
examples from these recent sats we're
going to talk about applying this
framework to each of those all right so
for 29 and this is me the trickiest of
the examples here
a quantity is decreased by 45 percent of
its value the resulting value is x which
expression gives the value of the
original quantity in terms of x well to
make this a little bit easier we're just
going to say that like our original
quantity
is going to be y
so what we know is we're decreasing y by
45 percent of its value and then it's
going to equal x well that's going to be
the same as y times 1 minus right
because this is a decrease our percent
expressed as a decimal so it's going to
be the same as 1 minus
0.45
is going to equal x
now this is going to give us y times
0.55 that's the same as 1 minus 0.45
is going to equal x so if we want to
solve for this so we can see what the
original equation what our original
value is right which is y we're just
isolating for that value
we're simply going to be dividing both
sides of this equation
by
0.55
and that's how we can see that b is our
right answer
now if this didn't click perfectly
strongly recommend you to kind of go
back through this with some values and
we could just say that well
y equals 100 so we're decreasing y by 45
percent that means that x is going to
equal 55 and if you do 55 divided by
0.55
it's going to equal 100. so this is a
little bit of a test trick we can use
with plugging numbers in to find your
original answer but if we can just
conceptually understand the framework we
can really start to make sense of these
questions easily now we'll go through
the next three that are all really
similar and quite a bit easier
hongbild hongbo sold x cell phones in
2013. the number of cell phones he sold
in 2014 was 128 greater than in 2013 so
this one here is exact same basically as
example two and this is going to be the
same framework we saw with example three
back in in our book here
so
the number that he sold in 2014 was 120
percent greater 128 greater than in 2013
so we'll just say that right
x is going to equal our 2013 value well
now this is going to be the same as 1
plus and since it's 128
it's going to be
1.28 is what we're adding in right 28
we'd be adding in 0.28 but 128 we're
adding in 1.28 and the number of cell
phones he sold in 2015 was 29 greater
than 2014
well that's going to be the same as 1
plus
0.29
so all we're now looking for here is
we're going to have x times
2.28
times
1.29
so now we just have to see which answer
choice gives us one that looks like that
and that's simply going to be d as long
as we understand our one plus or minus
we can really start to work through
these questions quite easily
now we'll take a look at these 29 and 30
from two other tests the expression
0.7x represents the result of decreasing
a positive quantity x by what percent
what we always know right it's 1 plus or
minus or percent expressed as a decimal
so all we're really looking for here is
well
1 minus basically we'll say y
is going to equal 0.7 this is just all
we're looking for is just the difference
between these two
and that's just simply going to give us
we'd have to have 1 minus 0.3
is going to equal 0.7
so that's going to tell us how much
we've decreased by
it's simply just going to be 30 because
all we're thinking is 1 minus 0.3 equals
0.7 you don't even really have to do all
this y stuff you can keep it extra
simple like that
very similar thing here with question
30. it's literally just the opposite of
what they put on this other test
the number of books in a library
increased by 30 percent from 2002 to
2014. there were x books in 2002
which expression represents the number
of books in 2014 in terms of x well here
we're simply doing a 30 increase so
we're simply doing one plus 0.3
well that's simply going to give us x
times 1.3 which is going to give us 1.3
x
30 increase we're going to see 1.3
30 percent decrease we're going to see
0.7
so hopefully you feel a lot more
comfortable with this concept and what
this video also kind of shows you is how
incredibly consistent the sat is with
what they put on the test
if you have any questions on this you
can always drop that in the comments
below i'd be more than happy to film
another video going a little more in
depth if anyone feels uncomfortable but
otherwise as always if this helps you
out please like subscribe share with us
with some of your friends
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