Never Miss A Percentage Question On The SAT: The Three Setups You MUST Know

Summary

This 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

00:00

📚 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.

05:02

📉 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.

10:02

📈 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.

Keywords

💡Percent Increase

Percent Increase refers to the rate at which a value has grown compared to its original amount. In the video's context, it is a key concept for solving SAT math problems, particularly those involving time extensions or quantity increases. For example, the script discusses a construction project that is estimated to take 12 percent longer due to bad weather, illustrating the application of this concept.

💡Percent Decrease

Percent Decrease is the inverse of percent increase, indicating the rate at which a value has reduced from its original amount. The video explains how to calculate decreases using the same mathematical framework as increases, but with division instead of multiplication. An example given is the price of a painting that decreased by 8 percent.

💡Calculator Section

The Calculator Section of the SAT is a part of the math test where students are allowed to use a calculator to solve problems. The script mentions that the discussed question types often appear in this section and are considered challenging, particularly questions numbered 29 and 30.

💡Multiple Choice

Multiple Choice is a type of question format where respondents select the correct answer from a list of options. The script refers to multiple-choice questions as the format for the SAT problems being discussed, with specific reference to questions 29 and 30.

💡Conceptual Framework

A Conceptual Framework in the context of the video is a methodological approach to solving a particular type of problem. The script emphasizes the '1 plus or minus' framework as a way to conceptualize and solve percent increase and decrease problems on the SAT.

💡Decimal

Decimal is a way of expressing fractions in terms of tenths, hundredths, etc., and is crucial in the script for converting percent increases or decreases into a form that can be used in calculations. The video teaches students to express percentages as decimals for ease of calculation.

💡SAT

The SAT, or Scholastic Assessment Test, is a standardized test widely used for college admissions in the United States. The video's main theme revolves around solving specific types of math problems that are commonly found on the SAT.

💡Problem-Solving

Problem-Solving in the script refers to the process of finding solutions to math problems, particularly those involving percent increases and decreases. The video aims to teach students how to approach and solve these types of problems on the SAT.

💡Percent Reversal

Percent Reversal is a term used in the script to describe a scenario where the effect of a percent change needs to be 'undone' to find the original value. An example is given where the number of tomatoes grown in 2019 is known, and the task is to find the amount grown in 2018.

💡Consistency

In the context of the video, Consistency refers to the predictability of the SAT in terms of the types of questions and concepts tested. The script points out that understanding the framework for percent increase and decrease can help students tackle similar questions that consistently appear on the test.

💡Test Preparation

Test Preparation is the process of studying and practicing for a test, such as the SAT. The video script is a form of test preparation material, providing strategies and examples to help students prepare for specific math questions on the SAT.

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