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[failedmagician]

Thank you in advance guys..


1. How is 20^5 = 2^10 x 5^5



2. Sales tax on sugar is reduced by 20%, if the revenue of sugar is unaltered, by what % must sales have been increased?

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[ttran9229]

Thank you in advance guys..


1. How is 20^5 = 2^10 x 5^5



2. Sales tax on sugar is reduced by 20%, if the revenue of sugar is unaltered, by what % must sales have been increased?

The first one is broken down by 20^5 = (4^5)(5^5) = (2^5)(2^5)(5^5)
= (2^10)(5^5)

By multiplying exponents together, they are actually added.

 

[failedmagician]

The first one is broken down by 20^5 = (4^5)(5^5) = (2^5)(2^5)(5^5)
= (2^10)(5^5)

By multiplying exponents together, they are actually added.

Thank you, but on the exam..how would ou know what 4^5 is? we have 1 minute per question?! lol

 

[americanpierg]

Thank you in advance guys..


2. Sales tax on sugar is reduced by 20%, if the revenue of sugar is unaltered, by what % must sales have been increased?

K, question 2 is impossible to solve, as the percent of sales increased changes depending on the starting tax percentage. the answer will be a complex function of a variable and not an actual percentange

 

[americanpierg]

Thank you, but on the exam..how would ou know what 4^5 is? we have 1 minute per question?! lol

laws of exponents... or just multiply everything out

20^5
20 * 20 * 20 * 20 * 20
4x5 * 4x5 * 4x5 * 4x5 * 4x5
2x2x5 * 2x2x5 * 2x2x5 * 2x2x5 * 2x2x5

 

[ttran9229]

Thank you, but on the exam..how would ou know what 4^5 is? we have 1 minute per question?! lol

If you actually had to determine the value of the problem, it would be best to work with 20^5 which equates to (2^5)(10^5) or 32 x 10^5 or 3.2 x 10^6.

To calculate 4^5, well, there's no easy way, but the approach I would take is 4^5=(2^5)(2^5)=(32)(32) and do it long hand which should take about 10-15 seconds.

 

[Streetwolf]

Thank you in advance guys..


1. How is 20^5 = 2^10 x 5^5



2. Sales tax on sugar is reduced by 20%, if the revenue of sugar is unaltered, by what % must sales have been increased?

#1 someone said. Rewrite 20 as (2*2*5). Then you have (2*2*5)^5. One exponent law says this equals 2^5 * 2^5 * 5^5. Another law then says it equals 2^10 * 5^5. If you don't know these laws I would definitely go back and review them. You should know them.

#2 is a terrible question but consider this question which asks for the exact same thing (the answer will be identical):

Shirts are marked on sale for 20% off. How much would the sale of the shirts (# sold) need to increase to make the same amount of money?

 

[americanpierg]

#1 someone said. Rewrite 20 as (2*2*5). Then you have (2*2*5)^5. One exponent law says this equals 2^5 * 2^5 * 5^5. Another law then says it equals 2^10 * 5^5. If you don't know these laws I would definitely go back and review them. You should know them.

#2 is a terrible question but consider this question which asks for the exact same thing (the answer will be identical):

Shirts are marked on sale for 20% off. How much would the sale of the shirts (# sold) need to increase to make the same amount of money?

Your 2nd question and his 2nd question are totally different. Your variables are directly related (inversely). His variables are not. A change in x for you will result in an equal change in y in the opposite direction on all occasions ( multiply by .8 for one variable leads to divide by .8 for the second variable [which is an increase of 25%]). A change in x for him will not always result in an equal change in y for his question, as the amount of change in y for him will always be dependent on what "x" is.


20% decrease of a 90% tax requires a lot more sales compensation to retain equal revenue than a 20% decrease of a 1% tax.


your equation is
x= $
y= # of shirts
z= revenue
y is inversely related to x

xy = z

Your change in y would be 1 / ((.8x)/(x)) or just 1/.8 or 1.25


his equation is
x= tax percentage
y= sales
z= revenue
y is inversely related to x+1
xy + y = z
y(x+1)=z

His change in y would be 1/((.8x+1)/(x+1))



very big dfference

 

[Streetwolf]

Your 2nd question and his 2nd question are totally different. Your variables are directly related (inversely). His variables are not. A change in x for you will result in an equal change in y in the opposite direction on all occasions ( multiply by .8 for one variable leads to divide by .8 for the second variable [which is an increase of 25%]). A change in x for him will not always result in an equal change in y for his question, as the amount of change in y for him will always be dependent on what "x" is.


20% decrease of a 90% tax requires a lot more sales compensation to retain equal revenue than a 20% decrease of a 1% tax.


your equation is
x= $
y= # of shirts
z= revenue
y is inversely related to x

xy = z

Your change in y would be 1 / ((.8x)/(x)) or just 1/.8 or 1.25


his equation is
x= tax percentage
y= sales
z= revenue
y is inversely related to x+1
xy + y = z
y(x+1)=z

His change in y would be 1/((.8x+1)/(x+1))



very big dfference

I'm 99% sure this question was posted in a recent thread and the answer was 25% increase. It was a POORLY written question.

 

[failedmagician]

I'm 99% sure this question was posted in a recent thread and the answer was 25% increase. It was a POORLY written question.

It is 25%. Thank you!

 

[failedmagician]

laws of exponents... or just multiply everything out

20^5
20 * 20 * 20 * 20 * 20
4x5 * 4x5 * 4x5 * 4x5 * 4x5
2x2x5 * 2x2x5 * 2x2x5 * 2x2x5 * 2x2x5

Ohhh okay. Easy! Thanks!

 

[americanpierg]

It is 25%. Thank you!

lol its not 25%

 

[failedmagician]

lol its not 25%

The answer is 25%. It's from Crack Math

 

[Pwn]

lol its not 25%

Lol ur not very good at math r u?

 

[UCB05]

a= price per shirt
x= number of shirts sold a original price (a)
y= number of shirts sold at 20% discount (.8a)

total revenues same meaning: (a) (x) = (.8a) >> x=(.8a) / (a)=.8y>>y=a/.8=1.25a>> 25% more

Going back to the original question, it should have read: Sales tax on sugar is reduced by 20%, if the tax revenue of sugar is unaltered, by what % must sales have been increased

 

[americanpierg]

Lol ur not very good at math r u?

2. Sales tax on sugar is reduced by 20%, if the revenue of sugar is unaltered, by what % must sales have been increased?

LOL obviously we can see that you're not since you think the answer is 25%


100% sales tax on $1,000 worth of sugar = $2000 total (tax + sales)
80% sales tax on $1000*1.25 worth of sugar= $2250 total (tax + sales)

$2000 does not equal $2250

Guess I had to spell it out for you in simple math terms without all the xs and ys since they must confuse you... even though common sense would've told you it couldn't have been a straight percentage.

BUT, if you were really intent on solving, use the equation I posted in my reply a couple posts up.

x= tax percentage
y= sales
z= revenue
y is inversely related to x+1
xy + y = z
y(x+1)=z

percent change in y = (1/((.8x+1)/(x+1))-1) * 100
(1/((.8(1)+1)/(1+1))-1) * 100 = 11.11...%

80% sales tax on $1000*1.11... worth of sugar= $2000 total (tax + sales)


What do you know.... same revenue!

Going back to the original question, it should have read: Sales tax on sugar is reduced by 20%, if the tax revenue of sugar is unaltered, by what % must sales have been increased

THANK YOU. THIS answer is 25%, and is a totally different question than what the OP stated, even if it differs by 1 word. Glad to see someone else can see this difference.

 

[Streetwolf]

THANK YOU. THIS answer is 25%, and is a totally different question than what the OP stated, even if it differs by 1 word. Glad to see someone else can see this difference.

This is all nice and good but the book gives the answer as 25%. The book made an error in the question and should have said tax revenue. It was an error in the wording of the question, not in the answer.

 

[americanpierg]

This is all nice and good but the book gives the answer as 25%. The book made an error in the question and should have said tax revenue. It was an error in the wording of the question, not in the answer.

Lol...thats not the point. The point is that there IS an answer to the "wrong" question, and that answer is NOT 25%.


You're compensating for the book providing a wrong answer to the question by assuming that the question itself is wrong. How is that gonna work on the DAT?



HYPOTHETICAL situation

An average healthy human heart pumps 20L of blood per minute
An average healthy human heart pumps 10L of oxygen-poor blood per minute

Q: An average healthy human heart pumps how much volume of blood per minute.

The answer given is 10L. Is the question wrong or is the answer wrong? 99.9% of people will say the answer is wrong, NOT the question. lol I've never seen anyone come to the DAT discussions and say, "Destroyer Question #48 is wrong, but answer is right." The answer is dependent on the question, not the other way around.

Independent variable = question.
Dependent variable = answer.

now to graph that on a cartesian plane...

 

[UCB05]

2. Sales tax on sugar is reduced by 20%, if the revenue of sugar is unaltered, by what % must sales have been increased?

LOL obviously we can see that you're not since you think the answer is 25%


100% sales tax on $1,000 worth of sugar = $2000 total (tax + sales)
80% sales tax on $1000*1.25 worth of sugar= $2250 total (tax + sales)

$2000 does not equal $2250

Guess I had to spell it out for you in simple math terms without all the xs and ys since they must confuse you... even though common sense would've told you it couldn't have been a straight percentage.

BUT, if you were really intent on solving, use the equation I posted in my reply a couple posts up.

x= tax percentage
y= sales
z= revenue
y is inversely related to x+1
xy + y = z
y(x+1)=z

percent change in y = (1/((.8x+1)/(x+1))-1) * 100
(1/((.8(1)+1)/(1+1))-1) * 100 = 11.11...%

80% sales tax on $1000*1.11... worth of sugar= $2000 total (tax + sales)


What do you know.... same revenue!




THANK YOU. THIS answer is 25%, and is a totally different question than what the OP stated, even if it differs by 1 word. Glad to see someone else can see this difference.

Actually, the equation can't be solved as originally stated by the OP. Using your variables and your assumption that revenue equals total sales plus sales tax:

x= tax percentage, and new tax percentage =.8x
y= sales (I assume for simplicity unit price is unchanged, only volume changes)
z= revenue
add w= new sales


y+ yx = z = w+ .8xw
y(1+x)= z = w (1+ .8x)
w/y=(1+x)/(1+.8x)

If you use 100% for x, you would get w/y=2/1.8=1.11 as you illustrated

BUT! try 30% original tax rate instead of 100%
w/y= 1.3/1.24=1.048

Plug in any number for the original tax rates (not given in the original question) and the ratio changes.

Finally, your own calculations will result in variable ratios for different x's using your formula

 

[Streetwolf]

Lol...thats not the point. The point is that there IS an answer to the "wrong" question, and that answer is NOT 25%.


You're compensating for the book providing a wrong answer to the question by assuming that the question itself is wrong. How is that gonna work on the DAT?



HYPOTHETICAL situation

An average healthy human heart pumps 20L of blood per minute
An average healthy human heart pumps 10L of oxygen-poor blood per minute

Q: An average healthy human heart pumps how much volume of blood per minute.

The answer given is 10L. Is the question wrong or is the answer wrong? 99.9% of people will say the answer is wrong, NOT the question. lol I've never seen anyone come to the DAT discussions and say, "Destroyer Question #48 is wrong, but answer is right." The answer is dependent on the question, not the other way around.

Independent variable = question.
Dependent variable = answer.

now to graph that on a cartesian plane...

The DAT doesn't ask overly complicated questions. A straightforward question like (x goes down 20%, what would y need to go up to compensate?) would certainly appear there. I've seen that question asked here so many times in so many different ways.

The DAT study guides can be full of errors. In general the DAT itself is not. If that question was on the DAT word for word then the answer would not be 25%. But since the book gives 25% as the answer and this resembles such a basic COMMON question I'd go and say the question itself is just poorly worded.