Formula Help

[Bobbi]

Please Help!

I am studying for the GRE and came across a question that I am struggling to solve. No "correct answer" is provided.

The question is:

DATA CHART QUESTION

What was the change in total health spending, as a percent, from 1990 to 2010 (rounded to the nearest tenth)?

Total Health Spending in 1990 = +5%
Total Health Spending in 2010 = +9%

I don't know the proper formula or approach to solving this question. :sad:

PLEASE HELP AS SOON AS POSSIBLE!

 

[tkhunny]

Are you sure you have included the entire question?

Perhaps it is intended that you observe the compound nature of percentage increases.

A five percent increase might be modelled as multiplicaion by 1.05
A nine percent increase might be modelled as multiplicaion by 1.09

Both, taken consecutively, then, might be 1.05 * 1.09 = 1.1445 or a 14.45% increase.

 

[Bobbi]

Are you sure you have included the entire question?

Perhaps it is intended that you observe the compound nature of percentage increases.

A five percent increase might be modelled as multiplicaion by 1.05
A nine percent increase might be modelled as multiplicaion by 1.09

Both, taken consecutively, then, might be 1.05 * 1.09 = 1.1445 or a 14.45% increase.

Thank you so much for your quick response. It is a multiple choice question and 14.45% is not one of the answer. I'll attempt to tell re create the chart and question exactly.

Question: What was the change in total health spending, as a percent, from 1990-2010 (rounded to the nearest tenth)?

Answers Choices:

A) 29.0%
B) 29.2%
C) 30.7%
D) 31.5%
E) 32.3%

	1990-1995	1995-2000	2000-2005	2005-2010
Education	+8%	+9%	+1%	-3%
Transportation	+2%	+5%	-3%	-5%
Police	+3%	+4%	+0%	-2%
Health	+5%	+8%	+7%	+9%
Other	+2%	+7%	-10%	-8%

 

[Deleted member 4993]

Thank you so much for your quick response. It is a multiple choice question and 14.45% is not one of the answer. I'll attempt to tell re create the chart and question exactly.

Question: What was the change in total health spending, as a percent, from 1990-2010 (rounded to the nearest tenth)?

Answers Choices:

A) 29.0%
B) 29.2%
C) 30.7%
D) 31.5%
E) 32.3%

	1990-1995	1995-2000	2000-2005	2005-2010
Education	+8%	+9%	+1%	-3%
Transportation	+2%	+5%	-3%	-5%
Police	+3%	+4%	+0%	-2%
Health	+5%	+8%	+7%	+9%
Other	+2%	+7%	-10%	-8%

Since you are taking Graduate RE - you should be able to think it through.

What do you get following TKs logic?

 

[Bobbi]

Since you are taking Graduate RE - you should be able to think it through.

What do you get following TKs logic?

I don't know if i'm over thinking this and it is as simple as adding the percents together showing that each year it rose __ % more then the last to get 29% or if there is actually some kind of formula.

 

[tkhunny]

No, you are underthinking it. Please reconsider my original response.

This is NOT the most conplicated question you will encounter. Are you SURE you are ready for this?

Exploration:

Start with 100
What is a 5% increase from 100? 100 * 1.05 = 105 -- It increased by 5.

Start with 105
What is a 5% increase from 105? 105 * 1.05 = 110.25 -- It increased by 5.25

No you must ask yourself, Why did the second one increase more than the first one?
Further, you must ask, If there is a 5% increase, followed by another 5% increase, why can I NOT just add the two 5s?

 

[Bobbi]

No, you are underthinking it. Please reconsider my original response.

This is NOT the most conplicated question you will encounter. Are you SURE you are ready for this?

Exploration:

Start with 100
What is a 5% increase from 100? 100 * 1.05 = 105 -- It increased by 5.

Start with 105
What is a 5% increase from 105? 105 * 1.05 = 110.25 -- It increased by 5.25

No you must ask yourself, Why did the second one increase more than the first one?
Further, you must ask, If there is a 5% increase, followed by another 5% increase, why can I NOT just add the two 5s?

Can you please just answer the question and then explain how you got it? I'm don't understand how to solve from your hints. Why did you calculate a 5% increase twice? Do you calculate a 5% increase for each year between 1990-1995?

Is this the right approach:

100 x 1.05 = 105
105 x 1.08 = 113.4
113.4 x 1.07 = 121.34
121.34 x 1.09 = 132.26

making a 32.3% increase?

I do realize this isn't the hardest question I will see on the GRE, I have been studying for sometime and have solved much more complex questions, however, this question has me stumped.

Thank you for helping/ teaching me how to solve this problems so that I may be able to solve similar problems in the future.

 

[Bobbi]

So how would the formula be written? ... base x %increase written as decimal = change


Ok, so, using the same table above. Check my work for solving a change in spending with a - % .

Use Change in total Transportation spending from 1990-2010 for an example.

100 x 1.02 = 102
102 x 1.05 = 107.1
107.1 x .97 = 103.9
103.9 x .95 = 98.7

100 - 98.7 = 1.3

Change in total transportation spending = -1.3%

 

[Bobbi]

There is no easy formula to memorize. It is a process.

The formula for the cumulative percentage change is: \(\displaystyle \displaystyle \left[\left[\prod_{i=1}^n\left(1 + \dfrac{p_i}{100}\right)\right] - 1\right] * 100\)

where p_i represnts the percentage change for period i and n is the number of equal periods. Do you really want to memorize that?

The formula just summarizes the process.

You turn the n percents into decimals by dividing by 100.

You add 1 to each of the n decimals.

You multiply all n of those sums.

You subtract 1 from the resulting product.

You multiply that difference by 100 to turn the decimal into a percent.

Wow, ok. Thanks for all of your help.