One year ago a window washing service charged $100 for setup and an

Question

﻿One year ago a window washing service charged $100 for setup and an additional $30 per hour for on-site washing. This year the company charges $20 for setup and an additional $50 per hour for on-site washing. Which of the following is equivalent to the percentage change from last year to this year that the company charges for setup and x hours of on-site washing?

A.  100(\frac{3x + 10}{2x - 8})\%

B.  200(\frac{x - 4}{3x + 10})\%

C.  200(\frac{x - 4}{5x + 2})\%

D.  200(\frac{4 - x}{3x + 10})\%

E.  200(\frac{4 - x}{5x + 2})\%

gmatophobia · Accepted Answer

Price that the window wash service charged last year for x hours of onsite washing =  100 + 30x

Price that the window wash service charged last year for x hours of onsite washing =  20 + 50x

Change in price =  20 + 50x - (100 + 30x)

=  20x - 80

Percentage change =  \frac{20x - 80 }{ 100+30x}*100

\frac{2x - 8 }{ 10+3x}*100

\frac{(x - 4) }{ 10+3x}*200

Option B

Bunuel · Answer

The general formula for calculating percent increase or decrease (percent change) is:  \frac{	ext{Difference in values}}{	ext{Reference value}}*100 . The reference value is the value you are comparing to.

When we are talking about percentage change from old value to new value, it would be  \frac{	ext{New Value - Old Value }}{	ext{Old Value}}*100 .

For the original problem, note that:

If x < 4, then we'd have a percentage decrease. For example, if x = 2, then we'd have a 25% decrease for 2 hours from $160 to $120. 
  If x = 4, then we'd not have a percentage change at all. For example, if x = 4, then both the old and new charges would be $220. 
  If x > 4, then we'd have a percentage increase. For example, if x = 10, then we'd have a 30% increase for 10 hours from $400 to $620.

Hope it helps.

JeffTargetTestPrep · Answer

percent change =   × 100%

new amount charged = 20 + 50x

old amount charged = 100 + 30x

percent change =   × 100% =

× 100% =

100 % =

200 %

Answer: B

Paras96 · Answer

﻿One year ago a window washing service charged $100 for setup and an additional $30 per hour for on-site washing. This year the company charges $20 for setup and an additional $50 per hour for on-site washing. Which of the following is equivalent to the percentage change from last year to this year that the company charges for setup and x hours of on-site washing?

Case 1:-

Total charge C1 = 100 +30x

Case 2:-

Total charge C2 = 20 +50x

Net change, C2-C1 = 20 +50x-(100+30x)
=> C2-C1=20x - 80

percentage change from last year to this year
= (C2-C1)*100/C1
= (20x - 80)*100/(100+30x)
= 20(x-4)*100/(100+30x)
=(x-4)200/(10+3x)

Hence B

lotif · Answer

Why is this not = (initial value - final value)/(initial value) * 100?

Example, percentage change if something was $10 now $8. Thats 20% which above gives you. The other formula puts a minus in front of it. But isn't convention when we want percentage change, its the value, not the sign.

horrorslive · Answer

why didnt we do 30x+100- 20-50x? Since the qs states % change FROM LAST YEAR to this year??

edthehead7 · Answer

Bunuel  can you explain your final steps of simplification?

I understand dividing the numerator by 10 to go from 20x-80 to 2x-8 but how does one know to then "peel out" 2 and create x-4 while multiplying theother side of the percentage to increase 100 from 200?

Feels a bit unnatural and a step I woudln't normally take --- thank you!

Bunuel · Answer

\frac{2x - 8 }{ 10+3x}*100  does not match any of the provided options. So, the next step should be trying to manipulate it such that it matches. Since all options but A have 200 multiplied by some expression, transforming  \frac{2x - 8 }{ 10+3x}*100  to that format could be the right way to go. This can be achieved by factoring out 2 from 2x - 8 and multiplying 100 by it to get  \frac{x - 4}{ 10+3x}*200 , which is option B.

Hope it helps.

sayan640 · Answer

KarishmaB   MartyMurray  why didn't we do (30x+100- 20-50x) Since the question states % change FROM LAST YEAR to this year?? How do I decide which value between the old and the new one , I should take as the reference ? 
Please help.

MartyMurray · Answer

The reference is the one the percentage changed "from" or the one such one value is "greater than" or "less than" it.

In this case, the percentage changed "from" the first. So, the first is the reference value, and the percentage will be a percentage of the first.

To get that value, we subtract the first from the second and divide by the first.

If you think about this, it's all logical. If we want to know how much something changed from its past value, we would use the past value as the basis of our calculations. We wouldn't use the new value as the reference for how much something changed from a past value.

KarishmaB · Answer

Last year pricing for x hours = $(100 + 30x) This year pricing for x hrs = $(20 + 50x) PercentageChange = * 100 = \frac{200(x-4)}{(3x+ 10)} Answer (B) Note that percentage change is calculated with base as the old value. A 10% increase means a value has been increased by its 10% so the percentage will be calculated on the original value. Some conceptual discussions on percentages are here: Percentages: https://youtu.be/HxnsYI1Rws8 https://anaprep.com/arithmetic-successi ... e-changes/ https://anaprep.com/arithmetic-markup-discount-profit/

KarishmaB · Answer

"from last year to this year" means we started with the last year values and now we have these new values. The percentage change is calculated as 
 \frac{New - Old}{Old} * 100

siddhantvarma · Answer

KarishmaB  is this always true? Can we safely assume that when dealing with percentage changes, we'll always do new - old and not old - new?

siddhantvarma · Answer

You said:
 
And the question states:
 
From last year to this year, the reference value should be the previous year's value, ie, the old value, which is 30x + 100. Here instead we're doing 20 +50x - 30x + 100. Can you please clarify this? What am I missing here?

KarishmaB · Answer

No. It depends on what the question is asking you.

By what percent has the value increased this year from last year?

\frac{(New - Old)}{Old} * 100

By what percent was last year's value less than this year's value?

\frac{(Old - New)}{New} * 100

You have to notice what the base value is. Usually, we have indicative words such as 'from' or 'than' to show base values.

Check:  https://youtu.be/HxnsYI1Rws8

siddhantvarma · Answer

KarishmaB 
One quick follow-up on this. The question says:
 
From this statement how do you infer if the percent value increased this year from last year or if it decreased?
 
Merely based on 'from' and 'then', how do we determine the base value? Especially for this question where we don't know if the percent value increased this year or decreased.

KarishmaB · Answer

You are given 'from last year to this year' so base value is last year i.e. last year value will be the denominator.

It will be (This year value -  Last year value)/(Last year value)
If you get it as positive, it means there is an increase, if you get this as negative, it means there is a decrease.

LamboWalker · Answer

To avoid algebra:

I tested for x = 5
Last year the total cost would have been 250.
This year the total cost is 270.
Percent change is 20/250 = 8%.

Now, substitute x = 5 in each of the options, only B gives a value of 8.

Dbrunik · Answer

https://www.youtube.com/watch?v=1hdRRbFSUIo https://youtu.be/1hdRRbFSUIo

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