for the above answer, I don't think it is calculated properly according to question. I the question there is percentage increase asked. here its merely the number of times the salary is more is calculated

Hey,

After the increase in Jacks salary and decrease in Anie's salary their salaries becam equal.

If you took the fraction of the original salaries it came out to be 1.1578.

So basically Arnies salary was 1.158 times Jacks or 115.8% of Jacks salary or 15.8% more than Jacks salary.

Regards,

My problem:

If Arnie's salary= 1.1578 times Jack's salary,how do we calculate the answer to the nearest 0.1% and get the answer as 15.8%.
Please provide me the stepwise solution from this step if possible.

We said that the salary is 1.158 times but you must express this number in terms of percentage. Therefore, you must express it * 100

1.15 *100 = 115.8 %

Our base (always) is 100. So, our difference is 15.8 %

Hope now is more clear to you.

For the rest of the process to come to a solution see my explanation above.

Regards

Thank you for the explanation.
My problem now is to understand this step:
Our base (always) is 100. So, our difference is 15.8 %

Dear ARIJOSHI

the rule for percentage is that the base is always 100 from which you do have a percentage increase or decrease.

Now if the equation is r = 115 percent of k and the base is 100 (the rule) the difference is 15; 115-100=15

So the percent difference is 15 %

Hope this helps now.

For refence see our gmatclub math book page 15

How is it that I would know to use Jack's 2011 salary as my "original value/denominator"? If I use Arnie's salary to solve for the % change I get a different answer. (Difference = 14.35 / Original = 105.26) x 100 --> 13.6%. Thanks!

Here we do not have a % change.

Here we do have an equation after SINGLE % change.

J goes UP whilst A goes DOWN and then they end up to be equal.

We do have a percent greater which in other words is a difference

regards

How come this isn't a percent change problem? Since it says "was what percent greater than" I assumed it was percent change

A % change is when you do have a single change from a period to another.

here we do have two salaries and what is the difference. Even though, this is expressed as %

Hope this helps Sir

Isnt 1.1 / 0.95 equal to 115.78% ? Even if it is rounded to 0.1% that should be 115.8% hows it 15.78?

Can you please repeat the question?

I think Carcass's explanation is perfect.

\(1.1578\) represents a multiplier so the increase will be \(15.78%\) and rounded to 0.1%, it will be \(15.8%\)

Please ask if the doubt remains.

As Jack and Arnie's annual salaries were equal in 2012, let's assume, Jack's salary = Arnie's salary = 100.

For Jack, his salary increased by 10% from 2011 to 2012,
which means, x+x*0.1 = 100, or 1.1x =100, or x=100/1.1= 90.9. So, the actual salary in 2011 was 90.9

For Arnie, her salary decreased by 5% from 2011 to 2012,
which means, y-y*0.05=100, or 0.95y=100, or y=105.3. So, the actual salary in 2011 was 105.3

Arnie’s annual salary in 2011 was ((105.3-90.9)/90.9)*100 = 15.8 percent greater than Jack’s annual salary in 2011.

short note= the denominator (original) should be the amount that is found in the question after "greater/less than". Here Jack is found after "greater than". that is why the 90.9 value is placed in the denominator.

\(\frac{1.1}{0.95}\)

Any suggestions on how to calculate the above? Calculator or something else?

I tried \(\frac{110}{100} * \frac{100}{95} \) = \(\frac{110 }{ 95 }\) = \(\frac{22}{19}\)


This didn't really help much though. Would anyone agree a calculator would be best for this calculation in the testing environment?

11/9.5

9.5 \approx 10

11/10

1.1

22/19=1.15

Done

2011 2012
Jack 100 110
Arnie 0.95 x 110

0.95x = 110
x = 15.789 = 15.8

100-115.8 / 100 = 15.8%

Answer is 15.8%

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