grassmonkey wrote:

Perhaps an easier way to thing about this is the successive multiplication of percentages. This is a pretty fundamental concept to percentage questions and it's one that I have screwed up about a billion times.

If you have some salary S and you increase it by 10% and then decrease it by 10%, the math looks like this:

S*(1.1)*(0.9) --> this is equal to S*(99/100). This is 99% of the original salary or a 1% decrease.

In this question they are giving you the end result and asking what it took to get there. Therefore, the math looks like this:

(S)*(1.3)*(what?)=1.04*(S) --> the S's are illustrative, they cancel out.

The answer is 20% but the way to think about it is, "if I increase by 30% and then decrease by some amount and get and increase of 4% as an end result, what was the decrease that happened after the increase?"

One other thing to note (as I've got caught out on this before) is that it doesn't matter in which order the increase and decrease occur.

This post, like

pushpitkc 's, is thoughtful in both senses of the word.

I would expand an important idea where you noted: "...they are giving you the end result and asking what it took to get there." One way to break down this idea ...

A) If the language is confusing, break the problem into steps or stages.

The phrase "was reduced [decrease] to 104 percent [increase]" certainly could confuse. Decrease AND increase?

It might appear that the same stage (1994) is being used twice, when instead the phrase refers to two different stages.

B) Stages / steps here:

Year 1 (1993): K earns a salary. Call it $1,000.** K earns $1,000.

Year 2 (1994): K gets a 30% raise. His salary is greater than Year 1. It is now $1,300.

Year 3 (1995): Much of K's raise gets taken away. His salary now is a lot less than Year 2. How much less?

104% of

Year 1. Put aside Year 2 here to calculate. The result needed here involves only Year 1: $1,000.

104% of 1,000 is $1,040. That is Year 3's resultant amount.

The "what percent less" then involves only Years 2 and 3: $1,300 vs. $1,040.

Ultimately, with this approach, we could "translate" the odd-sounding sentence.

Original: "In 1995, Kenneth’s annual salary was reduced to 104 percent of his 1993 annual salary."

Rewrite: "From Year 2 to Year 3, K's annual salary was reduced by a lot. The boss decided that K's Year 3 amount would be based on his Year 1 amount. In this third year, he got 104% of Year 1."

grassmonkey and

pushpitkc , your efforts to help are gracious and classy. Kudos.

**

as pushpitkc prudently did. IMO, when dealing with percent changes above 100, if amounts are assigned and confusion sets in, it's probably easier to "see" a 104% change with amounts that are in the thousands.
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