Dealing with percentages: noob question
May 28, 2013 4:02 AM   Subscribe

I've recently decided to transition to a new career path, accounting. Most firms round here do an online numeracy test as part of the application process. There is a type of % change question that often comes up and I can't find a proper answer about how to calculate it. There are two formulae suggested by different websites, but they give different answers. Which is right? (details inside)

A common question is:

"The share price of Mapple Inc is 545. Last year it was 15% lower. What was the share price last year?"

Method one: 545 x 0.85 = 463.25

Although this is recommended by a couple of (fairly reputable!) places it seems to be wrong. Trying to reverse the percentage change to check it, 463.25 x 1.15 does NOT equal 545.

Method two: 545 / 1.15 = 473.91

This looks like the correct method.

I've never been numero uno for maths. So mathematically inclined folks, is the second method definitely the right one?
posted by NoiselessPenguin to Education (10 answers total) 5 users marked this as a favorite
 
The actual difficulty seems to be in interpreting the meaning of "15% lower". Does that that the price last year was 85% of the current value, or does it mean that the current price is 115% of the price last year?

This seems ambiguous to me, and perilously close to one of those situations where there will be two opposed factions, each completely sincere in believing that they have the correct interpretation (see: move forward/back the meeting by an hour).
posted by thelonius at 4:16 AM on May 28, 2013 [1 favorite]


Method Two is wrong (based on the very specific wording used - careful !). As for the math conundrum, here's the resolution: 463.25/(1-0.15)=545 .
posted by Yowser at 4:16 AM on May 28, 2013 [3 favorites]


Best answer: First of all, you can't "check back" the way you're doing it. 10% off of 100 gives 90 and 10% back gives 99. That's because percent is relative to the value at the time.

Second--they are both right depending on the interpretation of the concept of percent. The first way is the more usual interpretation.
posted by Obscure Reference at 4:18 AM on May 28, 2013 [6 favorites]


Best answer: Yeah, Method One is right.

Interpreting the statement as "What is 15% less of 545?" means you want 15% of 545 which is 81.75, so 545 - 81.75 = 463.25.

Method Two is answering the question, "The share price of FOO increased 15% to 545. What was the old price?" which is solving the equation 1.15x = 545 for x.
posted by Elementary Penguin at 4:19 AM on May 28, 2013 [2 favorites]


The wording of the question determines what you need to calculate.

Last year it was 15% lower [than this year] should mean that the answer is defined in terms of the original price, $545. In this case, I'd use the 0.85 formula.

If the question had read The price has increased by 15% [over last year] then the answer would have been defined in terms of the original price, which is where you'd use your second formula.

As others have pointed out, 15% of the original price doesn't equal 15% of the new price, so you can't expect to get the same number by dividing by 0.85 and then multiplying by 1.15.
posted by FreelanceBureaucrat at 4:20 AM on May 28, 2013 [1 favorite]


The question you cite is ambiguous. Either answer could be correct.
posted by BenPens at 4:29 AM on May 28, 2013


Best answer: The question is not especially ambiguous to me, it would be worded differently if it was referring to a 15% increase on last year instead of last year being 15% lower than this year:

"The share price of Mapple Inc is 545. This is 15% higher than last year. What was the share price last year?" = Last year the price was X. This year it is X+15%, or X * 1.15.

"The share price of Mapple Inc is 545. Last year it was 15% lower. What was the share price last year?" = This year the price is 545. Last year it was 545-15%, or 545 * 0.85.
posted by EndsOfInvention at 5:31 AM on May 28, 2013 [3 favorites]


Method one is almost certainly the intended answer. If a stock goes down by 15%, it needs to go up by more than 15% from its new value to get back to where it started.
posted by deadweightloss at 5:34 AM on May 28, 2013 [1 favorite]


Response by poster: Thank you everyone for your help. It looks like I need to read the questions extra-closely to work out what I'm being asked, and then use the right formula.

The test questions are often intended to trip you up, hence a lot of my confusion. I had a feeling I was missing something - thanks again to everyone for helping to clarify this for me!
posted by NoiselessPenguin at 5:46 AM on May 28, 2013


Since there have been a few "could be either" answers, I'll add my opinion that the question unambiguously calls for Method One. The full sentence that it is abbreviating is "Last year it was 15% lower [than it is now]."

A way to ask a question that calls for Method Two would be to use the sentence "It has increased 15% over the last year [from what it was then]."

In the first case the comparison is clearly relative to the current price, and in the second case the comparison is clearly relative to the old price, as can be seen by completing the sentences.
posted by dfan at 6:11 AM on May 28, 2013 [2 favorites]


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