Percents: How do I know which way to go.....

[michael.fisher26]

For example, if I say revenue was 20% more in December than in January. And revenue was $100 in December. What is the revenue in January.

How do you know whether to say December is 120% of the revenue in January (100 = 1.2x, x= 83.3) vs. January was 80% of the revenue in December (.8x = 100, x = 80)?

Both values are less than 100 (and fairly close to each other) so you can't quickly fact check. I cant seem to wrap my mind around this.

Disclaimer: "based on" OG13 PS #57 p.159

[RonPurewal]

For example, if I say revenue was 20% more in December than in January...
How do you know whether to say December is 120% of the revenue in January (100 = 1.2x, x= 83.3)

this is the correct interpretation.

vs. January was 80% of the revenue in December (.8x = 100, x = 80)?

this is wrong; this would mean that january was 20% less than december. that's not the same thing at all.

if the difference isn't clear to you, then consider a bigger percentage.
if i tell you "x is 50% more than y", then that's x = 1.5y; in other words, x is one-and-a-half times as big as y.
but, if "y is 50% less than x", then that's y = 0.5x; in other words, x is now twice as big as y.

the main takeaway you should get here is simply that you can't reverse percent changes symmetrically; in other words, as long as N is not zero, an increase of N percent will never, ever, ever cancel out a decrease of N percent.
if you care about the "why" here, the reason is actually pretty straightforward: if you say x is N% more than y, then you are taking N% of y; but, if you say y is N% less than x, then you are taking N% of x this time.

[michael.fisher26]

Thanks Ron. I guess I was just reading it wrong.

Also I just noticed the second part should be x=.8(100)=80 but I think you got my point.

Thanks.

[RonPurewal]

Thanks Ron. I guess I was just reading it wrong.

Also I just noticed the second part should be x=.8(100)=80 but I think you got my point.

Thanks.

yep -- the understanding was there, so i didn't even notice that (i am not the "detail-oriented" type).

glad we could help