> This is a factor of 4 improvement!
This is a common mistake. It should read, "This is a factor of 3 improvement!"
x+x+x+x is an improvement over x of 3x not of 4x. The improvement factor is 3.
This is a common mistake. It should read, "This is a factor of 3 improvement!"
x+x+x+x is an improvement over x of 3x not of 4x. The improvement factor is 3.
The general equation for an increased quantity from A to B is
increase = B - A
increase * 100
(increase + A) * 100See: https://ell.stackexchange.com/a/52747
Maybe my problem is that I am missing "by".
B/A is the percentage of the new value relative to the old.
(B-A)/A is the percentage of the increase of the value.
This is algebra not English.
1) You start out with one rock. 2) You add another rock, getting a pile of two rocks. 3) The rock pile size is now 200% of the original size. But, the increase of the rock pile size is 100%. 4) According to the rules of algebra, 100% = 1. In this case 100% = 1 rock, since the unit under discussion is rocks.
That's absolutely wrong... When you multiply something you scale it by a factor. When you add to something you increase it.
1) 4A is 400% of A.
2) 4A in an increase of 300%.
3) 4A is an increase of 3A.
4) 4A is an increase of a factor of 3.
In the most charitable interpretation you are confusing the terms of exponential growth with linear scaling and misapplying from one to the other. A growth factor is not the same as an increase in a factor.
https://www.beatthegmat.com/word-translation-when-x-increase...
https://www.quora.com/Mathematics-What-does-it-mean-to-incre...
https://www.macmillandictionary.com/us/dictionary/american/b...
http://mathforum.org/library/drmath/view/74439.html
https://ell.stackexchange.com/questions/52706/what-does-redu...
Here are some other links from Google that explains why your vociferous insistence is wrong.
http://www.crackssat.com/isee/word-problems/question-250-ans...
https://english.stackexchange.com/questions/8680/how-much-ex...
https://forum.wordreference.com/threads/increase-by-a-factor...
https://books.google.com/books?id=wDKLXdzQL5AC&pg=PA182&lpg=...
http://econlog.econlib.org/archives/2010/05/the_wall_street....
In addition to the short explanation in the last link, some of the comments on that page may help shed light, such as:
I'm a college student, and for the past few years I've been an SAT
tutor to pay the bills. 95% of my students do not know how to
calculate percentage change. I spend hours teaching kids this.
They usually start to get it after working with the formula several
times, and then I show them this:
for any number "n"
100% increase = n*2 = double
200% increase = n*3 = triple
300% increase = n*4 = quadruple
...
x*100% increase = n*(x+1)
You seem to be stuck on the translation here. These are two different phrases with different meanings. Yes, they both refer to increases. Yes, they both can be interpreted as multiplications on the original term. No, they are not the same. You found exactly one case which does not use the same verbage and specifically points to percentages. I don't know how else to say that different phrases in English carry different meanings. You can't just say "a factor of X" is equivalent to "X00%". This just is not understood to be true. Even the GMAT and GRE present questions in this way with the understanding that "a factor of X" means to multiply by X.
I'm not going to continue to explain this to you. There's really nothing more to be said. If you attempt to solve problems presented in the format of "increased by a factor of X" such that X is not presented as a percentage, you will be marked as incorrect more often than not.
I'm not even explicitly arguing for a populism argument. I'm stating that the problem is presented in a different format than you are claiming it to be.