I never said that. Which kind of explains why you’re interpreting the question the way you are, you’re just not being as specific as I am. I realize that many years at law school changes the way I parce words, though - so I understand most people aren’t reading things the same way I am.
You say that people aren’t machines, and you’re not wrong. But when parcing language, it helps to behave like one. To some people, the definition of a word is as specific as a number, and the meaning of a sentence is viewed as a formula.
eta: I also spent a few years editing a law journal, which probably helped to increase that kind of mindset.
Well sure, you could interpret it that way. But a $300 raise without defining the unit of measure is meaningless, and to assume that you are talking about your “six month salary”, when the rest of the world negotiates pay in hourly or yearly units is a pretty poor assumption in my opinion.
You’re the befuddled one. There is plenty of ambiguity in the question.
I have printed the numbers in table form a couple times, with a couple different variations. Lay out your numbers in table form so you can prove your point.
I reread what Marilyn said and looked at my table of numbers. When she says you are “ahead” by a certain amount, what she seems to mean is that year 1 you make $300 dollars that you don’t make in the annual raise. Year 3, your salary for that year is $700 more than the salary at the $1000 annual raise. Year 5 your salary is $1100 more than the $1000 annual raise.
I pointed out before the first error with your calculation. You are assuming that at the end of year 1, you get paid that additional $1000. This is not true. At the end of year 1, you would be paid $10,000. It isn’t until year 2 that you make that $1000, which is the year you make $11,500 under the $300 more each 6 months plan.
You are right, someone else said it in the other thread. Still, that seems to be the way you are reading the intent of the statement, that the salary is stated as an annual basis so the raise should be stated as an annual basis. Correct?
I’m not arguing whether it is helpful or not to do so, I am saying that many people are not that specific, and a common understanding of “you will get a $300 raise every 6 months” is that you will get $300 more for that period, not that you will get $150 more for that period. I understand why it is a fair and probably more correct reading to read it the second way, but I am saying that many people are not that precise and will read it the way Marilyn presents it.
It’s probably a poor reading, but it is nevertheless a common reading. “$300 raise at the end of each six months” seems to specify a 6 month period for receiving the $300.
Let’s try a slightly simpler problem that may illustrate the math better.
I want to hire you to do a simple task over three days. I give you two choices how to be paid:
Plan A: I pay you $1 the first day. Then each succeeding day, I pay you $1 more than the day before (i.e. you get a $1 raise every day).
Plan B: I pay you $0 on the first two days, but then pay you $5 on the last day (i.e. I give you a $5 raise on the last day).
Which do you choose?
Let’s use the same analysis that you used in the quoted passage.
End of day 1, plan A ahead $1.
End of day 2, plan A ahead $2.
End of day 3, plan B ahead $2.
Using your analysis, you should choose Plan B because it will be ahead $2 at the end of the third day: You got $3 in raises under Plan A, but $5 in raises under Plan B.
Unfortunately, if you had chosen Plan A, you would have $6 in your pocket at the end of day 3 ($1 + $2 + $3). Whereas, if you had chosen Plan B, you would have $5 in your pocket ($0 + $0 + $5).
Cecil’s explanation is spot-on. Given the way Marilyn interpreted the question, she’s entirely correct — raising one’s 6-month salary by $300 every six months period is superior to increasing one’s 12-month salary by $1000 every year.
The trouble with that answer is that “6-month salary” is not, in the modern human experience, a thing that exists, and no rational person could be expected to consider the phrase “a $300 raise” to apply to such a scenario.
John W. Kennedy’s pedantry about a “semiannual annual pay raise” is well-taken in the context of the problem, but in the context of communication among native English speakers, I daresay that a poll of 1,000 random respondants would see a 100% consensus that the phrase “a $300 raise every six months” refers to a $600 increase in annual salary (also known as “salary”, “semiannual salary” also not being a thing that exists in any meaningful context.)
Basically, Marilyn’s answer to this problem has told us that the one word that is misspelled in the sentence “One word in this sentence is misspelled” is “misspelled.” For that, I award her a cookie, and this relevant xkcd — which is really all I need have posted in the first place.
The $1000 dollar raise clearly puts you ahead because it’s a $1000 raise for every period of time it takes a medium sized South American common lizard to run the length of 1.5 olympic swimming pools in optimal conditions. Which is about 20 seconds. meaning by the end of the year your pay would be increase by 1000 X 3 X 60 X 60 X 24 X 365 = $94,608,000,000
So you’d be a lot better off then the $300 raise which is an annual increase.
In order to come up with the extremely unusual interpretation that Marilyn did, you have to go out of your way to misinterpret the question.
I find it hard to believe anyone would actually be confused by the question. It’s more likely that her answer was an attempt to be clever or humorous. Or something.
OK, I’ll have to fess up and say I was dead wrong. If you take the question literally and add up the numbers the $300 every six months accumulates more money in the bank that the annual $1,000. At the end of the second six months you have banked $10,000 with the annual raise, $10,300 with the six-month raise. At the end of the third six months you have banked $15,600 (three $5,000 half-year salaries plus two $300 pay raises) with the $300 plan, $15,500 (three $5000 half-year salaries plus half of the $1,000 pay raise). Continue that pattern and look at the accumulated money.
It’s most helpful to think about base pay. Base pay for the $300 plan increases $50 per month every six months. Base pay for the $1,000 plan increases $83.33 per month every 12 months. So every year base pay rises $100 per month, only $83.33 per month in the $1,000 plan. Plus you get half the raise at mid-year.
You have to keep track of previous raises and add them in cumulatively.
$300 first raise. Next raise is $300 on top of that which is $600. Then you add what you got in the first six months ($300) to what you got in the second six months ($600) for a total of $900 in the first year.
Until you remember to keep adding up the cumulative raises as money pocketed and keep track of that, you won’t get it.
A $300 raise for a six month period works out to be $50 a month. So to put it another way, think of this as getting a $50 a month raise every six months.
A $1000 raise for a twelve month period works out to be $83.33 a month. So think of it as being a $83.33 a month raise every twelve months.
So in the first scenario, you will have gotten $100/month in raises at the end of twelve months. You’re already ahead.
But in addition to the higher monthly salary, you will also have collected it longer. A guy who gets a raise every six months will start receiving his higher pay half a year earlier than a guy who receives his raise every twelve months.
No, for purposes of the question, I believe that the period that the raise covers is irrelevant. It doesn’t matter if it’s hourly, monthly, semi-annual, or annual. The first question that matters is whether or not it’s different. And since there are no words to justify the difference, and because once we know that if there is no difference we can answer the question, there is no need to determine what period the raise covers.
That’s my interpretation. Wages are expressed hourly; salaries are either monthly or annual, and during negotiations, it’s always been annual in my experience.
Clearly, you wouldn’t see a 100% consensus, or there wouldn’t be so much confusion here. The phrase is definitely ambiguous. However, if that phrase were turned over to the typical HR employee, who just plunks a number in a box (annual salary), guess what would happen. It would change the annual pay, resulting in a monthly increase of $300/12.
xkcd ftw, as usual.
You’re making progress but you’re not quite there yet. Kudos for admitting your mistake, kudos for advancing, and kudos for trying. Don’t quit yet.
A lot of posters above need to read this, if they can’t be bothered to study the spreadsheets posted. However, you’re assuming one interpretation (the 300 raise is on semiannual pay vs annual pay). Both interpretations are logically meaningful, but only one interpretation (not yours) would typically be used by an HR worker using typical HR software. Regardless, you’re right that it’s the accumulated wealth that matters, not the instantaneous rate.
Actually, it’s worse than that. You have to wait 6 months before you begin to earn the monthly increase of either $50 or $25, depending on the employer’s HR department’s interpretation.
Well, I’d far rather get a raise of $300/hr than $300/yr. Wouldn’t you?
Interpretation 1: You get a semiannual raise of $300 on your annual pay rate.
Interpretation 2: You get a semiannual raise of $300 on your semiannual pay rate.
Interpretation 1 is what most HR departments would use, if the bolded words are omitted. Only by interpretation 2 does the semiannual pay increase win over the annual one, without even doing the careful math, because a 1000/yr raise is less than two 600/yr raises.
It’s a poor puzzle, IMHO.
I prefer this one: If there are two flights of stairs per floor, how many flights do you have to climb to get from the ground to the 7th floor?
