“Moot Point” vs. “Mute Point”

Often in print (or on Facebook) you will see people refer to a mute point, when they really mean a moot point. This common grammar mistake is referred to as a malapropism (the use of the wrong word in a common idiom), and is also an eggcorn (similar to free reign vs.free rein).

The word moot has caused lots of confusion over the years. Originally, a moot argument described any argument that was debatable — for which there was no clear answer — and students of debates would discuss such arguments in a moot. Over the years, since such discussions were generally about unsolvable problems and not actually deciding anything, the word moot slowly evolved to its modern usage to describe a discussion that is irrelevant.

So, the word moot now means the opposite of what it originally meant, and it’s too late to fix it. If you try to use the word moot in its original sense, you’ll simply confuse people. As a result, it’s probably just best to avoid using the word altogether.

However, you can’t avoid running across the common usage today: moot point refers to a point of discussion that has been made irrelevant (the time for decision is already past, or any decision on the point would be overridden by some other factor).

A “mute point” is just an understandable mistake — since moot and mute are homophones, or at least almost homophones, one who doesn’t know the word moot may replace it with mute. This mistake is understandable, since if the point were mute, then it would be silent, or of low volume (like a muted trumpet), and so it makes at least a little bit of sense.

A mistake like this is called an eggcornOther examples of eggcorns: “free reign” for “free rein”, “shoe-in” for “shoo-in”, “peak my interest” for “pique my interest”, and so on. Just watch your Facebook wall and you’ll see them flow past every day. These are good examples of errors that, once seen, cannot be “unseen” for the rest of your life.

Knowing proper grammatical style can help you in daily life, in your professional life, and on the SAT, ACT, GMAT, LSAT, MCAT, and GRE. If you are planning to take any of these tests, contact Bobby Hood Test Prep for more information!


“That” vs. “Which”

The difference between “that” and “which”, and how to choose between them, has been the subject of much debate. It took me a long time to finally understand the distinction, but once you do understand the difference, the clarity of your writing will improve significantly.

You can use this very simple rule of thumb: in most cases, the correct word you want to use to introduce a clause is that (not which), and whenever you use which, it must be preceded by a comma. The choice is between that or “[comma], which” — and if you’re not sure, use that.

So, why is that appropriate in most cases instead of which?  That is used to introduce restrictive clauses: clauses required for the sentence to be grammatically and logically sensible. Which, on the other hand, is used to introduce non-restrictive clauses: clauses that give additional information that is not necessary to the meaning of the sentence.

Consider the following sentence:

  • “My car that is parked out front is the Batmobile.”

In this sentence, the clause “that is parked out front” is restrictive — it helps define “My car” by identifying that although I have more than one car, the one parked out front happens to be the Batmobile.

Compare to this sentence:

  • “My car, which is parked out front, is the Batmobile.”

Notice the difference in meaning? In this sentence, which introduces a non-restrictive clause. This sentence tells you that I own only one car, and it’s the Batmobile. And, incidentally, it’s parked out front, but you didn’t need to know that for the meaning of “My car” to be clear.

There are several ways to make sure you get this right:

  • First, always use a comma before which and never use a comma before that. This will ensure that your reader knows that you intend which to be non-restrictive and that to be restrictive, as they should be.
  • Second, if you’re unsure, use that and not which.
  • Third, try removing the clause from the sentence. If it can be removed from the sentence without changing the logical meaning (if it’s extraneous, additional information), then use which; otherwise, use that.

Knowing proper grammatical style can help you in daily life, in your professional life, and on the SAT, ACT, GMAT, and GRE. If you are planning to do test prep for any of these tests, contact Bobby Hood Test Prep for more information!


Math Tricks Prove You Have Famous Ancestors

Everyone’s been fascinated during recent years about delving into their ancestry and family history.

I did a little work on ancestry.com and it wasn’t too hard to trace my ancestry back to some people who fought in the United States Civil War, and then to some who fought in the Revolutionary War, which was pretty cool, since it qualified me to join the Sons of the American Revolution.

But then, I kept going and found that I am, among other things, descended from King Edward III of England and his son, Edward the Black Prince of Wales, and that Geoffrey Chaucer is my 16th great-uncle.

At first, this seemed amazing, and I thought, “Wow! What are the chances of such a thing?”

Actually, using some basic statistics and probability, the chances are very likely that you are related to someone famous from the Middle Ages (about 400 A.D. to 1500 A.D.) or earlier, in whatever region of the world your ancestry comes from. 

As an example, let’s assume you were born in 1980, and that on average, a new generation comes along every 25 years. Then, each of your two ancestors would be descended from two more parents, and so forth. So, a century before, in 1880, that you would have 2 x 2 x 2 x 2 ancestors, or 2 to the 4th power, which would be 16 great-great-grandparents.

Add another hundred years to trace back to 1780, and the number of spots to fill in your family tree would equal 2^8, or 256 potential ancestors.

In 1680, the number of spots to fill would increase to 2^12, or about 4,000 potential ancestors.

In 1580, 2^16 (about 64,000 ancestors)

In 1480, 2^20 (about a million ancestors)

In 1380, 2^24 (about 16 million ancestors)

In 1280, 2^28 (about 250 million ancestors)

Just for fun, go another 50 years to 1230 A.D., making the exponent a nice round 2^30, which is over a billion ancestors.

But in 1230, there were only about 400 million people living on Earth.  What does that mean?

It means that there are LOTS of people over-counted in that family tree, because the lines actually come back together over and over. Not just because second, third, and fourth cousins marry each other — if you go far enough in time, everyone is technically a cousin to everyone else.

So, this means that you are you are descended from a lot of different people by a lot of different lines of inheritance — lots of VERY DISTANT cousins marrying each other — no matter what your ethnic background is.  There are a billion slots that have to be filled in on the ancestral tree, and only 400 million people to put in them, so a lot of people have to be filling multiple slots on your ancestral tree.

Does this mean you are descended from every person who was alive in 1230 A.D.?  No — depending on your ethnic background, your ancestry could be focused on groups in the Americas, or south Africa, or southeast Asia, China, Japan, and so forth, since those groups did not largely mix with other groups worldwide until later in history; and plus, there were many people alive in 1230 A.D. who don’t have living descendants today.

But if you know some of your ancestors were from Europe or around the Mediterranean, then the odds are that anyone who was alive in 1230 A.D., lived in Europe or around the Mediterranean, and has living descendants, is likely one of your ancestors, including all of the Holy Roman Emperors, and the peasants they ruled; William the Conqueror and many of his knights; Lady Godiva; Pope Innocent III; and so on.  Basically, everyone you read about in the history books; the conquerors and the conquered, the famous and the unknown — if they had descendants, there’s a pretty good chance they’re one of your ancestors.

Pretty cool, huh?

Math tricks like this are fun to play with. If you enjoy learning things like this, you might enjoy taking the GMAT or the GRE. Contact me anytime to discuss options for test prep and tutoring on the SAT, ACT, LSAT, GMAT, GRE, and MCAT!

LSAT Logic Games – The “Einstein Puzzle”

An LSAT student of mine alerted me to the Zebra Puzzle, which he found and sent to me. It’s often called “Einstein’s Puzzle”, and it’s said that Einstein wrote it as a child and “claimed that only 2% of the population would be able to solve it.” It was originally published in Life International Magazine on December 17, 1962, and the contents make it unlikely that Einstein was the actual author, but it’s fun anyway! When my student sent it to me, I actually pulled over on the side of the highway and worked it out for 30 minutes at a gas station because it’s such a cool puzzle.  I made a couple of edits, inside brackets, for clarity.  The solution to the puzzle can be found here, but try not to look immediately!

  1. There are five houses [in a row].
  2. The Englishman lives in the red house.
  3. The Spaniard owns the dog.
  4. Coffee is drunk in the green house.
  5. The Ukrainian drinks tea.
  6. The green house is immediately to the right of the ivory house [as viewed from the street].
  7. The Old Gold smoker owns snails.
  8. Kools are smoked in the yellow house.
  9. Milk is drunk in the middle house.
  10. The Norwegian lives in the first house.
  11. The man who smokes Chesterfields lives in the house next to the man with the fox.
  12. Kools are smoked in [a] house next to the house where the horse is kept. [The original puzzle says “the” house, but “a” house is more clear.]
  13. The Lucky Strike smoker drinks orange juice.
  14. The Japanese smokes Parliaments.
  15. The Norwegian lives next to the blue house.

If one resident drinks water, which is it?  If one resident owns a zebra, who is it?

The LSAT includes an Analytical Reasoning section (which we call “Logic Games”) that tests your ability to make deductions and solve problems like the above (but a good deal less complex).  If you like problems like this, you might enjoy LSAT prep and going to law school.

Contact me for information about test prep classes and tutoring, either locally in Austin or online via The Princeton Review’s LiveOnline classrooms!

The “Choosing Among Three Doors” Problem

“On a game show, a new car is hidden behind one of three doors. You choose Door 1. The host opens Door 3 — empty — and gives you the option to change your choice. Would you switch to Door 2 or stick with Door 1?”

This question is often called the “Monty Hall Problem”, after the show “Let’s Make a Deal”, and was discussed in the movie “21”.

The question can be answered using knowledge of basic math probabilities.

Probability is always described as a number between zero (no change of something happening) and one (100% chance of something happening), and is calculated using the formula P(outcome you desire) = \frac{desired}{possible}.

When you make your initial choice between the three doors, the chance is \frac{1}{3} that your choice has the prize behind it. Thus, the probability that you have chosen correctly is \frac{1}{3}, and the probability that you have chosen incorrectly is \frac{2}{3}. So, there is a \frac{2}{3} chance that the car is behind either Door 2 or Door 3.

When the host opens Door 3, revealing that it does not contain the price, he has given you additional information, but the original odds remain the same.  There is now a \frac{1}{3} chance that your original choice (Door 1) was correct (Door 1) and a \frac{2}{3} chance that one of the other doors (now, only Door 2) contains the prize, and you should switch to Door 2.

This requires assuming, of course, that the host always offers the chance to switch and that you can’t gain any information from his behavior.

If it’s difficult to see why this makes sense, imagine the same scenario with a million doors.  You pick Door 1, and the host opens 999,998 other doors, showing them to be empty, leaving only your door and one other door.  Would you switch?  There’s a \frac{1}{1,000,000} chance that you picked the correct door, and a \frac{999,999}{1,000,000} chance that the other remaining door holds the prize.

The GMAT Test includes many questions that test your ability to break down and solve problems involving probability.  If you like problems like this, you might enjoy taking the GMAT and earning an MBA.  Contact Bobby Hood Test Prep for information about classes and tutoring, either locally in Austin or online via The Princeton Review’s LiveOnline classrooms!


Although it’s not tested on standardized tests, and so isn’t directly helpful for test prep, zeugma is a fun grammatical trick to have in your repertoire and a laugh at.

Zeugma (pronounced “zoog-ma”) occurs when one word in a sentence governs the meaning of two or more other words in the sentence and as a result is used in two different senses at once, creating a dissonance that could be considered a form of irony.

Another word often used for this concept is syllepsis, but the distinctions between the two are a subject of much disagreement, so it’s easiest and safest to use zeugma in all cases.

The simplest way to describe zeugma is to show it in action.  The first sentence of this post, for example, uses zeugma: “have in your repertoire” and “have a laugh at” are two different idioms that are not often combined.

Here are some examples from music, literature, and popular culture:

  • “He’s got one hand on the steering wheel, the other on my heart.” (Taylor Swift, “Our Song”)
  • “…both how I’m living and my nose is large” (Digital Underground, “The Humpty Dance”)
  • “There’s people on the street using guns and knives, taking drugs and each others’ lives.” (Flight of the Conchords, “Think About It”)
  • “My teeth and ambitions are bared; be prepared!” (Scar, The Lion King)
  • “She blew my nose and then she blew my mind.” (The Rolling Stones, “Honky Tonk Women”)
  • “You held your breath and the door for me.” (Alanis Morissette, “Head Over Feet”)
  • “You are free to execute your laws, and your citizens, as you see fit.” (Star Trek: The Next Generation, “Angel One”)
  • “You can put me out on the street / put me out with no shoes on my feet / But put me out, put me out, put me out of misery.” (The Rolling Stones, “Beast of Burden”)

Knowing proper grammatical style can help you in daily life, in your professional life, and on the SAT, ACT, GMAT, and GRE. If you are planning to take any of these tests, contact Bobby Hood Test Prep for more information!

The “Shared Birthday” Problem

“If a room has 23 people in it, what is the approximate chance that at least one pair of people in the room share the same birthday?” 

This question is similar to GMAT math questions that test your knowledge of probability theory.  It requires too much calculation to actually be used as a GMAT question, but the technique for solving it is exactly the same.

Often, it’s easier to calculate the probability of a set of events NOT happening than it is to calculate the probability of that set of events actually occurring. 

We can use the fact that, for any given set of events, the probability that it WILL occur plus the probability that it will NOT occur equals 1:

  • P (birthday is shared) + P (nobody shares a birthday) = 1

So, since it’s easier to solve for the probability that nobody shares a birthday, we can solve the equation for the probability that there is at least one shared birthday:

  • P (birthday is shared) = 1 – P (nobody shares a birthday)

So, what is the chance that nobody shares a birthday?  

Start with the chances of two people not sharing a birthday.  For the first person chosen, we choose from 365 choices of birthdays available: \frac{365}{365}, which equals a chance of 1.  For the second person, we have 364 remaining birthdays to choose from out of 365:  \frac{364}{365}.  Multiply the two together and you get a chance of \frac{364}{365}, or about 99.7%, that those two people have different birthdays, and \frac{1}{365}, or 0.3%, as the chance that they share a birthday.

For each person added, we have one fewer birthday to choose from (363, 362, 361, etc.) out of the 365 days; multiply them all together to get the result:

  • \frac{365}{365}\frac{364}{365}\frac{363}{365}\frac{362}{365}...\frac{343}{365} =

Do all the painful math (a spreadsheet helps a lot, unless you are a math savant), and you get about 49.3% chance that a birthday is NOT shared; subtract from 100% and you have a 50.7%, or about 1 in 2, chance that a birthday is shared between at least two people in the room.

So, next time you’re at a party and you count 23 people, it’s a fun bet to make that there will be a shared birthday.  32 people brings the odds up to 75%, and 40 people puts it right about at 90%.

(Yes, I know we’re ignoring the poor folks who were born on February 29 and only have a quarter as many birthdays to celebrate as the rest of us, but they change the odds only a tiny amount.)

If you enjoy math problems like this, you would probably enjoy, and do well on, the GMAT test.  Contact Bobby Hood Test Prep and I’d be happy to discuss the various class and tutoring options for the GMAT, both locally in Austin and online through The Princeton Review’s LiveOnline classrooms.

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