Deceptively easy math word problems for high school kids

Not trying to sound snarky or lecturing, but, the point of the question is to read the entire problem before answering it. Some would immediately start counting the people, others would read the whole thing, realize the question, and then start counting.

It’s along the lines of a 50 question college entrance exam I once saw, where at the top of the first page, above where you write your name it says, “Do not write anything on this test before reading all the questions first.”

On page 5, question 50 says: Do not write anything on this test.

It’s tricky, but simple if you read everything before you start.

See, but those are infuriatingly incorrect. I once got into an argument with my 4th grade teacher over a similar type busy-work assignment. Look, the top of the sheet does not say “Do not write anything on this test before reading all the questions first, and then follow the instructions of question 50.” I may very well read question 50 and accept the fact that it states I should not write anything on the paper, but the instructions have not yet told me to follow any other directions. By the time I am to the point where I should technically follow question 50, I have already completed the other 49 (well, unless question 2 says “Skip the next 47 questions” or something like that). You get to question 50, and your test is invalid because you have already written things down. But you still need to go through the motions to cause the invalidation.

No matter how many times I explained it to the guy, he just couldn’t grasp that I was correct by completing all of the numbered questions. Had he never seen a paradox plot point in a time travel movie before? Gaah, it’s been 20 years and I’m angry all over again!

I gave a similar test to a class I was once teaching. A few of them had done something like it in the past, so they weren’t fooled; and a few followed the instructions to the letter, so they had no problem. But a couple didn’t–and they ended up standing on chairs, shouting their name, stating, “I’m on Question 15,” and so on. At least they were good sports about it, when they realized what it was all about.

My contribution to the thread: How long is a piece of string?

Twice as long as half its length.

Then it isn’t empty.

yup, he dumped the water down the sink. he didn’t empty it.

Yeah, I don’t see why, when given conflicting instructions, it has to be the instruction that is followed and the other 49 instructions disobeyed, rather than the other way around.

Put another way, giving anyone a test with conflicting instructions is dooming them to failure, one way or another; there’s no call to feel smug, then, when they happen to fail the unpassable test.

No, it was pretty simple for me. You have to make two cuts in a board to get three pieces. If it took 10 minutes to cut it into two pieces, then it will take twice as long to make two cuts, or 20 minutes.

Well, near be it from me to look at a problem wrong, and/or to overlook the obvious, but for me the answer of 20 minutes assumes that each cut has to take the same amount of time.

But regardless of how long the first cut takes – for example, assuming that the board is of equal consistency throughout, then cutting off a corner of the board – the second cut can be to cut off a corner of the smaller piece. And the second cut would take a shorter time than the first cut, no? So an answer would be 10+ minutes.

This thread is giving me flashbacks to 4th grade, when my heinous thundercunt of a teacher would throw a bunch of these at us and then mock me and refuse to help (“If you were paying attention you should understand it!” Bitch I ALWAYS paid attention I just didn’t freaking get it!) while the other kids snickered and I got more and more frustrated and ashamed and stupid-feeling until I finally broke down in tears. I hope the vicious old sea hag died alone in a puddle of her own piss and was eaten by her cats.

Whew. Didn’t realize I still had that much raeg about word problems. Don’t mind me; we now return you to your regularly scheduled mathy thread.

Unless the track curves…


Or how about this:

A train leaves New Orleans heading North at 40 miles an hour, and after reaching Arkansas, this train continues west at 90 miles an hour. At the exact same start time, a train leaves from Los Angeles at 80 miles an hour going east. Once this eastbound train passes Nevada, it turns slightly southeast and increases speed to 100mph . The trains never stop. Time passes. It is now 3 hours since each of these trains began its trip. Now which one is closer to LA?

The one that left New Orleans

You might have the right answer, but how is that computed? Or am I missing something obvious? It appears that without knowing the distance between NO and LA and their relative positions on a map, you have insufficient data to compute an answer.

I stand by my answer —though I suppose you could look at it another way…

LA is the abbreviation for Louisianna

Even if the cuts are of equal length, if you use my saw, the second cut will take a lot longer than the first, because the teeth got dull from the first cut.

It’s also the abbreviation for Los Angeles, so the question is ambiguous at best, and the antecedent for “LA” is, in this problem, “Los Angeles.”

Furthermore, there are two states and two cities mentioned here. Neither state is mentioned by its 2-character postal abbreviation, but its full name. So introducing another place name without qualification doesn’t suggest a state at all.

I get the intention of the problem designer, but it’s not a well-designed problem in the slightest.

I disagree.Sure you do. It’s the only way to keep the whole sordid affair secret.

There are two barrels filled with an equal amount of water. One has two, one-inch diameter holes, the other has one, two-inch diameter hole. Which barrel will drain the water faster?

Surprisingly easy, especially if you draw it. Most kids will say they’ll drain water at an equal rate.

Having trouble with this one:

  1. If the barrels are both filled with 0 liters water, they’ll drain water at an equal rate.
  2. If barrel 1 has the hole on top, and barrel 2 has one hole on top and one hole on bottom, barrel 2 will drain water faster.
  3. If barrel 1 has the hole on bottom, and barrel 2 has the holes both on top, barrel 1 will drain water faster.

and so on.

Two barrels.

Assume both barrels are made of identical materials. Holes through the bottom of each. Assume they’re both corked until the water is ready to be drained. Assume the the corks are pulled at the same time. Assume there is no lid on the top of the barrels to act as a vent hole. Assume both barrels are filled with water of equal density, temperature, and viscosity. Assume both barrels are next to each other on the same planet, same plane, same height, and are drained at the same time of day, under the same phase of the moon.

The lid is a big one–if I understand you, both barrels are open on top. In that case, unless I’m drastically missing something, it seems totally obvious than the 2-inch-diameter hole drains fastest, since the hole is larger. Am I missing something?

[edit: just to be pedantic, I’m assuming that the holes are all cylindrical–otherwise we lack sufficient information to solve the problem).