Total Math Geek Question

Please answer and explain the following real SAT question. “How many three-digit numbers have the hundreds digit equal to 3 and the units digit equal to 4?” The only restriction stated is: “All numbers used are real numbers.”

Related question: Is there a meaning of the term “three-digit” that would cause negative numbers to be excluded?

I hope I didn’t read that question wrong, but here goes…

  1. 304
  2. 314
  3. 324
  4. 334
  5. 344
  6. 354
  7. 364
  8. 374
  9. 384
  10. 394

Answer : 10 numbers.

If I’m wrong, someone correct me.

Louie: young guy, possibly a bit green, but smart as paint. - Greg Charles

According to my dictionary, “digit” is defined as any of the Arabic numerals 1 through 9 and usually the symbol 0 (zero).

So, if they are counting positive and negative numbers, and 0 as a digit, then the answer is 20.

Is that an option?

Is 10 an option?

How about 9 or 18?

Supposed “math” questions like this make me wanna puke. If you ever look at sample math tests from Japan you’ll see simple questions that require a solid understanding of algebra or trig or whatever to solve. We get crap like “How do you think the College Board defines the word ‘digit?’”

Let me get this straight. That question was in the SAT (is it Standard Aptitude Test?). Now, all I know of the American education system is from TV so bear with me. Does a high score in this test win you a scolarship and determine your suitability for University? Is the test multiple choice?

MadHun, your understanding of the SATs is correct. This question demonstrates that the SATs has nothing to do with one’s knowledge of mathematics (Math Section) or vocabulary (English section). It has to do with some pompous peon being proud that they have thought up some crazy twist.

The worst part is that such “trick” questions are used to trump-up stats to say why “little Johnny” can’t read, write, do math, or identify the US on the map! Our so-called educators that we hold upon high have just been kissing the ole Blarney stone!

“They’re coming to take me away ha-ha, ho-ho, hee-hee, to the funny farm where life is beautiful all the time… :)” - Napoleon IV

Thanks for that. I ask because I was about to launch into a tirade about how proposterously lame it is and thought I should be sure of my facts. So, and this is not some half-assed attack on the USA, all you have to do is score well in a multiple choice test (I say test because exam hardly seems appropriate). If the question posted by the OP is typical (of difficulty, not ambiguity) then I can only imagine there are Universities being built on a daily basis to accomodate the 90% or so who must surely make the grade.

Mad Hun, I’m afraid you’re under some misconceptions. The SATs are not entrance exams (some colleges, like my alma mater, don’t even consider SAT scores). They are a general aptitude test designed to determine what a student knows.

A college can’t be sure what a grade means in a particular high school. Different schools (and even different teachers within a school) grade more leniently or more strictly; that’s just human nature. So if you have two students from different schools, both with 90% averages, a college can’t always tell if those numbers are comparable.

The SATs are designed to try to make the numbers comparable. In theory, if you have two students with a 90% average, with one with 600/600 on the SATs and the other with 500/500, the former is probably the better student.

(As an explanation, general SATs contain a reading and math component, thus the two grades. There are also SAT achievement tests for specific subjects – biology, math, etc.)

In theory. In reality, there are issues about the fairness and what exactly the SATs are actually testing (other than the ability to take SATs).

Most colleges take other factors into account – type of courses taken, essays (most students are required to write one), participation in school activities, etc. A low SAT score is only one factor in making the decision to admit.

“What we have here is failure to communicate.” – Strother Martin, anticipating the Internet.

Hello all. I don’t quite feel comfortable defending standardized tests as a whole (and that should be done in GD) but I do have some insight to share. I am a part-time teacher for Kaplan’s SAT and LSAT courses. One of the things we convey to students is the why of the test. Not just why they should be taking said test (pretty much a no-brainer there - to get into the school of their choice) but also the why of a particular question. Although the case is typically a bit stronger with LSAT questions, there is some good reasoning behind SAT questions.

Jinx was right, the primary purpose of the SAT is not to test one’s knowledge of mathematics. The exception to this are the Subject Tests RealityChuck mentioned. The regular SATs even provide basic geometry formulas at the beginning of the section. Students proficient in math may have a very slight advantage, but the top scores generally go to those students who have better reasoning abilities. I am constantly amazed (as are my students) at the dramatic increase in the score of a student who realizes this and turns it to his or her advantage.

Looking at the OP question as if one was taking a math test, one might be inclined to write out each possibility or go through each possibility in one’s head, counting along the way. But look at the question. Recognize that the three and the four in the hundreds and units position is extraneous information. The question is essentially asking ‘how many single-digit real numbers are there?’ This is not a ‘trick’, it is an insight into the question. The test is designed so that for the most part (and here is the math-inclined student’s advantage) one does not have the time to mathematically solve each question. But if one can think through the question and see what it is really asking, one will generally (there are always exceptions) answer questions quicker. Do this and keep track of important information (the possibility of negative numbers, for example) and one will answer more questions correctly. Do this consistently throughout the test, and you will have a higher score. This reasoning ability is one of the things (see RealityChuck’s comments as to the other things) that admissions officers look for in potential candidates.

This is not the best question to use as and example (I leave it up to the test’s editors to defend their inclusion / exclusion of zero as a digit) but it does (I hope) show that the SAT is more than an annoying math quiz filled with trick questions. It also has a verbal section :slight_smile:

Thanks for listening,


Once in a while you can get shown the light
in the strangest of places
if you look at it right…

In 1980, I was admitted to the University of California at Berkeley based solely on my SAT scores. Since I had some attitudinal problems with authority, my 11th grade (my last year of high school) GPA was 2.01.

I hate to get back on topic here, but what number system is this problem for? I’m assuming decimal (since it says “hundreds digit”). If we can use other number systems, you get all sorts of new possibilities. In hexadecimal, for instance, you can also use 3A4, 3B4, 3C4, 3D4, 3E4, and 3F4. (technically, the third “digit” is now the 256ths digit, but 256 is still in the “hundreds” as it were). And these are all real numbers too.

In fact you could make up your own numbering/symbolic system and the answers could go on forever.

To get back off topic, I never took the SAT. I took the ACT and got a 32, but then I went to tech school and they didn’t give a rat’s ass.

After our SAT scores were returned to the high school, the counselors meet with every student and said the score says you should enter this carrier after high school. They didn’t tell you the score either, but ma did.

I placed out in the middle of nowhere on their chart. Miles away, but closest was scientist, mathamatician, or such stuff. Computer geek wasn’t on the chart then. They didn’t know what to tell me.

Graduating class book did deem that I would be the computer guru in the future. Class mates were close, and consider that this was 1980. The school had a computer phoneline terminal.

Have we landed in Cuba yet?

I was trying to say that the SAT scores are not accurate for what they try to use them for.

Thanks, Rhythmdvl. You were addressing exactly what I mean. The problem is that the “answer” is 10. I refer you to page 600 of your “Ten Real SATs” book that I assume you have. I too teach these classes (verbal) and I hope you use that book. If you don’t, shame on you.

How the heck is the answer not 20? P.S. - 0 is a numeral. The numerals in the “places” are always positive, it’s the number as a whole that’s negative.

Attack or defend.