An SAT math question..

[Adolescent09]

I know this isn't exactly the best place to post this, since this is a literary forum and not an arithmetic forum, but this problem has been bugging me all day... and I want to know if it is just me, or can anyone else solve this?:

How many 3 sets of consecutive numbers multiplied by each other, less than 1,000 are "tri-factorable"... (in other words, factored by at least 3 individual numbers)

You can't spend all day doing it as well... You have only a minute to answer the question...


Considering, that on most of my timed SAT practice exams I score 720-760, I feel pretty stupid, not knowing how to do this in less than a minute. Can any of you do it?

[papayahed]

The consectutive numbers multiplied are less then 1000? or consecutive numbers under 1000?

If it's the second that would be a huge number.

[Adolescent09]

The consectutive numbers multiplied are less then 1000? or consecutive numbers under 1000? The consecutive numbers are less than 1000 though. The set of three numbers multiplied by each other are less than 1000. The numbers themselves are less than 1000. You're supposed to find out how many three consecutive numbers under 1000 are "tri-factorable"

[Shalot]

But what does "tri-factorable" mean? Maybe you shoud subscribe to a math journal...

Since you're still preparing for the test, you should take it to some Math teacher at a college --- maybe they can direct you to the proper "smart person".

Google, the all-knowing oracle of the Internet, doesn't even know what tri-factoring is. Is this a newly discovered mathmatical technique similar to e or something?

(BTW: don't take me seriously---I'm mathmatically retarded) Good Luck

[papayahed]

If I'm getting this right then the highest 3 consectutive numbers that are less then 1000 are 9*10*11 = 990

The lowest is 1*2*3 = 6 so

2*3*4
3*4*5
4*5*6
5*6*7
6*7*8
7*8*9
8*9*10
9*10*11


All will products will be even so 10.


At least I think so.....Tal? Virgie?

[papayahed]

And don't worry there are quite a few hidden and not-so-hidden math types lurking about this bored.

[kathycf]

And don't worry there are quite a few hidden and not-so-hidden math types lurking about this bored.
Is that what is known as a Freudian slip? ;)

Ok, please don't get mad, math people. I am just making a silly joke. I would not have the slightest clue how to solve the problem. I only lurk around this board to make foolish jokes.

[papayahed]

Is that what is known as a Freudian slip? ;)

Ok, please don't get mad, math people. I am just making a silly joke. I would not have the slightest clue how to solve the problem. I only lurk around this board to make foolish jokes.

HaHa! Opps wrong website. Actually No. On another website they always substitute "Bored" for "Board" and I've also gotten into the habit.

[cuppajoe_9]

The easiest way to solve all the math problems on the SAT is to go to university in Canada.

Sorry I can't be any more help than that, but I'm an English major.

[Adolescent09]

If I'm getting this right then the highest 3 consectutive numbers that are less then 1000 are 9*10*11 = 990

The lowest is 1*2*3 = 6 so

2*3*4
3*4*5
4*5*6
5*6*7
6*7*8
7*8*9
8*9*10
9*10*11


All will products will be even so 10.


At least I think so.....Tal? Virgie?

Wow, you got it right... but 10 is wrong lol.. The answer is 9.. But you typed it down correctly:

1) 1*2*3
2) 2*3*4
3) 3*4*5
4) 4*5*6
5) 5*6*7
6) 6*7*8
7) 7*8*9
8) 8*9*10
9) 9*10*11

Sadly enough... there is no way I could answer this problem in less than 1 minute :(.. and it's a level 5 problem.. I'm too slow and stupid. Thanks for helping me though :)

[papayahed]

Sadly enough... there is no way I could answer this problem in less than 1 minute :(.. and it's a level 5 problem.. I'm too slow and stupid. Thanks for helping me though :)


I'm sure you're not slow and stupid. For questions like that first figure out the three highest consecutive numbers that are less then 1000. If you don't have a clue just pick a random set like I did then work from there. Once you have the set you can determine which are trifactorial.

All numbers are at least divisable by 2 numbers so you know that each set all have at least 2 divisors. There is at least 1 even number in all the sets so they are all going to be even numbers (even * odd = even, odd*odd = odd, even*even = even). Even numbers are always divisable by the number 2 so viola all sets are trifactorial.


There maybe a better way but it's been a long time since I've taken a math class.

[Koa]

I'm not even trying...the day maths was out of my life was a happy happy one :D

[mcilroga]

I'm not even making an attempt, precisely for the same reason as Koa's: I hate Math. When you need help with Phrasal Verbs, I'll be there in a flash. :D

[optimisticnad]

I'm sorry, I'm far too dumb for this kinda stuff!

Back to my alphabets. A for apple....

[Weisinheimer]

The question does really make that much sense to me. If it's a set of three numbers, of course the product will have three factors, right? I don't know, it's been a while since I've done any math.

[Weisinheimer]

Oops, I meant to say that it DOESN'T make sense. I noticed right after I posted, but my computer is really slow for some reason, so it's quicker to make another post.

[Adolescent09]

The SAT math is a sagaciously improvised hoax. What they do, is twist the fundamentals of math into their own intricate puzzles and heavily obscure their concepts so as to make the problem seem almost impossible to solve. Thanks for posting, everyone :)

[Koa]

It's not a fundamental question, but just out of curiosity, what is SAT?

[Adolescent09]

It is based on fundamentals--in this case--multiplication, but it doesn't look like it because they twist it into their own little games. That's what I meant.Standard Achievement Test---I believe it is required throughout The United States.

[kiz_paws]

The SAT math is a sagaciously improvised hoax. What they do, is twist the fundamentals of math into their own intricate puzzles and heavily obscure their concepts so as to make the problem seem almost impossible to solve. Thanks for posting, everyone :)

LoL, Adol, you are soooo good with words! :lol:

And don't feel bad and berate yourself over not being able to get the answers quickly -- math was never my forte, either. I think it was very cool the way that you were able to post here and get help from friends. Isn't this the best site, I mean it!! :)

[Virgil]

I know this isn't exactly the best place to post this, since this is a literary forum and not an arithmetic forum, but this problem has been bugging me all day... and I want to know if it is just me, or can anyone else solve this?:

How many 3 sets of consecutive numbers multiplied by each other, less than 1,000 are "tri-factorable"... (in other words, factored by at least 3 individual numbers)

You can't spend all day doing it as well... You have only a minute to answer the question...


Considering, that on most of my timed SAT practice exams I score 720-760, I feel pretty stupid, not knowing how to do this in less than a minute. Can any of you do it?

Oh sorry I'm just seeing this now and i have not read the entire thread to see if there is an answer. But aren't all three consecutive numbers multiplied tri-factorial? Except for zero. So I would think it's
1*2*3 (1)
2*3*4 (2)
3*4*5 (3)
and so on to
998*999*1000

Does that add up to 998?

That's my answer.

[Virgil]

It's not a fundamental question, but just out of curiosity, what is SAT?

It's a college entrence exam here in the US.

[Virgil]

Considering, that on most of my timed SAT practice exams I score 720-760, I feel pretty stupid, not knowing how to do this in less than a minute. Can any of you do it?

I can't believe one only has a minute for this. But 720 is an outstanding score Adol. 800 is perfection. You have nothing to be ashamed of. I only scored in the 500's. The high 500's. ;)

You should be able to get into a great college. And so who says home schooling doesn't work? Your mom ought to be proud of you, and you should be proud of your mom for making such a smart young man.

[Adolescent09]

Why, thanks virgil. I've recieved nothing but kind words from you. Yes, she is quite content with me and I with her. There is no disappointment in our mother-to-son relationship :)

Then again the SAT's and which College you go to doesn't determine the rest of your life. I've seen so many people with high grades attend elite schools and end up flunking. They think the SAT is all they need to sail through college and they are gravely mistaken. Random timed tests, with silly questions and ridiculous limits don't determine anything. I think it is the effort and initiative you reserve for a task that makes you excell in life. And doing what you love is a major bonus. My mom is shoving me towards being a doctor although I wan't to be a lawyer (and an author on the side)... but that's a whole different matter lol. Thanks for posting, Virg.

[Adolescent09]

LoL, Adol, you are soooo good with words! :lol:

And don't feel bad and berate yourself over not being able to get the answers quickly -- math was never my forte, either. I think it was very cool the way that you were able to post here and get help from friends. Isn't this the best site, I mean it!! :)

Yes this is a truly singular site--in a good way. Thanks for the comment and your post :D

[RobinHood3000]

Actually, SAT no longer stands for anything. Throughout the years, it has been an acronym for a variety of things, usually some combination of Scholastic/Standard, Aptitude/Achievement, and Test. There is no current meaning, however. Go figure ~shrug~.

Although I do sympathize with your plight, the SAT Math is more problem-solving based than a lot of other tests. There are worse tests that REALLY feel like the writers picked an answer and worked backwards. As it stands, scoring above 700 is EXCEPTIONALLY good.

To solve the problem, the trick behind it is knowing that that, because the final product is the product of three numbers, EVERY number received from multiplying three consecutive numbers is "tri-factorable." Knowing that the cube root of 1000 is 10 (hence 10 * 10 * 10 = 1000) and that 9 * 11 is less than 10 * 10 (hence 9 * 10 * 11 < 10 * 10 * 10) yields 9/10/11 as the highest set of three and 1/2/3 as the lowest - hence, there are (9 - 1) + 1 = 9 sets.

[Virgil]

I took the qestion to be how many consecutive sets under 1000 when multiplied. Robin, you seem to have taken it as how many sets when multiplied are under 1000. I wonder which is the right way to interpret that question? Does anyone have the correct answer?

And thanks Adol. Lawyer?? I was hoping that with math grades like that you would say science or engineering or medicine. If you're an engineer and my place is hiring, I would hire you. So think about that. :)

[RobinHood3000]

That does seem to be the question of the day, doesn't it? I think Adol posted that the right answer was 9, so I assume it was the former. The latter method would mean that the highest set would be 997/998/999 and the correct answer would be 997, right? Well, inclusive would mean 998, but there's no mention of that, so I guess it's the former.

[Virgil]

Thanks Robin. I guess that's why I didn't get 720 on my SAT. :D

[Adolescent09]

Actually, SAT no longer stands for anything. Throughout the years, it has been an acronym for a variety of things usually some combination of Scholastic/Standard, Aptitude/Achievement, and Test. There is no current meaning, however. Go figure ~shrug~.

Although I do sympathize with your plight, the SAT Math is more problem-solving based than a lot of other tests. There are worse tests that REALLY feel like the writers picked an answer and worked backwards. As it stands, scoring above 700 is EXCEPTIONALLY good.

To solve the problem, the trick behind it is knowing that that, because the final product is the product of three numbers, EVERY number received from multiplying three consecutive numbers is "tri-factorable." Knowing that the cube root of 1000 is 10 (hence 10 * 10 * 10 = 1000) and that 9 * 11 is less than 10 * 10 (hence 9 * 10 * 11 < 10 * 10 * 10) yields 9/10/11 as the highest set of three and 1/2/3 as the lowest - hence, there are (9 - 1) + 1 = 9 sets.

Great post and great explanation. Yes, I understand how you solved the problem and you did it using a methodology I would never think of! The cubed root of 1000. That's interesting. Thanks a lot for posting Robin and by the way; are you very good at math?

[Adolescent09]

And thanks Adol. Lawyer?? I was hoping that with math grades like that you would say science or engineering or medicine. If you're an engineer and my place is hiring, I would hire you. So think about that. :)

That's what my mom and tutor says when I insinuate that I aspire to be a lawyer :P. Well I definately might contemplate it and change my mind... Teenagers are so volatile. :p

[papayahed]

And thanks Adol. Lawyer?? I was hoping that with math grades like that you would say science or engineering or medicine. If you're an engineer and my place is hiring, I would hire you. So think about that. :)


What the heck Virgie??????? You know I'm looking!;). I'd have to second engineering - so that's settled Engineering. I guess Virgie and I will have to fight over which discipline.


I knew there would be an easier explanation to that problem, unfortunately I'm to far removed from school to remember any of that.

[RobinHood3000]

You're welcome, Adolescent, and yes, math is one of my stronger points. I'm glad my post could help, and best of luck with any other math problems you may encounter.

[Shalot]

:confused:

I have a math question of my own and rather than starting a new thread, I thought I would be economical and just post my question in this. It's not quite an SAT math question (we're not that advanced here) but since there are some people here who seem to like it and know it, I thought I'd ask:

It's about graphing logarithmic functions and the notation.

Say you have a function f(x) = 2 - log x (assuming base 10)

What does the 2 do to the graph? I understand that the -log x indicates a reflection about the x-axis. But does that 2 stretch or shrink it or does it move it up or down?

Does that mean to vertically shift the graph two units down, and if that's the case, why don't they just put f(x)= log x - 2?

f(x) = log(x-2) indicates a horizonal shift.

f(x) = log x -2 indicates a vertical shift down, right?


Or does f(x) = 2 - log x mean to stretch the graph vertically and then reflect it about the x-axis?

It's the placement of the 2 that is throwing me.

If it said f(x) = -2log x (assuming base 10) I would know exactly what to do with it. (told you I was mathmatically retarded)

[kilted exile]

I believe a positive shift of 2 on the y axis


y= 2 - logx = - logx + 2 as to y = -logx

y = - log1 + 2 = 2 as to y = 0
y = - log5 + 2 = 1.3 as to y = -0.699
y = - log10 + 2 = 1 as to y = -1


However, my brain has turned to mush doing my current menial job, so I may be completely wrong

[Adolescent09]

I believe a positive shift of 2 on the y axis


y= 2 - logx = - logx + 2 as to y = -logx

y = - log1 + 2 = 2 as to y = 0
y = - log5 + 2 = 1.3 as to y = -0.699
y = - log10 + 2 = 1 as to y = -1


However, my brain has turned to mush doing my current menial job, so I may be completely wrong

That sounds on the right track to me...

Here is what I've come up with, including adequate whole number values for X in order to derive integer values for Y. I did basic graphing of logarithms some time back so I bet I'm rusty...

f(x) = 2 - log x

X | Y
10 | f(10)=y= 2 - log (10)= 2 - 1 = ---1---
100 | 2 - log (100)= 2 - 2 = ---0---
1000 | 2 - log (1000)= 2 - 3 = ---- -1---
10000| 2 - log (10000)= 2 - 4 = ---- -2 ---

I believe that the gargantuan numerical value of x is irrelevant. The result should be this... because for every value X, Y covers the whole line...:

http://img362.imageshack.us/img362/5746/grapphhmc5.png

[papayahed]

Even though it's not a straight line it still fits the classic equation for a line.

Y = mX + B

where:
m = slope of the line
B = y intercept of the line (the point where the line crosses the Y intercept.)


In this case B = 2, which as kilted and Adol have said is the shift of Y

[Adolescent09]

Ach! I want her to reply! I'm itching to know whether we got it right or not :D

[Nightshade]

oh help :S I feel dizzy just looking at these but then again past 5th grade maths by the skin of my teeth and swapping countries and jumping a year I manged to avoide alot of the nastys and get left with things I could actually get my head around like algebra... Im very found of algebra.

But the only book I have ever diberatly destroyes and danced on was my maths book when I fianlly got to give it up!
Frankly anyone who can make a calulator work is amazing in my book...I still cant figure out how 1+1 could possibly =-1

[Shalot]

I think kilted is right -- it shifts the graph up by two. They have just placed the terms in strange places to mess with the mathmatically inept.

Still, I think that is bad form (hmph)

[bernard.schrieb]

Hi,
This is the way I worked the problem:

Start out backwards:

The last 3 consecutive integers whose product is less than 1000 is 9, 10, 11 (=990). You can guess that since 10 mulitplied by itself 3 times is 1000, so we have to look for 3 consecutive integers whose product is as close as possible but less than 1000.
Note that the first integer is 9.
The next series would be 8, 9, 10; then 7, 8, 9, and so forth until 1, 2, 3. Obviously, the smallest integer has to be 1, since 0 is not a positive integer.
Counting from integers from 1 -9 = 9 series of 3 consecutive integers whose product is less than 1000.

Hope this helps.

B

[bernard.schrieb]

:confused:

I have a math question of my own and rather than starting a new thread, I thought I would be economical and just post my question in this. It's not quite an SAT math question (we're not that advanced here) but since there are some people here who seem to like it and know it, I thought I'd ask:

It's about graphing logarithmic functions and the notation.

Say you have a function f(x) = 2 - log x (assuming base 10)

What does the 2 do to the graph? I understand that the -log x indicates a reflection about the x-axis. But does that 2 stretch or shrink it or does it move it up or down?

Does that mean to vertically shift the graph two units down, and if that's the case, why don't they just put f(x)= log x - 2?

f(x) = log(x-2) indicates a horizonal shift.

f(x) = log x -2 indicates a vertical shift down, right?


Or does f(x) = 2 - log x mean to stretch the graph vertically and then reflect it about the x-axis?

It's the placement of the 2 that is throwing me.

If it said f(x) = -2log x (assuming base 10) I would know exactly what to do with it. (told you I was mathmatically retarded)


You are right; f(x) = -log(x) is reflection of f(x) = log(x). For any f(x) = log(x), the value for -log(x) is its negative equivalent (remember order of operations).
The function may be less confusing if rewritten f(x) = -log(x) +2, which means that for any f(x) = -log(x) you shift the graph up by 2. You can think of that way: take f(x) = -log(x) and add 2 for any -log(x).
f(x) = -log(x) intercepts x at 1: f(1) = -log(1) = 0, just like f(1) = log(1) = 0.
Note that for f(x) = -log(x) + 2, f(1) = 2, so is shifted up by 2.
Hope this helps.