posted
Ok, So I'm taking the SAT's in the morning, and I've been taking online practice tests. I'm fine on everything except for a certain kind of question from Algebra 1 (which i took 4 years ago). Can Anyone around here explain how to do this problem to me.
If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks?
2 minutes and 44 seconds
2 minutes and 58 seconds
3 minutes and 10 seconds
3 minutes and 26 seconds
4 minutes and 15 seconds
The answer is 2 minutes and 44 seconds, but i can for the life of me figure out how to get it...
Posts: 1094 | Registered: Mar 2004
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posted
One piece of advice for the math portion of the SATs: Don't worry too much if you think the answer is not enough information. You can always come back to the problem later, and if there really isn't enough information you could spend way too long on a given problem.
I say this because I barely finished half of the questions on the math section my first time taking the test.
Posts: 2437 | Registered: Apr 2005
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7 1/3 drinks/minute * X minutes = 20 drinks 20/7.3333 = 2.7 something, which translates to 2 minutes 44 seconds.
That's the long way. The easier way, the way you're supposed to do it, is to say 3 minutes gives you 12 + 6 + 4 = 22 drinks, thus it has to be the 2:44 answer.
Posts: 10177 | Registered: Apr 2001
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posted
Good luck on getting a perfect + 400 points. That would be impressive. But as Squick and ricree say, best to try to intuit what the answer ought to be than to actually pound through formulas on a timed test.
Do the easy ones first, then come back to the hard ones is my advice. That's what I did on the F.E.
Posts: 5462 | Registered: Apr 2005
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JT, I got a perfect score on the SAT, I used to tutor for it, and two of the big pieces advice I can give you is 1) stressing over it is a really bad idea and 2) there are tricks, like the multiplying by 3 minutes (which is suggested by the only fractional proportion being 1/3 and the answers clustering around the 3) to many of the problems that make them much easier to solve. I don't know that the night before the test is the best time to think about that, but keep in mind when you're taking it that, if a problem seems very complicated, there's probably a silly little trick like that that will make it much easier. (Oh, and watch out for the pos/neg switch, especially when dealing with square (and any even power) roots and be on the look out for the things that work except when x = 0.)
posted
Thanks Mr.Squicky... I am trying my best not to stress over this stupid test, but i've been accepted into NYU pending my SAT scores... And NYU is my first choice for next year...
Posts: 1094 | Registered: Mar 2004
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posted
JT, If you don't get it this time, it's not the end of the world. You'll have at least one more chance to take it in the spring. Best advice I can give you is to stop thinking about the score you have to get. Put it out of your mind. You'll do much better on the test if you can do this. Strange as it may sound, taking the SAT can be kinda fun, if you approach it the right way. I was out at a party the night before I took em.
Posts: 10177 | Registered: Apr 2001
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posted
They have a math section, a writing section, and a critical reading section. The essay contributes to the writing score. They basically split up the verbal section into two other sections. It's out of 2400 now. I'll be taking the SAT myself in the semi-near future. I'm hoping to score in the 2200+ range.
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posted
Critical reading, eh? Do they still do the analogies and antonyms and such or is it all crit reading?
Posts: 10177 | Registered: Apr 2001
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Many schools ignore the writing section or count it as an SAT-II score. I personally hate the new format. My dad had me practicing for years, and they changed it on us
Good luck JT (and Mr.Funny). I'm taking the IIs tomorrow; hoping I do just as well on this one...
posted
The answer is actually 3 minutes exactly. Not what they're looking for, I'm sure, but it's correct nevertheless. At 3 minutes, Steven has just finished mixing his 12th drink, Sue her 6th, and Jack his 4th. Which comes to 22 drinks total. But a second before the 3-minute mark only 19 drinks have been mixed. To get their answer you'd have to assume that three bartenders can work together exactly as efficiently as they would alone, a pretty dubious assumption. I'm actually surprised no else has pointed this out. *looks around the thread to make sure*
(And somehow I got a perfect score on my math SAT and not on my verbal. Hmm. )
Posts: 1810 | Registered: Jan 1999
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quote:Originally posted by El JT de Spang: Steven mixed drinks at a rate of 20drinks/5minutes = 4 dpm Sue mixes at 2 dpm Jack mixes at 1.3 dpm
Together they mix (4+2+1.3) = 7.3 dpm
7.3 drinks/min = 20 drinks/x min
Cross multiply and solve for x.
The computer scientist in me says this answer is absolutely ridiculous, and indicative of the cloud of unreality that math professors usually walk around in.
20 drinks / 7.3 drinks/min = 2.739726027 minutes, or 2 minutes, 44.383561644 seconds. There are two problems with this answer, and the people making the SAT should be smarter than this.
First, if you round down, you'll get an answer that's too low. If you divide it back out - 20 / 2.733333333 - you get a combined rate of 7.317073171 drinks/min, which is faster than the combined drink-mixing rate of 7.3 drinks/min. They should round up instead.
Second - and worse - this assumes all three are capable of mixing the same drink at the same time without any reduction in efficiency. (Huh?) That's a really bad assumption, so let's take it out. In 2:44 minutes, Steven can mix 10.933333333 ~ 10 drinks. Sue can mix 5.466666666 ~ 5 drinks, and Jack can mix 3.553333333 ~ 3 dinks. 10 + 5 + 3 = 18 drinks.
(Assuming they can work on the same drink at the same time - totally infeasible, of course - Sue and Jack would mix one final drink together, and then both of them would help Steven with his last.)
Let's try having someone mix a non-fractional number of drinks and see what happens to the others.
Let's have Steven mix 11 drinks exactly. That's 11 / 4 = 2.75 minutes. Then Sue can mix 5.5 ~ 5 drinks, and Jack can mix 3.575 ~ 3 drinks. 11 + 5 + 3 = 19 drinks. Too short.
Okay, Sue's turn. She mixes 6 drinks: 6 / 2 = 3 minutes. Then Steven mixes 12 drinks, and Jack mixes 3.9 ~ 3 drinks. That's 6 + 12 + 3 = 21 drinks.
If Jack does 4 drinks, 4 / 1.3 = 3.076923077, which is larger than 3 - so that won't work either. We need an answer between 2.75 and 3.0 minutes.
Okay, that didn't work. Hey - one of the answers is 2.966666667 (2:58) minutes. Let's try it: Steven does 11.866666667 ~ 11, Sue does 5.933333333 ~ 5, and Jack does 3.856666667 ~ 3. 11 + 5 + 3 = 19 - whoops. I really thought they'd have it.
Well, it turns out this problem cannot be solved. Here's why: at 3.0 minutes, both Sue's and Steven's number of drinks roll over to an integer. At 3.0 minutes, they go from 19 drinks to 21 drinks.
Like I said, whoops. The SAT people really messed up on this one.
The worst thing is that people like me (both mathematical and incessantly pragmatic) would spend way too long on a problem like this to verify that they'd got it wrong. I'd finally put down 2:44 because that's what they were looking for.
posted
There was a case many years back (though this story might be apocryphal) that there was an unintentional trick question on the math SAT that ended up being successfully appealed. The question was this: if you take a regular tetrahedron and regular octahedron whose faces have the same area and glue them together along one face, how many faces does the resulting figure have? The answer they were looking for, 8 + 4 - 2 = 10, is not correct. Don't believe me? Look here. (OK, so I skipped a few steps. Sue me. )
[Edited the link so it makes slightly more sense.]
Posts: 1810 | Registered: Jan 1999
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Incidentally, if a hen and a half lays an egg and a half in a day and a half, how many and a half that lay better by half will lay half a score and a half in a week and a half?
Posts: 1810 | Registered: Jan 1999
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posted
Who are Sue and Steven, and when did Jack get so fast, I thought he had to drink them in between. Good job kid, I hope you can get as far away from this town as humanly possible.
Posts: 5362 | Registered: Apr 2004
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Incidentally, if a hen and a half lays an egg and a half in a day and a half, how many and a half that lay better by half will lay half a score and a half in a week and a half?
I think that the answer is 20/21 hens. The original hen lays 1 egg every 1.5 days. Thus, better by a half would be 1 egg per day, so the new set of hens lays at 1 egg per day. A week and a half is 10.5 days. The number of eggs to be layed (laid?) is a half a score and a half, which is 15. Since it's "how many and a half", the many part will lay 2/3 of the total eggs, or 10 eggs. Thus, the many portion will lay 10 eggs in 10.5 days. This must mean that there are 20/21 of a hen for the "many" portion, since the hens lay at 1 egg/day.
Posts: 1466 | Registered: Jan 2003
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posted
I think the way it's supposed to be interpreted is that "half a score and a half" is 10.5 rather than 15. That way the numbers work out better. It is rather ambiguous the way it's written, though, neh?
Posts: 1810 | Registered: Jan 1999
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