^ This one is easier than my 5th grade math question (40 years ago).
Here is a solution:
- The warehouse can receive 3⋅60⋅8 = 1440 hectoliters of the solvent per day, or equivalently, 1440⋅100 = 144,000 liters of the solvent per day. Therefore the number of bottles that can be accepted each day is 144,000/5.2 ≈ 27,692.30769. The maximum number of bottles that the warehouse can accept in one day is therefore 27,692, choice (C).
Notes: (1) Since there are 60 minutes in an hour, “3 hectoliters per minute” is the same as 3⋅60=180 hectoliters per hour.
Similarly, since the warehouse can accept the solvent for a maximum of 8 hours per day, “180 hectoliters per hour” is equivalent to a maximum of 180⋅8 = 1440 hectoliters per day.
(2) In the above solution we combined the two conversions given in note (1) into a single conversion: “3 hectoliters per minute” is equivalent to a maximum of 3⋅60⋅8 = 1440 hectoliters per day.
(3) Since 1 hectoliter equals 100 liters, we can convert hectoliters to liters by multiplying by 100. So
1440 hectoliters is equal to 1440⋅100 = 144,000 liters.
(4) We can convert between hectoliters and liters more formally by setting up a ratio. The two things being compared are “liters” and “hectoliters.”
liters 100 x
hliters 1 1440
Now draw in the division symbols and equal sign, cross multiply and divide the corresponding ratio to find the unknown quantity x.
100/1 = x/1440
1x = 100⋅1440
x = 144,000
(5) Instead of converting 1440 hectoliters to 144,000 liters, and then dividing by 5.2, we can instead convert 5.2 liters to 5.2/100 = .052 hectoliters, and then divide 1440/.052 ≈ 27,692.30769, giving the same answer of 27,692, choice ©.
^ Again, another mostly computational problem that I don’t find much interest in (of course, opinions may differ, but I don’t find the newer SAT problems very interesting compared to the older ones).
Also, I don’t think I’ve seen the word “hectoliter” used before…
This problem falls under the category “Problem Solving and Data Analysis.” Many of these problems are about interpreting either a paragraph, table or graph, and then doing some computations (usually involving percents or ratios).
The new SAT will have lots of words such as “hectoliter” that most students have not seen before. Notice that the conversions to liters was given in the problem. The College Board wants to see if students can convert between units they haven’t heard of when the conversion formula is given.
The new SAT, in my opinion, will be much less interesting than the current version. But it’s coming, and my job is to prepare students for it, not to criticize it.
^ Exactly right! But for all of us who have been in the field for a long time, I do expect that we will miss the old sat when it is gone. Not because the new one will be prep-proof or that it will put us out of business. I am confident that neither of those things will be the case. But the old SAT has some qualities that I will miss. Sadly, SAT prep was frequently the only place where students discovered the playful side of math. Math is supposed to be a creative field, not a rigid, cook-book class. The current SAT has at least some of that going for it. The bizarre, never-seen-before, can-you-read-think-play…I just hope the new SAT manages to retain at least a hint of that. But I suspect it won’t. What they have released so far is certainly manageable but not exactly elegant. Oh, well. As @DrSteve has said, it’s coming and we have to prepare.
I am trying to build a strong foundation for my DD now. She is class of 21 and will have to take the new SAT. Hopefully she will not have too many gaps. Currently she is working through Paul Foerster "s Algebra I which is filled with great word problems.
The above describes the element of the SAT that has been most often misunderstood by its critics. Of course, the critics were often cut from the same clueless and misguided fabric that drapes the “anti-test” band of morons.
What many called --erroneously-- tricks and traps were none other than the creative and often amusing “counter” approach to the stale math education that accounts for the “learn today and forget tomorrow” accounts.
The College Board knows better but this is a time they HAD to kowtow to the picks and forks brandishers of our education system. If that means an alignment to the Common Core or whatever new fad will face the students, it remains that the old SAT was hardly the enemy. It should have been and was the friend of many who could parlay a few dollars and hours of hard work into a score that might elevate them above their less industrious peers.
On a personal note, I am not horrified by the presence of terms such as hectoliter, and this because I believe that such terms SHOULD be part of the arsenal of any graduating HS senior worth his or her salt. It reminds me of the excuse offered by the teacher’s union to defend the low scores on PISA. A problem was using centimeters and the unions thought that it was the cause of the failure to measure the size of a ribbon around a box. Of course, the unit was completely irrelevant as it could have been inches or meters.
Perhaps the new SAT or future tests simply miss the mark entirely in trying to espouse the (deficient) HS curriculum! They should adopt a totally different test that might be a PISA on steroids, full with metric units, hints of maps from countries Joe SixPack only heard if they have a NFL team, and full of foreign words.
Perhaps, by then, some might understand how lacking our K-12 has become in terms of international comparisons. When you have kids who barely can afford a pencil and some paper beating our clock, the response should be to ring another alarm a la A Nation At Risk. What we do is change the test to delay the inevitable. If education was a medical process, our answer would be to invent a new thermometer to lower temperatures.
The bottom line? I am now definitely out of this “game” and will join the dinosaurs who liked the older tests a lot better. Good luck to yall!
Level 4 Heart of Algebra:
2x + y = 7 – 2y
5y – x = 5 – 4x
If (*x*,*y*) is a solution to the above system of equations, what is the value of (*y*+1)/*x* ?
(A) -11
(B) -1/2
(C) 2
(D) 20
b… this is like school… not current sat
^I disagree. The system of equations above is a very common SAT-type problem. There’s more to it than a typical SAT problem, but its still primarily testing the ability to solve a system of equations.
@Suly99 That’s correct. This thread is for the revised SAT beginning in March 2016.
Here is a similar thread I started a while ago for the current SAT: http://talk.collegeconfidential.com/sat-preparation/1639760-sat-math-problems-thread.html#latest
@CHD2013 This one is a bit questionable. I do agree that on a few rare occasions a system of equations somewhat similar to this has shown up on the current SAT. But the hardest one I can remember was still a bit less involved than this one.
Most systems on the current SAT would allow you to perform a simple operation to get the answer quickly. In the rare case where elimination or substitution had to be used, the question would simply ask for x or y as opposed to the more complex expression asked for here.
I agree that this problem is harder than a typical problem on the current SAT. But I think it is primarily testing systems of equations, which are commonly tested on the current test. I now think I see the point of the problem though, which is that the new test would seem to use systems of equations as part of a more complex problem.
Looking at the previous problem, I feel that the purpose of the (y+1)/x part is to discourage the previous strategy of mindlessly plugging in the answers - if the question was simply “what is the solution (x,y) to this system?” then one could easily plug in the choices. Now it actually forces you to solve for x and y. But it can still be solved with a graphing calculator.
@MITer94 I think there’s a little more to it than that. This problem involves more than 2 steps. Regardless of which method you choose to solve this, you will have to manipulate the equations algebraically first. If you choose to use your graphing calculator you will need to solve both equations for y (and also if you solve by substitution). If you choose to use the elimination method or Gauss Jordan reduction, you will have to bring all the variables to the left. On the current version of the SAT you would always need only 1 or 2 steps to solve the problem.
So this problem is testing
(1) algebraic manipulation
(2) finding the unique solution to a system of equations
(3) evaluating an expression at a given point
I don’t think that there has been an SAT problem that required all 3 of these skills in 1 problem. If there is one, it would most likely be a rare Level 5 problem. If you have one I would be really curious to see it.
Well, I find this problem to be very interesting for meta-math reasons. It illustrates what we are all up against as the SAT changes. When I looked at it, I thought: OK, this is a system of 2 equations and 2 unknowns. The math teacher side of me knows how to solve those and then you can plug in to the expression…but the SAT teacher sees the expression and suspects that there is an easy work-around. It used to be something you could rely on – that seemingly weird requests to evaluate random-seeming expressions where actually an invitation to a shortcut. But now, we just don’t have enough data to know if the rules have changed. So this time, it may save time to just go ahead and solve the system.
For the record, I have never seen a current-style actual SAT problem that requires a simultaneous solution of a system of 2 eqns. There has always been a work-around. But now we have to wait and see…
@pckeller I have seen at least 1 actual (current or possibly pre-2004) SAT problem where you had to actually solve the system (but you only needed to find one variable). Just adding or subtracting the equations didn’t work. In this problem the first 2 skills I mentioned above were being tested, but not the third. This problem was an anomaly however - I haven’t seen one in quite a while. I do always teach my super-advanced students how to do Gauss-Jordan reduction on their calculator as a precaution (only students going for an 800).
Based on the information I have read from the College Board I am fairly certain of 3 things (let’s say 90%):
(1) the College Board still intends to put systems of equations on the test where applying a simple operation like addition, subtraction, multiplication, or division will give the answer quickly.
(2) the College Board will also have systems of equations that need to be solved completely.
(3) there will be many more multi-step problems (especially at the higher levels) where students will be expected to complete more than 2 tasks (with more than 2 different skills) in a single problem.
I should perhaps phrase it this way - at this moment in time the College Board probably intends to do these things. It is entirely possible that the College Board may change their mind about certain things after looking over the data they receive from the experimental sections on these last few and next few SATs. As test prep professionals the best we can do is keep our eyes on all information and sample problems as they are released, and continue to adjust accordingly as we acquire new information.
Does anyone know when “the point of no return” is for creating an SAT? For example, by what date will the March 2016 SAT be written, and is there a last date when the test can no longer be modified?
Level 4 Passport to Advanced Math
1/x + 3/x = 1/2
Dennis is helping Billy assemble his new computer desk. Billy can put the desk together three times as fast as Dennis, and together Billy and Dennis can finish assembling the desk in 2 hours. The equation above represents this situation. Which of the following describes what the expression 3/x represents in this equation?
(A) The fraction of the job that would be completed by Billy in 1 hour.
(B) The fraction of the job that would be completed by Dennis in 1 hour.
© The time, in hours, that it takes Billy to complete one third of the job.
(D) The time, in hours that it takes Billy to assemble the desk by himself.
I read the above comments regarding needing three steps, having to solve for both x and y, or this being a traditional SAT problem. I understand what everyone is saying … except that I happen to think that this problem can be solved in one step as it requires a negative value for [(y+1)/x] and 11 is not an appealing solution.
Maybe I missing a key mathematical concept here, but if the above does not work, it can still be solved in two steps by first subtracting the two equations and then solving for … (y+1)/x through a simple manipulation from x + 2y = -2.
I must be missing something here.
B.