Where can I find sample arithmetic problems like this one!
July 15, 2013 1:17 PM
I'm taking a standardized test on Wednesday with the Government of Canada and they ask individuals four types of questions. The type that I struggle with are the arithmetic problems... specifically determining the formulas to solve word problems. I was hoping someone might be able to point me in the direction of a website or easily accessible textbook to practice today and tomorrow before the test.
I'm very rusty on this type math and just need some practice. Once I'm told the right answer, it makes perfect sense to me and I can actually figure out the right answers (not the formulas) with relative ease. I just seem to make things more complicated in my head making the simple answer seem too simple. The site provides a few example questions, but nothing in the form of an extended practice and there is no one to email/call for tips.
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Here's the example cut and pasted from their website.
Arithmetic problems
For the arithmetic questions, your task is to determine the formula for solving a problem and then to choose the correct formula among the five proposed. Try this example:
Question 2
An employee worked 11 hours in a day; 7 1/2 hours were regular hours and the rest was overtime, for which she received payment at time and a half. If she was paid $112 for the day, what was her regular rate per hour?
112 / (11 - 3.5)
112 / (11 - 1.5 × 3.5)
112 / (7.5 + 1.5 × 3.5)
112 / (11 × 1.5)
None of the above formulas
The employee is paid for 7.5 hours in regular time and for 1.5 × 3.5 hours for her overtime. The total number of paid hours is 7.5 +1.5 × 3.5. The regular rate is the amount paid for the day, $112, divided by the total number of hours paid. The correct answer is the third option.
I'm very rusty on this type math and just need some practice. Once I'm told the right answer, it makes perfect sense to me and I can actually figure out the right answers (not the formulas) with relative ease. I just seem to make things more complicated in my head making the simple answer seem too simple. The site provides a few example questions, but nothing in the form of an extended practice and there is no one to email/call for tips.
-------
Here's the example cut and pasted from their website.
Arithmetic problems
For the arithmetic questions, your task is to determine the formula for solving a problem and then to choose the correct formula among the five proposed. Try this example:
Question 2
An employee worked 11 hours in a day; 7 1/2 hours were regular hours and the rest was overtime, for which she received payment at time and a half. If she was paid $112 for the day, what was her regular rate per hour?
112 / (11 - 3.5)
112 / (11 - 1.5 × 3.5)
112 / (7.5 + 1.5 × 3.5)
112 / (11 × 1.5)
None of the above formulas
The employee is paid for 7.5 hours in regular time and for 1.5 × 3.5 hours for her overtime. The total number of paid hours is 7.5 +1.5 × 3.5. The regular rate is the amount paid for the day, $112, divided by the total number of hours paid. The correct answer is the third option.
You want to look for sample civil service exams. I ran into a lot of these a few years ago when I tested for jobs with the city.
These kinds of questions were only almost the most annoying. Came in second to "watch a 4 minute video of someone doing something stupid, and of these multiple choice options, tell us how you would react." (Hint: the answer is NOT "help Samuel steal the office supplies.")
posted by phunniemee at 1:33 PM on July 15, 2013
These kinds of questions were only almost the most annoying. Came in second to "watch a 4 minute video of someone doing something stupid, and of these multiple choice options, tell us how you would react." (Hint: the answer is NOT "help Samuel steal the office supplies.")
posted by phunniemee at 1:33 PM on July 15, 2013
"x" is your friend. "x" is the unknown. You need to solve for the unknown. This is linear algebra.
Turn the words into math.
The unknown is their hourly rate = x
Time and a half is 1.5 times their hourly rate = 1.5x
Therefore 7.5x + 3.5*1.5x = $112
Solve for x.
7.5x + 3.5*1.5x = (7.5 + 3.5*1.5)x = $112
x = $112 / (7.5 + 3.5*1.5)
All they've done in the above is not write down "x".
If this stuff is confusing, don't do it in your head, write it all down. And make a symbol (x,y,z, a,b,c whatever) to represent all the word items in the question.
posted by St. Peepsburg at 1:35 PM on July 15, 2013
Turn the words into math.
The unknown is their hourly rate = x
Time and a half is 1.5 times their hourly rate = 1.5x
Therefore 7.5x + 3.5*1.5x = $112
Solve for x.
7.5x + 3.5*1.5x = (7.5 + 3.5*1.5)x = $112
x = $112 / (7.5 + 3.5*1.5)
All they've done in the above is not write down "x".
If this stuff is confusing, don't do it in your head, write it all down. And make a symbol (x,y,z, a,b,c whatever) to represent all the word items in the question.
posted by St. Peepsburg at 1:35 PM on July 15, 2013
The easiest way to solve a word problem is to translate what the "words" mean. So when you see these words, "is, are, was, were, will be, gives, yields, sold for" they translate into the action "equals"
Purple Math explains it very well.
Good luck!
posted by JujuB at 1:42 PM on July 15, 2013
Purple Math explains it very well.
Good luck!
posted by JujuB at 1:42 PM on July 15, 2013
Oh I wanted to add... you could also try Spark Notes, they have a listing of word problems and may have books you can buy.
posted by St. Peepsburg at 1:44 PM on July 15, 2013
posted by St. Peepsburg at 1:44 PM on July 15, 2013
This isn't so much an arithmetic problem but an algebra problem. I would not do as duien suggests (checking the results of all the options with your answer) because these tests are timed and doing as suggested, you'll likely run out of time before you even finish 1/2 of the questions.
I'd suggest looking over some videos on Khan Academy about algebra (here's a good one). I've taken this exam before and I don't remember there being questions with more than a single variable. Once you've got the basics, it's just a matter of practice. (google for "algebra word problems").
posted by reformedjerk at 2:01 PM on July 15, 2013
I'd suggest looking over some videos on Khan Academy about algebra (here's a good one). I've taken this exam before and I don't remember there being questions with more than a single variable. Once you've got the basics, it's just a matter of practice. (google for "algebra word problems").
posted by reformedjerk at 2:01 PM on July 15, 2013
I was coming in to say what St Peepsburg said, almost verbatim. Write stuff down! Including what you know and what you want to figure out.
(FWIW, I do math (admittedly, not arithmetic) for a living, and that's a weird, confusing question. The *only* way I could get through it was by doing the algebra---that is, by saying 'okay, I want the hourly rate. Suppose that's x. Then she earned 112=7.5x [normal hours]+ (11-7.5)(1.5x) [overtime]'. Etc. )
posted by leahwrenn at 2:21 PM on July 15, 2013
(FWIW, I do math (admittedly, not arithmetic) for a living, and that's a weird, confusing question. The *only* way I could get through it was by doing the algebra---that is, by saying 'okay, I want the hourly rate. Suppose that's x. Then she earned 112=7.5x [normal hours]+ (11-7.5)(1.5x) [overtime]'. Etc. )
posted by leahwrenn at 2:21 PM on July 15, 2013
What some of you may be missing is that there isn't enough time to do these problems in a systematic algebraic way. I recommend doing as many practice problems as possible, it's the only way to get good at them so that you won't burn up time on the actual test.
posted by Yowser at 2:58 PM on July 15, 2013
posted by Yowser at 2:58 PM on July 15, 2013
buy a used algebra I textbook off of the internet. try to get one that's an older edition. it should cost $0.01 for the actual book an $3.99 for shipping and handling.
posted by cupcake1337 at 8:27 PM on July 15, 2013
posted by cupcake1337 at 8:27 PM on July 15, 2013
If you're having trouble "starting from scratch" to come up with a formula, try working backwards from the possible answers you're given. Since you have a list of possible solutions to choose between, you can just go down the list looking at the answers and deciding if they're crazy or potentially useful solutions.
You've got a few numbers: $112 earned total, 11 hours total, 7.5 hours regular, 3.5 hours overtime (which you have to get by taking 11 total -7.5 regular), and 1.5 overtime rate.
You're looking for an income($) per hour, and all the possible answers are a fraction with $112 on top, and some number of hours on bottom, so you're just left with the question 'how many hours?'.
11-3.5 doesn't make sense, because that's just the 7.5 regular hours.
11x1.5 doesn't make sense, because you're not getting overtime pay for all 11 hours.
The other two options have 1.5*3.5 in them, so you consider whether that makes sense, and what it means... and yes, that's 3.5 hours of overtime at a rate of 1.5x normal pay, that makes sense. So now, the thing that's left is to account for non-overtime pay for the other 7.5 hours.
Look at all the answers, and see what's similar about them, and what's different. Things that are similar, you can use to guide you into understanding the problem - for example, all of those answers said $112/(some number of hours), and most had 1.5x(some number). It will *usually* be true that is there's one of the four that's got an obviously different structure (like the one that doesn't have 1.5xsomething) then it will be one of the wrong answers - but don't take that too literally, since the right answer here is the only one that doesn't use the number 11. Safer to say, if there's one that's noticably different, it's worth looking at.
posted by aimedwander at 11:35 AM on July 16, 2013
You've got a few numbers: $112 earned total, 11 hours total, 7.5 hours regular, 3.5 hours overtime (which you have to get by taking 11 total -7.5 regular), and 1.5 overtime rate.
You're looking for an income($) per hour, and all the possible answers are a fraction with $112 on top, and some number of hours on bottom, so you're just left with the question 'how many hours?'.
11-3.5 doesn't make sense, because that's just the 7.5 regular hours.
11x1.5 doesn't make sense, because you're not getting overtime pay for all 11 hours.
The other two options have 1.5*3.5 in them, so you consider whether that makes sense, and what it means... and yes, that's 3.5 hours of overtime at a rate of 1.5x normal pay, that makes sense. So now, the thing that's left is to account for non-overtime pay for the other 7.5 hours.
Look at all the answers, and see what's similar about them, and what's different. Things that are similar, you can use to guide you into understanding the problem - for example, all of those answers said $112/(some number of hours), and most had 1.5x(some number). It will *usually* be true that is there's one of the four that's got an obviously different structure (like the one that doesn't have 1.5xsomething) then it will be one of the wrong answers - but don't take that too literally, since the right answer here is the only one that doesn't use the number 11. Safer to say, if there's one that's noticably different, it's worth looking at.
posted by aimedwander at 11:35 AM on July 16, 2013
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You say you can figure out the right numerical answer, so I'd start there. It looks like all the given formulas produce different answers, so here's how I'd approach it:
Look at the question, and completely ignore the answers. Solve it as if it were a fill-in-the-blank numerical answer problem. Use scratch paper and show your work. Once you have an answer, figure out what each formula gives, and select the one that produces the same answer.
You may still run into some problems where multiple formulas give you the same answer, but this will at least let you play to your strengths for many of them. And, at that point, you'll probably have at least narrowed the field of possible correct formulas, and you can look at how you arrived at your answer, and see which formula seems equivalent.
posted by duien at 1:26 PM on July 15, 2013