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Word Problems
The basics
SAT word problems are notoriously convoluted. Especially during a nearly four-hour test, you can easily become ruffled sorting through all the words, trying to figure out what the question is asking. Below are several vital points you need to remember when dealing with word problems.
Additionally, there are also three questions, from medium to challenging, which will apply to the different points.
Strategies for word problems
1. One piece at a time
SAT word problems were not written so that they would be easy to understand. Indeed, there is simply too much information for the question to be easy to understand. However, many students try to read the entire problem at once, instead of slowing down to absorb each piece of
information. So slow down. And bite off only as much as you can chew.
2. Always remember the question
Sometimes it is easy to get lost in all the words. When we finally have figured out what the
question is asking, we rush to come up with a solution, forgetting that the problem had thrown in a specific word at the very end (“even”, “integer”, “positive”, “not” are some of the usual
suspects). If you find yourself making many careless errors along these lines, make sure to
underline the actual question. That way, once you’ve come up with your answer, you’ll be to make sure that the question is actually asking for that.
3. It’s probably not that easy
If it seems way too easy, it probably is (unless you are on the first few questions). Make sure you’ve read the question carefully.
4. It’s not about just the formula; it’s about thinking
SAT problems aren’t just about plugging numbers into some formula and having the answer appear magically before you. A formula is just one part of the unraveling process. So understand what the question is about, follow the necessary steps, and at the very end–and only then–a formula will be handy.
Point #4 especially applies for the more difficult questions. Also, there are sometimes shortcuts, so you don’t have to even use the formula (as you’ll see in one of the questions below).
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Practice word problems
Below are several questions that will incorporate aspects from the four points above. In doing these problems, you should constantly refer to points #1-4, and see which one(s) are most relevant.
Instead of just calling them 1, 2 and 3, I’ve labeled them according to where they would probably show up in an SAT math section. That way, if you are dealing with a high-numbered, or difficult question, and it seems easy…well, just keep in mind point 3.
10. Kyle drives 40 miles due north and stops. He then heads due west for 60 miles and stops.
Finally, he heads north another 40 miles and stops. How far is he from his starting point?
50 miles 80 miles 92 miles 100 miles 160 miles
13. A bag contains only red, blue, and yellow beads. If half of the beads are red and a third of the remaining marbles are blue, how many beads are yellow if there are a total of 36 beads in the bag?
17. A book setter wants to print pages from a book. For each number at the top of the page, she has to pay 5 cents. For example, printing page 1 would cost her 5 cents, whereas
printing page 100 would cost her 15 cents. If the book setter pays a total of $1.05 for 11 consecutive pages, what is the highest page number the book setter decides to print?
9 11 19 20
Cannot be determined by the information provided.
Find the answers on the next page!
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Question #10
10. Kyle drives 40 miles due north and stops. He then heads due west for 60 miles and stops.
Finally, he heads north another 40 miles and stops. How far is he from his starting point?
50 miles 80 miles 92 miles 100 miles 160 miles
For this one, you want Point #1 to be your guide: bite off one piece of info at a time. First off, draw the picture out by using a straight, vertical line. This line should denote 40 miles north. At the top of the line, next draw a line branching out perpendicularly to the first line (this will be the 60 miles due west line). Finally, draw a vertical line at a right angle to the horizontal line. This line will be the last leg of Kyle’s trip.
Now if you found yourself reading and re-reading the question several times, only to give up in frustration, know that is not you or your math aptitude, but your approach (something easily changed!). So, again, start with one piece of info at a time.
Next, we can complete this vertical line so that we end up getting a triangle. And, just like that, we have our 3:4:5 ratio. So, the answer is 100 miles. (D). If you found yourself scrambling to the calculator after wracking your brain for the Pythagorean formula, remember point 4 and shortcuts.
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Question #13
13. A bag contains only red, blue, and yellow beads. If half of the beads are red and a third of the remaining marbles are blue, how many beads are yellow if there are a total of 36 beads in the bag?
6 12 15 18 24
The trick to this problem is noticing the wording “remaining” marbles. If you just sped through the question, thinking, heck, that’s easy, I’ll just add 1
3+1
2=5
6 and the remaining fraction 1
6 times 36 will give me 6, answer (A), remember point #3: it’s probably not that easy.
See, once you throw the “remaining” 1
3 in there, it changes how many beads are yellow, and, by extension, how many are blue. So if 12 of the beads are red, of the remaining 18, 13 (or 6) are yellow, then that leaves us with 12 blue beads, or answer (B).
So make sure to slow down and read carefully.
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Question #17
17. A book setter wants to print pages from a book. For each number at the top of the page, she has to pay 5 cents. For example, printing page 1 would cost her 5 cents, whereas
printing page 100 would cost her 15 cents. If the book setter pays a total of $1.05 for 11 consecutive pages, what is the highest page number the book setter decides to print?
9 11 19 20
Cannot be determined by the information provided.
This is the toughest of the questions. Mostly, because both the context (pages and book setters) and what the question is asking seem vague. But read slowly, bite off a piece at a time, and you should be able to get it.
At first, the question may seem unsolvable. For there are a number of different ways in which she could print eleven pages and end up spending $1.05, right? So isn’t the answer just (E)? Well, remember point #3. It’s probably not going to be that straightforward. There has to be exactly one set up that conforms to 11 pages/$1.05. At this point, you may think, 'Oh, but I need to know some formula for that … and I don’t know the formula.'
But remember Point #4: it’s not about the formulas. This question tests your raw thinking
mechanisms. In others, you have to experiment a little. How many ways can you get 1.05? Well, if you start from page 1 and move up to page 9, you get 45 cents worth. Then you would need 6 more two-digit pages (page 10, page 11, etc.). That would give us 15 pages, which is way over eleven.
We can’t use an even number of single-digit pages, or we won’t get the .05. Since 15 is way off, it is good to start from the other side of the spectrum. What if we only have one single-digit page, meaning page 9. Well, that costs 5 cents. And that leaves me with 1.00, which corresponds to, at 10 cents a page, the double-digit numbers (10, 11, and so on).
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But we are not out of the woods yet. What is the 10th double-digit page? You may be tempted to add 10 + 10 =20, but that answer is wrong. See, the number 10 counts as one of the numbers, and therefore costs 10 cents. You wouldn’t say that two pages, including page 10, would give you 10 + 2 = 12. That would be three pages – 10, 11, and 12 – and therefore 30 cents. So, since we are
including page 10 in our 10-page count, we just want to add 9 to 10 to give us page 19. Answer (C).
Takeaway
The takeaway from this lesson is to apply the above to questions that are at your difficulty level. If question #17 completely blew your mind, that is fine. You don’t have to be able to get the
toughest word problems right off the bat. If all three questions were tough, then you can start with word problems under question #10. The key is to improve from your current level.
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